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Hydrogenaudio Forum => Scientific Discussion => Topic started by: Axon on 05 October, 2006, 04:50:17 PM

Title: What is "time resolution"?
Post by: Axon on 05 October, 2006, 04:50:17 PM
So I've become involved in a rather colorful argument (http://www.stevehoffman.tv/forums/showthread.php?t=85436) (I'm Publius in the thread) with somebody on stevehoffman.tv. The original thread revolved around shooting down an old audiophile canard, about how subsample delays cannot be represented in PCM. In the course of that debate, I've begun to question a couple things.
Title: What is "time resolution"?
Post by: benski on 05 October, 2006, 05:04:43 PM
Subsample delays are relatively easy to implement and commonplace (especially with reverb).  It's certainly not impossible
Title: What is "time resolution"?
Post by: Axon on 05 October, 2006, 05:19:51 PM
Well, duh.  I showed in that thread that 1/20,000 sample delays are doable.
Title: What is "time resolution"?
Post by: krabapple on 05 October, 2006, 05:28:47 PM
So I've become involved in a rather colorful argument (http://www.stevehoffman.tv/forums/showthread.php?t=85436) (I'm Publius in the thread) with somebody on stevehoffman.tv.


Good luck with that.  I got booted for persistently mentioning the DBTs,and for questioning the moderators.  That place is the Bizarro world hydrogenaudio. Theres's a  typically absurd discussion going on there now about solid state audio gear burn-in, too (it's all down to capacitors, don't you know...they need hours and hours of burn in to sound right, or at least to get the molecules lined up right...prior to that, they sound *terrible* ...I'm thinking someone had best tell the telecommunications industry, the calibration gear industry, the computer industry, the aerospace industry, and heck, anyone who uses high-perforance electronic devices).
Title: What is "time resolution"?
Post by: saratoga on 05 October, 2006, 05:57:55 PM
Is it ever accurate to use the term "time resolution" in any sort of technical context? To the best of my knowledge, it has no universally agreed upon technical definition. Most of the times I've seen it used are either for SACD/DVD-A marketing fluff, or to describe FFT window lengths. I'm tempted to just go quasi-logical-positivist on everybody and say that it is a completely meaningless phrase.


I don't see why not.  It just refers to how precisely you can localize energy in the time domain.  Generally this is just the sample period, but not always.  Looking at my DSP text, they don't actually say time resolution, but they frequently mention frequency resolution, and by duality whatever applies to frequency would apply to time if you sampled in the frequency domain.
Title: What is "time resolution"?
Post by: ChiGung on 05 October, 2006, 06:07:57 PM
Yo, that was me (felimid)
Quote
Is there any meaningful time-domain constraint on audio quality that is directly related to the sampling period?

Ask yourself:
"is there any meaningful space-domain constraint on visual quality that is directly related to the pixel width"

(note that regardless of the quality of anyones particular video card system, bandlimited 'acoustic type' interpolation can be applied to visual data as well as audio (and is a rather good way to treat it, if not the optimal (?))

I know i've put more than enough waffle into that thread to explain why I consider, pixel-width or sample width the explicit limit of record resolution.... maybe just one more try if you have time:
The subsample accuracy of frequency resolution (and collections of frequencies) is about the..what do you call it..."potential losslessness" of manipulating recordsafter downsampling, not about the accuracy of reproduction of the original (natural, pre-record, pre-processed sound) of the downsampled record.

I honestly havent been argueing 'for the sake of it' I'd like this to be understood.
But everyone is free to draw their own conclusions.

best regards'
Title: What is "time resolution"?
Post by: Woodinville on 05 October, 2006, 06:20:03 PM
So I've become involved in a rather colorful argument (http://www.stevehoffman.tv/forums/showthread.php?t=85436) (I'm Publius in the thread) with somebody on stevehoffman.tv. The original thread revolved around shooting down an old audiophile canard, about how subsample delays cannot be represented in PCM. In the course of that debate, I've begun to question a couple things.
  • Is it ever accurate to use the term "time resolution" in any sort of technical context? To the best of my knowledge, it has no universally agreed upon technical definition. Most of the times I've seen it used are either for SACD/DVD-A marketing fluff, or to describe FFT window lengths. I'm tempted to just go quasi-logical-positivist on everybody and say that it is a completely meaningless phrase.
  • Is there any meaningful time-domain constraint on audio quality that is directly related to the sampling period? Subsample delays (as I've shown above) are not meaningfully related. Bandwidth is a frequency-domain attribute. Pre-echo potentially gets more audible at lower sampling rates, but this is not a concern with sigma-delta ADCs, and it is of debatable audibility at 44.1 to begin with. Some DSP operations may be harder to implement at lower sample rates, but most of the issues involve seem implementation-related. I'm suspecting that there are no clear general limits as to what can and cannot be accomplished in PCM, except with respect to very domain-specific or system-specific situations; and so any claims of 44khz always being limited in ways different from bandwidth may be regarded with skepticism.


Having read that thread, or some of it, it's clear that there are several issues being confuted by people who do not want to let go of their pet belief system.

The first issue is that of pure delay. You've killed that. You can point out that if you store the data in 16 bit signed, that yes, there is a limit, it's directly related to the sampling rate times the number of levels available for quantization...  i.e. directly related to the SNR and the sampling rate.

The second is that of jitter. You need to beat on these people to point out that jitter is different for each sample, and your time delay is not.

Time delay has been reported as audible down to 5 to 10 microseconds in binaural settings with a great deal of care and signal prep involved.  No lower.

The cited nanosecods, etc, are just stuff and nonsense.

What you need to do with the jitter crowd is to point out that the spectrum of the jitter is the big deal.

You can have 1 part in 1000  (relative to sample period) if the jitter has only frequencies below 1 Hz.

You can hear much more than that if you have high frequency jitter, and a high frequency signal.

Looking onward, we see the twirp who insists that things have to be periodic in order for subsample resolution to work.

Perhaps he needs to be acquinted with both the Nyquist theorem and the fact that for all real signals, Fourier synthesis works.

I'm not going to get an ID to go argue with those guys. Blah.
Title: What is "time resolution"?
Post by: Axon on 05 October, 2006, 07:11:29 PM
Yo, that was me (felimid)

Oh! Damn. We've come full circle now. 
Quote
Is there any meaningful time-domain constraint on audio quality that is directly related to the sampling period?

Quote
Ask yourself:
"is there any meaningful space-domain constraint on visual quality that is directly related to the pixel width"

(note that regardless of the quality of anyones particular video card system, bandlimited 'acoustic type' interpolation can be applied to visual data as well as audio (and is a rather good way to treat it, if not the optimal (?))

I know i've put more than enough waffle into that thread to explain why I consider, pixel-width or sample width the explicit limit of record resolution.... maybe just one more try if you have time:
The subsample accuracy of frequency resolution (and collections of frequencies) is about the..what do you call it..."potential losslessness" of manipulating recordsafter downsampling, not about the accuracy of reproduction of the original (natural, pre-record, pre-processed sound) of the downsampled record.

I honestly havent been argueing 'for the sake of it' I'd like this to be understood.
But everyone is free to draw their own conclusions.

best regards'

I mainly posted here to try to get a different take on what was spinning in my head about terminology. I didn't want to start a rantfest about the SH forums - although to be honest, the reason I posted here was simply because I perceive that the regulars here are just flat-out more technically competent in audio engineering than SH as a whole. (ie, HA people tend to have one or more DSP textbooks.)

Mike may be right. "Frequency resolution" has a clear frequency-domain definition, so it makes sense that "time resolution" would have an analogous time-domain definition. In which case.. you're right. However, it is surprisingly hard to actually find a definition of resolution itself. I don't recall such a definition in my textbook (Lathi).

And I still have trouble reconciling the notion of time resolution being directly coupled to the sampling rate, against so many things being resolvable at the subsample level - delays, peaks, etc. (Ignoring the fact that some of those things, like peaks, can change drastically after a resample.) Perhaps there are two classes of "resolution" - one is based on the sampling rate and represents what any given algorithm sees, while the other is based on the real-valued signal the signal reconstructs to, and represents values that are related to a large number of samples (due to FIR reconstruction), and so can exceed the sample-rate resolution limitation.

And for either class of resolution, the error in your measurement is also affected by your choice of algorithm - ie, a measurement may change significantly if downsampling 96->44.1 as compared to 88.2->44.1, because of the added ringing.
Title: What is "time resolution"?
Post by: legg on 05 October, 2006, 07:28:38 PM
AFAIK, time resolution is most commonly used to refer to the time that a given block represents when converted to the frequency domain. "The short window has a time resolution of 128 samples, while the steady state block has a time resolution of 2048 samples".

As for other uses, I'm sure there are some, I just haven't read the term in other areas.
Title: What is "time resolution"?
Post by: Woodinville on 05 October, 2006, 07:35:49 PM
Well, considered for Guassian vs. Gaussian,

dt * df >= 1.

You could make that as an argument for time resolution.

But what these guys are talking about is the relative timing of interchannel delays, which is a different question and one that is of order 1/(fs * number of quantization levels), which is a pretty small number.
Title: What is "time resolution"?
Post by: ChiGung on 05 October, 2006, 07:46:34 PM
Quote
The first issue is that of pure delay. You've killed that. You can point out that if you store the data in 16 bit signed, that yes, there is a limit, it's directly related to the sampling rate times the number of levels available for quantization...  i.e. directly related to the SNR and the sampling rate.

Just me doing the arguing in that thread really. On the fly (though it was never a prime point) I hedged that what you refer to as 'delay' is dependant on the measure size like you state.
However you seem also unwilling to acknowledge too, that such 'delay' is no definite attribute of the undownsampled source, it is an attribute summed circumspectly from the phases of frequencies surviving the downsample. The frequencies which didnt survive the downsample, contained the information required to resolve the true subsample detail of 'time localised energy spikes'.
 
Quote
The second is that of jitter. You need to beat on these people to point out that jitter is different for each sample, and your time delay is not.

Comments about jitter came right at end... or maybe its grown...eek, anyway there enough on the plate already.

Quote
Time delay has been reported as audible down to 5 to 10 microseconds in binaural settings with a great deal of care and signal prep involved.  No lower.

Informative, although I have never argued the against the subsample time resolution of frequencies surviving the implicit lowpass of the sample rate. The arguement was about whether such precision can be fairly refered to as 'time-resolution'

Quote
Looking onward, we see the twirp who insists that things have to be periodic in order for subsample resolution to work.

Ahem* that would be me, but an unkindly misrepresented myself.
Again, my point is -"subsample resolution" of what exactly? the subsample levels implied in PCM have to assume all energy above the nyquist frequency is zero - so yes 'things' do have to be periodic, specificaly the component periods of the frequencies which inform the spaces between samples all have to be less than 2 samples in length - because shorter frequencies are not informed by the record. Subsample detail of the waveform is for standardisation purposes assumed to be consistent with the remaining information, because the origional information is lacked. So what can 'time resolution of PCM' refer to? any synthetic measurement we can take? Is there not already a fair candidate for this term?

Quote
Perhaps he needs to be acquinted with both the Nyquist theorem and the fact that for all real signals, Fourier synthesis works.

I am acquainted with it thanks, and understand some limitations. Just trying to pass that on.

Quote
I'm not going to get an ID to go argue with those guys. Blah.

You didnt need to 
Title: What is "time resolution"?
Post by: kjoonlee on 05 October, 2006, 07:47:39 PM
Does "higher sampling rates mean higher temporal resolution" count?
Title: What is "time resolution"?
Post by: ChiGung on 05 October, 2006, 07:57:01 PM
Does "higher sampling rates mean higher temporal resolution" count?

Apparently not.
Quote
I mainly posted here to try to get a different take on what was spinning in my head about terminology.

Heh, sorry dude - but its not that I tracked you down'
I dont like but cant help making a twerp out of myself in forum, so Ill give you peace to work out your own conclusions.

I hope its been stimulating in an ok way anyway.

-appreciating all your outputs'
*
Title: What is "time resolution"?
Post by: saratoga on 05 October, 2006, 09:10:46 PM
Quote
Looking onward, we see the twirp who insists that things have to be periodic in order for subsample resolution to work.

Ahem* that would be me, but an unkindly misrepresented myself.
Again, my point is -"subsample resolution" of what exactly? the subsample levels implied in PCM have to assume all energy above the nyquist frequency is zero - so yes 'things' do have to be periodic, specificaly the component periods of the frequencies which inform the spaces between samples all have to be less than 2 samples in length - because shorter frequencies are not informed by the record. Subsample detail of the waveform is for standardisation purposes assumed to be consistent with the remaining information, because the origional information is lacked. So what can 'time resolution of PCM' refer to? any synthetic measurement we can take? Is there not already a fair candidate for this term?

Quote
Perhaps he needs to be acquinted with both the Nyquist theorem and the fact that for all real signals, Fourier synthesis works.

I am acquainted with it thanks, and understand some limitations. Just trying to pass that on.



You mention periods "less than 2 samples in length".  This is a band limited signal, there are no such periods.  I think you are trying to say that since you can't have frequencies higher then the nyquist frequency, then it must be true that you cannot have frequencies closer together then 2/fs.  However, this is not true.  The Nyquist theory allows exact reconstruction for band limited signals, which means you can resolve infinately many points between any two points within the reconstructed waveform just by upsampling and filtering.

Let me give an example.  If you sample at 10Hz and are bandlimited to 5Hz, you can resolve the amplitudes at 1Hz, 1.0000000000000000000001Hz, etc perfectly.  Its just that since you're bandlimited, you have no new information at these interpolated points (I.E. they're exactly determined by the value of the adjecent points).  But you can still retrieve their values using resampling, sinc interpolation or whatever.

Regarding your periodic remark, I'm afraid I don't follow.
Title: What is "time resolution"?
Post by: ChiGung on 05 October, 2006, 11:30:39 PM
The subsample levels implied in PCM have to assume all energy above the nyquist frequency is zero - so yes 'things' do have to be periodic, specificaly the component periods of the frequencies which inform the spaces between samples all have to be less than 2 samples in length - because shorter frequencies are not informed by the record. Subsample detail of the waveform is for standardisation purposes assumed to be consistent with the remaining information....

You mention periods "less than 2 samples in length".  This is a band limited signal, there are no such periods.

Exactly, frequencies of that period are required to render time localised energy between the samples, which we obviously dont have until we have access to non-downsampled records.

Quote
I think you are trying to say that since you can't have frequencies higher then the nyquist frequency, then it must be true that you cannot have frequencies closer together then 2/fs.

I would never knowingly say anything to that effect'

Quote
Regarding your periodic remark, I'm afraid I don't follow.

I didnt exactly make the periodic remark, I think woodinville was refering to explainations in the other thread like this:

Quote
It was shown that the phase of a sinusoidal pattern which is assumed as perfect and constant can be resolved to a fraction of the sampling interval.
This subsample accuracy was possible because the pattern recorded is not a discrete event, it's impression is recorded throughout many consecutive samples and its exact formation is inferable (idealy).
For all discrete or unassumable events, PCM records can only specify time of occurence to within a whole length of the sampling interval. Time resolution can only be improved when a known pattern can be observed throughout multiple samples -which is the case for computing the phase of synthetic frequency components, but not at all when trying to refine the temporal location of unassumed events.


For conversion and processing purposes etc PCM is interprated as a composite of exclusively periodic entities (frequencies) But localised energy need not fit into any periodic cycle, so we cant locate it precisely with the periodic tools (frequencies) even though we can locate all the individual tools precisely. 

techie: "captain we have located a 'spike' event on the PCM sensor"
captain:"what is the position of the spikes peak teki?"
techie:"324.37643 sampling intervals exactly captain"
captain:"how can you be so precise?"
techie:"because time delays are quite precisely encodable in PCM"

But a natural spike, will have an unknown frequency spectrum, the tools to locate the true peak with certainty  had to be removed before the downsample, so we can make the best guess by assuming the 'subsample deviators' were all flat anyway but thats just a guess, the true peak could have been anywhere in the sample interval. If it was actualy somewhere other than the record suggests most likely, that information was contained in the lowpassed higher frequencies which now manifest as the unrecorded gaps between samples.

waffle, waffle, waffle.

Quote
'It just refers to how precisely you can localize energy in the time domain. Generally this is just the sample period, but not always.

That is how I seesaw it. Ive just been clumsily trying to explain this really, from a few different angles.
Title: What is "time resolution"?
Post by: krabapple on 06 October, 2006, 01:21:33 AM
Quote
The second is that of jitter. You need to beat on these people to point out that jitter is different for each sample, and your time delay is not.

Comments about jitter came right at end... or maybe its grown...eek, anyway there enough on the plate already.


Actually they appeared as early as the third post (http://www.stevehoffman.tv/forums/showpost.php?p=1888404&postcount=3) in the thread.
Title: What is "time resolution"?
Post by: saratoga on 06 October, 2006, 01:27:45 AM


The subsample levels implied in PCM have to assume all energy above the nyquist frequency is zero - so yes 'things' do have to be periodic, specificaly the component periods of the frequencies which inform the spaces between samples all have to be less than 2 samples in length - because shorter frequencies are not informed by the record. Subsample detail of the waveform is for standardisation purposes assumed to be consistent with the remaining information....

You mention periods "less than 2 samples in length".  This is a band limited signal, there are no such periods.

Exactly, frequencies of that period are required to render time localised energy between the samples, which we obviously dont have until we have access to non-downsampled records.


No.  I'm saying that no such information ever existed.  Not just in the sampled signal.  Ever.  The signal is band limited to no more then half the sampling rate, therefore there is NO information between between samples, either in the information we have or the original analog signal.


Quote
I think you are trying to say that since you can't have frequencies higher then the nyquist frequency, then it must be true that you cannot have frequencies closer together then 2/fs.

I would never knowingly say anything to that effect'


You just did.  "Frequencies of that period are required to render time localised energy between the samples"  Surely you realize how these statements are equivilent?

Quote
Regarding your periodic remark, I'm afraid I don't follow.

I didnt exactly make the periodic remark, I think woodinville was refering to explainations in the other thread like this:

Quote
It was shown that the phase of a sinusoidal pattern which is assumed as perfect and constant can be resolved to a fraction of the sampling interval.
This subsample accuracy was possible because the pattern recorded is not a discrete event, it's impression is recorded throughout many consecutive samples and its exact formation is inferable (idealy).
For all discrete or unassumable events, PCM records can only specify time of occurence to within a whole length of the sampling interval. Time resolution can only be improved when a known pattern can be observed throughout multiple samples -which is the case for computing the phase of synthetic frequency components, but not at all when trying to refine the temporal location of unassumed events.




I was refering to your statement that "things have to be periodic".  That doesn't seem related to what you posted above because you make no mention of periodicity, or if it is I cannot follow your logic.


For conversion and processing purposes etc PCM is interprated as a composite of exclusively periodic entities (frequencies) But localised energy need not fit into any periodic cycle, so we cant locate it precisely with the periodic tools (frequencies) even though we can locate all the individual tools precisely.


PCM does not assume anything is periodic.  No frequency treatment is required to dervive it either.  The frequency/time trade off you're refering to is a property of the fourier transforms, but not of PCM which could be implemented with nothing but time domain tools.


techie: "captain we have located a 'spike' event on the PCM sensor"
captain:"what is the position of the spikes peak teki?"
techie:"324.37643 sampling intervals exactly captain"
captain:"how can you be so precise?"
techie:"because time delays are quite precisely encodable in PCM"

But a natural spike, will have an unknown frequency spectrum, the tools to locate the true peak with certainty  had to be removed before the downsample, so we can make the best guess by assuming the 'subsample deviators' were all flat anyway but thats just a guess, the true peak could have been anywhere in the sample interval. If it was actualy somewhere other than the record suggests most likely, that information was contained in the lowpassed higher frequencies which now manifest as the unrecorded gaps between samples.


We're assuming the signal is band limited, so we absolutely can exactly locate your spike.  Think about how an ideal sinc interpolator works.  You superimpose sinc functions to get the exact value of the function at that point.  There is no approximation like  you seem to be thinking.  It really is exact. 

What you're saying would be true of a signal that was not band limited, but if it was not bandlimited, we would not be able to reconstruct the signal anyway.  Alternatively, it would be true if you assumed the signal was not bandlimited, but that you had an antialiasing filter in place to band limit it.  In that case,  you could in fact say that the antialiasing filter delocalizes your spike by discarding the extra frequency content needed to exactly localize it.  However this is NOT what everyone else is discussing which is why they keep saying PCM and not antialiasing filter.  We're assuming that input signal is already bandlimited, and thus it can be perfectly reconstructed.
Title: What is "time resolution"?
Post by: Woodinville on 06 October, 2006, 03:26:43 AM
However you seem also unwilling to acknowledge too, that such 'delay' is no definite attribute of the undownsampled source, it is an attribute summed circumspectly from the phases of frequencies surviving the downsample. The frequencies which didnt survive the downsample, contained the information required to resolve the true subsample detail of 'time localised energy spikes'.

Goodness me.

A properly done resampling contains all of the frequencies in the original. All of them.

If you started with a bandlimited signal (i.e. a properly sampled signal), say of DC to 20K, down 96dB at 22.05, and you used a good resampling filter, you have all the frequencies you started with.

If you didn't start with a bandlimted signal, you violated the Nyquist theorem.
Quote
Quote
Time delay has been reported as audible down to 5 to 10 microseconds in binaural settings with a great deal of care and signal prep involved.  No lower.

Informative, although I have never argued the against the subsample time resolution of frequencies surviving the implicit lowpass of the sample rate. The arguement was about whether such precision can be fairly refered to as 'time-resolution'


Why not? You can easily distinguish times, so you're resolving time.
Quote
Ahem* that would be me, but an unkindly misrepresented myself.

Sorry. I've been through this argument a few 100's of times with people who have failed to consider the implications of Fourier analysis and/or proper sampling and reconstruction.
Quote
Again, my point is -"subsample resolution" of what exactly? the subsample levels implied in PCM have to assume all energy above the nyquist frequency is zero - so yes 'things' do have to be periodic, specificaly the component periods of the frequencies which inform the spaces between samples all have to be less than 2 samples in length - because shorter frequencies are not informed by the record.

I have absolutely no idea what concept you are trying to convey. Did you perhaps swap out a "longer" sans "shorter" or vice versa here?
Quote
Subsample detail of the waveform is for standardisation purposes assumed to be consistent with the remaining information, because the origional information is lacked. So what can 'time resolution of PCM' refer to? any synthetic measurement we can take? Is there not already a fair candidate for this term?

Again, I have no idea what you mean.  In the OP over there, the ability to resolve time is demonstrated, end of discussion.

What "original information" is missing? I see none.

Quite frankly I have no idea what you're trying to convey.  The OP at the other board refutes what you seem to be somewhat unclearly claiming.

More I can not say until you can express yourself better.

Do not forget that there is no representation of frequencies outside of the Nyquist bandwidth in PCM at any time, so there was never anything there to lose.

Having been one of many people to try sampling (done properly) using a one-shot triggered with some delay around the sampling frequency, I simply can't see what you're worried about.  You can easily capture sub-sample delays in input, you can create sub-sample delays digitally, etc.
Title: What is "time resolution"?
Post by: 2Bdecided on 06 October, 2006, 05:30:52 AM
ChiGung,

You can prove sub-sample time domain accuracy using a simple single impulse (or conceptually, a Dirac Delta or Dirac pulse). In a correct system, you can show that the location of the inter-sample peak matches that of the original impulse, even though the pulse itself will be spread out (due to the band limiting).

The reference to periodic functions doesn't mean that sub-sample accuracy doesn't work for any other signal! The sub-sample inter-channel delay of sine waves is a nice example, but you can do just the same thing with a single impulse.

While we're avoiding mathematics, and getting by with examples and hand-waving concepts, consider this: since it works for theoretical infinitely long sine waves, and for theoretical infinitely short impulses, and for practical length "longish" sine waves and for practical length "shortish" impulses (i.e. both theoretical and practical extremes!), that should alert you to the fact that it probably works for any signal in between - including any real world signal.

Cheers,
David.
Title: What is "time resolution"?
Post by: ChiGung on 06 October, 2006, 11:32:29 AM
Quote
We're assuming the signal is band limited, so we absolutely can exactly locate your spike.

You are all assuming that and confidently browbeating with resulting certainties.
It is not a valid assumption > for defining PCMs capabalities of accurately reproducing source.
The term 'source' is meaningless if it cannot differ in detail from 'record'
Of course if the source is known to be bandlimited suitably, the PCM record of it is perfectly complete - there is nothing to discuss in this case. With the precondition that the source is already suitably bandlimited, any samplerate can precisely store any such compliant source -that is not news to me.

I cant believe the loose reasoned, ignorance assuming flack Im taking here....
Corrections about whenever 'jitter' was first transiently refered to in the other thread? 

Please gimme a break.

Its probably not worth it for me to explain anything again - cause it will be read with such presumption of error that any realisations possible will not make it from the readers page to their predisposed mind.

Quote
...such 'delay' is no definite attribute of the undownsampled source, it is an attribute summed circumspectly from the phases of frequencies surviving the downsample. The frequencies which didnt survive the downsample, contained the information required to resolve the true subsample detail of 'time localised energy spikes'.

How stupid do you guys suppose I am if I was talking about a suitably bandlimited source there? Is it ambiguity about the term 'undownsampled?' -If I meant 'upsampled record' I would could have used that simpler term. Does 'undownsampled source' not translate to 'a source which was not downsampled' -therefore being capable of holding higher frequency detail than the downsampled one? I dont think there is any real ambiguity there, or too much following to figure out what I am actualy talking about.

I am talking about aspects of PCMs resolution of unassumable sources. Like how accurately 16kHz samplerate record could render localised details a 44~kHz record on a CD could render, or how accurately CDs format, could render details which the mastering formats used in production process could render. Why is that a strange interpratation of the term 'resolution' with regads to the capabilities of a digital format?
When you guys ponder the resolution of a digital camera, do you say it perfectly records what it is pointed at if you take pictures out of focus? Yes it might record the 'out of focus picture perfectly precisely', how in focus does the picture need to be before the digitised record of it neccessarily looses information and is therefore an imprecise record of? Most fundamentaly, how accurately can the digitised record be used to render the actual 'scene', with its near infinite complexety emergent from the natural universe?

You know Im obviously talking about somethings which many of you have not considered before. Then you might benefit from reading my points properly instead of the hypercritical attention shown so far.

Good luck with that'

edit: paranoid disambiguations
Title: What is "time resolution"?
Post by: krabapple on 06 October, 2006, 11:54:01 AM
I cant believe the loose reasoned, ignorance assuming flack Im taking here....
Corrections about whenever 'jitter' was first transiently refered to in the other thread? 

Please gimme a break.


Perhaps it's bias, but I don't see what was either poorly reasoned, or ignorant, about pointing out your mistake re: when jitter entered the SHtv thread.


Quote
I am talking about aspects of PCMs resolution of unassumable sources. Like how accurately 16kHz samplerate record could render localised details a 44~kHz record on a CD could render, or how accurately CDs format, could render details which the mastering formats used in production process could render.


All of those sources are bandwidth-limited, of course. 


Quote
Why is that a strange interpratation of the term 'resolution' with regads to the capabilities of a digital format?
When you guys ponder the resolution of a digital camera, do you say it perfectly records what it is pointed at if you take pictures out of focus? Yes it might record the 'out of focus picture perfectly precisely', how in focus does the picture need to be before the digitised record of it neccessarily looses information and is therefore an imprecise record of? Most fundamentaly, how accurately can the digitised record be used to render the actual 'scene', with its near infinite complexety emergent from the natural universe?

You know Im obviously talking about somethings which many of you have not considered before.


You flatter yourself.

Quote
Then you might benefit from reading my points properly instead of the hypercritical attention shown so far.

Good luck with that'

edit: paranoid disambiguations



You don't appear to take correction well.  I suggest you get used it...particularly as you've implied, in the SHtv thread, and here, that Nyquist/Shannon is in need of significant revision.  That constitutes an extraordinary claim, and you are going to have to present an extraordinarily well-supported case to back it up.  And your writing is going to have to be much, much more clear.  Good luck with that.
   
But perhaps for starters, you can describe in much more detail the attributes of the 'unassumable sources' you are talking about.  In what sense are they NOT bandlimited?
Title: What is "time resolution"?
Post by: ChiGung on 06 October, 2006, 12:08:03 PM
Quote
But perhaps for starters, you can describe in much more detail the attributes of the 'unassumable sources' you are talking about.  In what sense are they NOT bandlimited?

Im not taking criticism well at this point, because Ive been at this for many posts now.
Look. A 44kHz record is bandlimited at 22kHz right? A 22kHz record is bandlimited at 11kHz. A downsample from 44 to 22kHz looses the information for the band 22kHz to 11kHz.....r i g h t ?
If we could all assume that when we downsample, all the information information involved is already suitably bandlimited, that would be an easy world where we could make the claim that 'time resoltuion of PCM' is near as hey perfect -and make it stick. But it is for the very reason that that is an unrealistic assumption, that lowpassing (removing of high frequency energy) is required during good quality downsampling conversion.
Specificaly, yes you can say (and I have said it) that a records information is implicitly bandlimited. But you cannot say that it is therefore bandlimited enough to losslessly survive any following downsamples.

Quote
You don't appear to take correction well. I suggest you get used it...particularly as you've implied, in the SHtv thread, and here, that Nyquist/Shannon is in need of significant revision.

I said common reports and opinions drawn from it where.

Trying to get back to the topic>

Ask yourself:
"is there any meaningful space-domain constraint on visual quality that is directly related to the pixel width"
Title: What is "time resolution"?
Post by: Axon on 06 October, 2006, 12:49:59 PM
Okay, so this has gone completely f*cking off topic. Thanks everybody. Yes sir, lots of insightful comments here.
Title: What is "time resolution"?
Post by: krabapple on 06 October, 2006, 03:51:48 PM
Okay, so this has gone completely f*cking off topic. Thanks everybody. Yes sir, lots of insightful comments here.



Sorry, what in particular are you miffed about?  "Time resolution" has not stopped being discussed.  There *are* lots of insightful comments about it here (I refer to Mike's and Woodinville's especially, as being of rather recent vintage).
Title: What is "time resolution"?
Post by: saratoga on 06 October, 2006, 03:54:06 PM
Quote
We're assuming the signal is band limited, so we absolutely can exactly locate your spike.

You are all assuming that and confidently browbeating with resulting certainties.


We are assuming it because it is true.

It is not a valid assumption > for defining PCMs capabalities of accurately reproducing source.


PCM is always bandlimited.  If it is not, then you do not have PCM.  The source may not be bandlimited, but so what?  Thats why you have an antialiasing filter.

The term 'source' is meaningless if it cannot differ in detail from 'record'
Of course if the source is known to be bandlimited suitably, the PCM record of it is perfectly complete - there is nothing to discuss in this case. With the precondition that the source is already suitably bandlimited, any samplerate can precisely store any such compliant source -that is not news to me.


Then what have you attempted to say these past few posts?
Title: What is "time resolution"?
Post by: krabapple on 06 October, 2006, 04:11:56 PM
Quote
But perhaps for starters, you can describe in much more detail the attributes of the 'unassumable sources' you are talking about.  In what sense are they NOT bandlimited?

Im not taking criticism well at this point, because Ive been at this for many posts now.
Look. A 44kHz record is bandlimited at 22kHz right? A 22kHz record is bandlimited at 11kHz. A downsample from 44 to 22kHz looses the information for the band 22kHz to 11kHz.....r i g h t ?
If we could all assume that when we downsample, all the information information involved is already suitably bandlimited, that would be an easy world where we could make the claim that 'time resoltuion of PCM' is near as hey perfect -and make it stick. But it is for the very reason that that is an unrealistic assumption, that lowpassing (removing of high frequency energy) is required during good quality downsampling conversion.



All you need to show, then, is either that

1) for digital audio generally at whatever chosen sample rate: there is information *originally within the band* that necessarily gets excluded by the bandlimiting requirement, and thus becomes unrecoverable

or

2) for redbook PCM specifically: the 22 kHz bandlimit is insufficient to capture what is audible in your unassumable sources -- which translates to, showing that there is audible information above 22 kHz in either
live recordings, or analog tape sources.


(And reconcile them with these facts: all recording and playback methods are bandlimited.  And all hearing is bandlimited too.)

So good luck with that.


Quote
Specificaly, yes you can say (and I have said it) that a records information is implicitly bandlimited. But you cannot say that it is therefore bandlimited enough to losslessly survive any following downsamples.


Hold on...  are you defining 'lossless' perceptually, or strictly in terms of data?  If you 'lose' frequencies that cannot be heard, the downsample is technically lossy, but not perceptually.
Title: What is "time resolution"?
Post by: ExUser on 06 October, 2006, 04:20:01 PM
Quote
Ask yourself:
"is there any meaningful space-domain constraint on visual quality that is directly related to the pixel width"


Your analogy is flawed. Drop the analogy and you might start to understand. All that sampling rate / pixel width does is limit the frequency of the signal that can be encoded. It says nothing about the phase of the signal. Phase is not really visually perceptible. Time resolution (ie. phase in a sense, and also subsample delay) is a function of both the bit depth and the sampling rate, not just the sampling rate.
Title: What is "time resolution"?
Post by: kwwong on 07 October, 2006, 12:12:44 AM
Does "higher sampling rates mean higher temporal resolution" count?

Apparently not.


Apparently yes.. For a fixed frame size, sampling rates can have an effect on temporal resolution.

Actually, time resolution exists in trade-off with frequency resolution. The higher the time resolution, the lower the frequency resolution and vice-verse.
Title: What is "time resolution"?
Post by: ExUser on 07 October, 2006, 03:04:38 AM
Exactly, kwwong. ChiGung, consider this: In the context of your video/audio analogy there is no maximum frequency for video. We do not use a format that arbitrarily limits our sampling frequency (ie. pixel width) in video. 640x480 has, relatively, higher frequency than 320x240. We can perceive that difference easily. We cannot perceive increases in audio bandwidth, as our ears are physically limited to (populistically speaking) 20KHz or so. Below that frequency, we have complete frequency reproduction (according to Nyquist) within a certain signal to noise ratio. Increases in time resolution imply increases in sampling frequency. Below half the sampling frequency, all timing details are perfectly coded (provided technical competence).
Title: What is "time resolution"?
Post by: MedO on 07 October, 2006, 05:43:40 AM
Look. A 44kHz record is bandlimited at 22kHz right?

Right.
A 22kHz record is bandlimited at 11kHz. A downsample from 44 to 22kHz looses the information for the band 22kHz to 11kHz.....r i g h t ?

Yes. Frequencies present above 11khz will have to be filtered out before downsampling and cannot be preserved in this case.
I don't think anyone here assumed downsampling is always lossless.

Ask yourself:
"is there any meaningful space-domain constraint on visual quality that is directly related to the pixel width"


No, there isn't. You can have peaks in image data at any(*) position between the pixels.

*assuming arbitrary bitdepth.
Title: What is "time resolution"?
Post by: cabbagerat on 07 October, 2006, 01:00:46 PM
No, there isn't. You can have peaks in image data at any(*) position between the pixels.

*assuming arbitrary bitdepth.
That assumption is a bit of a problem, in my mind. As has been mentioned earlier in the thread, there is a relationship between sampling rate, bit depth and maximum temporal resolution (or phase resolution). If you define maximum phase resolution as the minimum difference in phase that can be resolved, then it's a fairly straight forward calculation can be used to set a limit on the resolution.

A little playing with the numbers suggests that the maximum phase resolution of 44100 16bit PCM is on the order of 6e-9 wavelengths. I would bet a case of beer that this effect is inaudible.
Title: What is "time resolution"?
Post by: MedO on 07 October, 2006, 01:42:24 PM
Quote
That assumption is a bit of a problem, in my mind. As has been mentioned earlier in the thread, there is a relationship between sampling rate, bit depth and maximum temporal resolution (or phase resolution). If you define maximum phase resolution as the minimum difference in phase that can be resolved, then it's a fairly straight forward calculation can be used to set a limit on the resolution.

A little playing with the numbers suggests that the maximum phase resolution of 44100 16bit PCM is on the order of 6e-9 wavelengths. I would bet a case of beer that this effect is inaudible.


Of course there is a limit. If there wasn't, you could store an infinite ammount of information in the exact position of that peak. Turning this the other way, you cannot store audio data in a way which completely preserves this information. However, the way it is it should be accurate enough. My point was that you can place your "brightness-peak" on a great number of positions between the pixels.
Title: What is "time resolution"?
Post by: cabbagerat on 07 October, 2006, 03:57:45 PM
Of course there is a limit. If there wasn't, you could store an infinite ammount of information in the exact position of that peak. Turning this the other way, you cannot store audio data in a way which completely preserves this information. However, the way it is it should be accurate enough. My point was that you can place your "brightness-peak" on a great number of positions between the pixels.
Well, I hadn't thought of it in the context of information storage, but that's a very nice way to visualize the limit. I would imagine that this is certainly not one of the limiting factors on the quality of digital storage, but there are certainly people who would say otherwise. You can't really pretend that any mechanical analog system (tape, vinyl, etc) could do better.
Title: What is "time resolution"?
Post by: ChiGung on 07 October, 2006, 06:18:06 PM
Of course there is a limit. If there wasn't, you could store an infinite ammount of information in the exact position of that peak. Turning this the other way, you cannot store audio data in a way which completely preserves this information. However, the way it is it should be accurate enough. My point was that you can place your "brightness-peak" on a great number of positions between the pixels.

What is 'accurate enough' is a different matter id not like to confuse the main investigation with.

The situation is, that the positioning of the brightness peak in the record is limited by the fact that the record has an implicit bandlimit. The position of the brightness peak in the source image is not implicity restricted by this limitation. (edit: yes the peak could be precisely positioned if we could employ all of the information stored in surrounding samples to do so - but all those other samples have information of their own to carry*) .

Depending on the characteristics of the information conveyable from the origional media (lenses, microphones, physics of air etc) it may be suitably restricted for precise capture/repoduction by certain samplerates, but because the source media may also not be suitably restricted (and very often is not) we have to allow for this possibility. It's surprised me that there has been a strong tendency to discount this as recognising source media may have finer resolution than target samplerates is fundamental to sensible statements of how accurately target samplerates can record the information of various sources.

Back to the 'peak of brightness', or 'peak of level' example (whichever is easier to visualise) The position of the peak in the source image or sound will in almost all cases be altered by the lowpass of conversion.
The record will then indicate a very precise position, but its disagreeance with the source will be unknown, the precise position of the peak in the source may be anywhere between the enclosing sample points

Then this makes clear my objection to stating the time resolution of PCM as near perfect. That the position in time of any time-localisable details, like peaks, attacks, cliffs etc, cannot be known to agree with the position of such details in the source, except when we can assume convienient limitations of the source. >A clause which basicaly passes on the limitations of the PCM record, to the source record. That is if we assume the source and the records limitations are the same, then to determine the accuracy limitations of the record, we must determine the limitations of the source. Only then can it be said that the record has no limitations with regards the assumable source. It becomes a confusingly convoluted case.

Another way of stating the case, is that the gaps between the samples, embody the unstateable frequencies above the implicit bandlimit. (By implicit bandlimit I mean to imply the one enforced by the nyquist frequency cuttoff, not arbitrary ones which may or may not have been applied on the record by extra conditioning)

Regarding the validity of the 'screen resolution' metaphor; when it was introduced earlier this reminder was made: -
Quote
(note that regardless of the quality of anyones particular video card system, bandlimited 'acoustic type' interpolation can be applied to visual data as well as audio (and is a rather good way to treat it, if not the optimal (?))


In other words it can be a fair, almost identical analogue, but if its not accessible to some, they may just have to try to skip over it.

Id remind again, that phase never indicates a point in time, it indicates conditions of a period located throughout time. So the fact that phase can be stated in a record quite precisely, does not mean any real position in time can be stated in the record as precisely.

Some are refering to limits of perceptability which are only discernable with physiological experimentation, limits of technical capability are not affected by what it is possible to hear or see. 

Other queries have been raised all of which I hope the answers to will become clear, when the overall matter is realised 

I exhibited some more underdog fatigue earlier  Im glad to see that did not harm anyones curiosity.

best regards'

...............
extras
Title: What is "time resolution"?
Post by: MedO on 07 October, 2006, 07:13:54 PM
the precise position of the peak in the source may be anywhere between the enclosing sample points -as confirmed by med0.

Please don't misquote me. I said that it is possible to record the position of a peak in a bandlimited signal even if the peak is between two samples, but the precision will be limited (as in "Bill Gates has a limited ammount of money").

If you sample at 1hz (and your signal is limited to 0.5hz), you can record and reconstruct a signal with a peak at 5.23 seconds. If you used a low bitdepth, the peak may be shifted a bit (like 0.01s). If you used a high bitdepth, the position of the peak will be more precise. The point I was making was, you cannot have *infinite* precision. But you can get pretty close.
Title: What is "time resolution"?
Post by: ExUser on 07 October, 2006, 07:26:07 PM
ChiGung, it is increasingly apparent you are not investing any effort in trying to understand what we are saying.  I am not unused to this behaviour from you. I will try something concrete to show you what we are saying, then I advise that people stop posting here. This is a foolish response to trolling that is solved by a little bit of focused EE research on CG's part.

Consider a sine wave at a frequency 22050-(1/32768) Hz, perfectly encoded in 44.1KHz/16bit CD Audio. Nyquist's theorem proves that this can be perfectly encoded. This should have the property that (edit: the absolute value of) each successive sample is a single number smaller than the previous. Given a certain phase shift, 2^15 samples should have the form (-32768,32767,-32766,32765,...,0). This has an interesting property: every other 16-bit value represents a different phase shift! It may seem counter-intuitive, but such a data set does not decrease in volume, provided accurate reproduction. That means that for such a high-frequency value, the "time resolution" is essentially 2^15 times greater than the sampling frequency. I would suppose the maximum time resolution of the CD audio format to be something near that value, though it is  possible that the upper maximum could be 2^16.
Title: What is "time resolution"?
Post by: ChiGung on 07 October, 2006, 07:28:20 PM
the precise position of the peak in the source may be anywhere between the enclosing sample points -as confirmed by med0.

Please don't misquote me. I said that it is possible to record the position of a peak in a bandlimited signal even if the peak is between two samples, but the precision will be limited (as in "Bill Gates has a limited ammount of money").

Im sorry I did misquote you, I was just in the process of editing it out after noticing your corrections before your reply.

Quote
If you sample at 1hz (and your signal is limited to 0.5hz), you can record and reconstruct a signal with a peak at 5.23 seconds. If you used a low bitdepth, the peak may be shifted a bit (like 0.01s). If you used a high bitdepth, the position of the peak will be more precise. The point I was making was, you cannot have *infinite* precision. But you can get pretty close.

My point was that you can only get closer than the samplerate, by sacrificing the accuracy of all the other samples in the record - and then you would need to a record of accuracy weighting per sample, to interprate the record as intended

ChiGung, it is increasingly apparent you are not investing any effort in trying to understand what we are saying.  I am not unused to this behaviour from you. I will try something concrete to show you what we are saying, then I advise that people stop posting here. This is a foolish response to trolling that is solved by a little bit of focused EE research on CG's part.

I see we are back to this are we. Forget it then.
Title: What is "time resolution"?
Post by: ExUser on 07 October, 2006, 08:05:16 PM
I've provided a mathematical example of why your position is in error and an analysis of your posting style. We are back to nothing. You seem to think your position is somehow without flaw, despite the elaborate and time-consuming explanations of many. I'm simply recommending that people realize that further discussion appears to be utterly futile. You have your position, and no amount of reasoning will change that.

Edit: on consideration, the values for the data set I've given may be in error. It still remains that for such a high-frequency value, there is a great number of values that would represent varying phase shifts for that signal.
Title: What is "time resolution"?
Post by: cabbagerat on 08 October, 2006, 03:07:19 AM
For your viewing pleasure, here's a quick demonstration that 16/44.1 PCM can resolve 10ns differences in time between two signals. The code is MATLAB, but if you don't have MATLAB, then download Octave (it's free) which will run this code without modification.
Code: [Select]
fs = 44100; %sample rate
ts = 1/fs; %sample period
bd = 16; %bit depth
f0 = 1e3; % frequency of wave
bd_scale = 2^(bd-1);
x=0:(1/fs):0.01;
y = round(cos(f0*2*pi*x)*bd_scale);
y2 = round(cos(f0*2*pi*(x+1e-8))*bd_scale);
plot(x, y1-y2, 'r');

Chigung's assertion that you sacrifice the accuracy of other samples is, in my mind, quite a stretch. Do you have a demonstration of this (in code, or in a theoretical treatment)?
Title: What is "time resolution"?
Post by: ChiGung on 08 October, 2006, 10:02:33 AM
For your viewing pleasure, here's a quick demonstration that 16/44.1 PCM can resolve 10ns differences in time between two signals. The code is MATLAB, but if you don't have MATLAB, then download Octave (it's free) which will run this code without modification.
Code: [Select]
snip statement demonstrating the precise resolution of known variables

Chigung's assertion that you sacrifice the accuracy of other samples is, in my mind, quite a stretch. Do you have a demonstration of this (in code, or in a theoretical treatment)?

I am happy for this practical request.

Regarding:
Quote
The situation is, that the positioning of the brightness peak in the record is limited by the fact that the record has an implicit bandlimit. The position of the brightness peak in the source image is not implicity restricted by this limitation. (edit: yes the peak could be precisely positioned if we could employ all of the information stored in surrounding samples to do so - but all those other samples have information of their own to carry*) .

-------------------------------------------------------------------
Visualise a sequence of samples:

a,b,c,d,e,f,g,h,i,j

Suppose we are interested in the records solution between e and f. Perhaps we are looking for the precise location of the summit of a spike or perhaps the precise location when the recorded level achieves a value, like level=0. You must be able to propose a condition of the level to locate in time, in order for any statements about the records ability to locate detail in time to have meaning.

Propose a condition to locate then.
Then arrange any test values you like for all the levels.
Then locate your condition between e and f.

You will be able to do so, to the degree of precision noted frequently throughout this thread.

Then change the value of any single sample.
The location of your condition will change.
The location of the condition can be altered to occur anywhere between the bounding samples by altering the other samples in the record. (note ,depending on the condition sought, it may also be possible to make it not occur at all)

This is because the location of that condition is the result of a calculation which employs simultaneously all of the levels. The information which is used to store the conditions location, is that which is contained in all the samples. But that is an unnatural reading of the record (it is not being interprated just as normal PCM) We are effectly using a long 'read in' and 'read-out' period to achieve the accurate placement of the condition. We are treating the other samples as disposeable, when in normal PCM recording, each sample must have essentialy attributed the same importance as each other.

Its as though, we are trying to discover PCMs ability to precise locate details in time, so we test its ability to locate a single detail in time -arranging the whole record to do that locating. It is an unnormal reading of the record - an overreading of the relevance of the levels indicated conditions at the interval we are focusing on with an assumption of compliance of all the other levels.

To try to alter the indicated travel of the level to fit our intentions, is like trying to poke lumps out of a mattresse and finding when we do so, lumps appear in other parts of the mattresse. We can only arrange the shape we like in one bit of the mattrese by causing distortion in the rest. After doing so, if we could discard the rest of the mattress, then shape we had arranged would dissappear as it was the whole mattresse which informed the shape of the little part we were interested in.
Title: What is "time resolution"?
Post by: ExUser on 08 October, 2006, 10:28:34 AM
So because sinc() interpolation is weird, PCM fails...
Title: What is "time resolution"?
Post by: cabbagerat on 08 October, 2006, 10:51:54 AM
This is because the location of that condition is the result of a calculation which employs simultaneously all of the levels. The information which is used to store the conditions location, is that which is contained in all the samples. But that is an unnatural reading of the record (it is not being interprated just as normal PCM) We are effectly using a long 'read in' and 'read-out' period to achieve the accurate placement of the condition. We are treating the other samples as disposeable, when in normal PCM recording, each sample must have essentialy attributed the same importance as each other.
I can't really follow your argument. Are you saying that it's impossible to reconstruct a properly sampled signal from a set of arbitrarily accurate samples using only causal filters? If so, that's quite profound and almost certainly wrong, but if you have evidence that this is true, the IEEE transactions on signals and systems is the right place for it, not HA.

If you are saying that, in PCM, distortion is introduced by the impulse response of the system, then please demonstrate that this distortion is even plausibly audible.

Quote
So because sinc() is weird, PCM fails... rolleyes.gif
Title: What is "time resolution"?
Post by: ChiGung on 08 October, 2006, 11:10:42 AM
I can't really follow your argument. Are you saying that it's impossible to reconstruct a properly sampled signal from a set of arbitrarily accurate samples using only causal filters?

Nope. The demonstration was quite clear and explainations have been labouriously reworded for the comprehension of whoever seeks it.
Title: What is "time resolution"?
Post by: KikeG on 08 October, 2006, 12:59:37 PM
As others have said, time resolution of PCM is the inverse of sampling rate multiplied by nº of discrete levels. In other words,

T = 1/(fs*2^n)

Where n is nº of bits. And that's all.
Title: What is "time resolution"?
Post by: ChiGung on 08 October, 2006, 01:14:00 PM
As others have said, time resolution of PCM is the inverse of sampling rate multiplied by nº of discrete levels. In other words,

T = 1/(fs*2^n)

Where n is nº of bits. And that's all.

So your, considered 'contemporary' definition of 'time resolution' of PCM becomes finer as the number of included levels increases. And you appreciate no further clarification of what your definition practicaly means for the resolution of details throughout time in the record. Fine, but the scope of this topic provided for a wider discussion.
Title: What is "time resolution"?
Post by: KikeG on 08 October, 2006, 01:24:22 PM
So your, considered 'contemporary' definition of 'time resolution' of PCM becomes finer as the number of included levels increases.

Yes. Resolution is limited by sampling rate and dynamic range or SNR or quantization noise, call it as you prefer.
Quote
And you appreciate no further clarification of what your definition practicaly means for the resolution of details throughout time in the record. Fine, but the scope of this topic provided for a wider discussion.

Resolution refers about the smallest time event that can be resolved. Why make it more complicated?
Title: What is "time resolution"?
Post by: ChiGung on 08 October, 2006, 01:55:31 PM
Resolution refers about the smallest time event that can be resolved. Why make it more complicated?

Nice question  I may try to reiterate but to save my effort let me first requote some explaination already provided which may have been missed:
Quote
such 'delay' is no definite attribute of the undownsampled source, it is an attribute summed circumspectly from the phases of frequencies surviving the downsample. The frequencies which didnt survive the downsample, contained the information required to resolve the true subsample detail of 'time localised energy spikes'.


There is a difference between the 'time resolution' commonly presented, and the ability to record in PCM the temporal location of events accurately. Basically this common use of the term 'time resolution' is (apparently) widely misunderstood. Detail of any time localisable events, will be distorted by the implicit lowpass of conversion by an unknowable amount (post conversion) by upto a sample-period-width of difference. The common demonstration to prove the ability to record the location of events to finer than a sample width accuracy, depends on the precise aggreance (exclusive employment) of many samples to place just one test detail within a whole run of samples - it is a very unfair demonstration and actualy demonstrates my point -that to achieve subsample positioning of a single detail requires the use of more than one sample. In a normal PCM record, the altering of other sample points to maintain subsample positioning of details in the origional waveform, cannot be done, all details are susceptable to be shifted by unrecoverable amounts up to the new sample interval (and of course some details may be lost altogether) Downsampling, involves introducing uncertainty of the waveforms precise form (as information is discarded)
So the practical 'time resolution' of PCM, as in 'how accurately can the temporal placement of events in the origional waveform which survive conversion be known, is (sublimely) to within the limits of the sample period - because we do not have the lost high frequency information of any events anymore.
Title: What is "time resolution"?
Post by: Woodinville on 08 October, 2006, 02:37:52 PM
So your, considered 'contemporary' definition of 'time resolution' of PCM becomes finer as the number of included levels increases. And you appreciate no further clarification of what your definition practicaly means for the resolution of details throughout time in the record. Fine, but the scope of this topic provided for a wider discussion.



Your words here are meaningless. "Appreciate no further clarification" is meaningless, at least without your providing some clear, testable, verifiable "clarification" that you believe necessary.

With the understanding stated above, the issue is settled.  You have your answer, and you might as well live with it.  I don't see any reason to engage you further until you use language that those skilled in the art can actually recognize as having technical meaning.

Detail of any time localisable events, will be distorted by the implicit lowpass of conversion by an unknowable amount (post conversion) by upto a sample-period-width of difference.



This is completely incorrect. Please do not state it as a fact, and please do not reproduce this myth where it may confuse others.

You clearly have no understanding of the function and effect of the antialiasing filter at the input to the sampling process, or of the meaning of a bandwidth limited signal.

Try this:  Create a gaussian pulse. Since you are making expert judgements here, you should have no trouble doing that.

Create a gaussian pulse that is down 90dB at 22.05 kHz. Surely that will be easy, since it involves the simplest Fourier Identity in existance.

Now, figure out the sample values for that. Shift the time by 1/10000th of a sample time, and figure out the sample values. They are different.

Q.E.D.
Title: What is "time resolution"?
Post by: ChiGung on 08 October, 2006, 02:57:01 PM
Your words here are meaningless. "Appreciate no further clarification" is meaningless, at least without your providing some clear, testable, verifiable "clarification" that you believe necessary.

You dont like my online persona, and I sure dont like yours woody lets leave it a that.

Others regard the level of attention I am up against here.

Clear, testable, verifiable clarifications have been provided for those sincerely intereseted in them.

Quote
Detail of any time localisable events, will be distorted by the implicit lowpass of conversion by an unknowable amount (post conversion) by upto a sample-period-width of difference.

This is completely incorrect. Please do not state it as a fact, and please do not reproduce this myth where it may confuse others.

It is fact - there will be people using this forum with the understanding and experience to realise it.
Perhaps in your haste to offend me, you forgot the type of conversion being discussed is neccessarily a downsample (ie. a type involving an implicit lowpass)

Quote
Try this:  Create a gaussian pulse. Since you are making expert judgements here, you should have no trouble doing that.
Create a gaussian pulse that is down 90dB at 22.05 kHz. Surely that will be easy, since it involves the simplest Fourier Identity in existance.
Now, figure out the sample values for that. Shift the time by 1/10000th of a sample time, and figure out the sample values. They are different.

Yeah you did forget that. There is no downsample involved there, just a shifting of a record.
Pay the thread better attention before posting please.

Quote
Depending on the characteristics of the information conveyable from the origional media (lenses, microphones, physics of air etc) it may be suitably restricted for precise capture/repoduction by certain samplerates, but because the source media may also not be suitably restricted (and very often is not) we have to allow for this possibility. It's surprised me that there has been a strong tendency to discount this as recognising source media may have finer resolution than target samplerates is fundamental to sensible statements of how accurately target samplerates can record the information of various sources.
Title: What is "time resolution"?
Post by: ExUser on 08 October, 2006, 03:08:55 PM
ChiGung, despite your frequent reassertions to the contrary, we are still not following you. Your explanations have not been clear, precise, testable, or verifiable.

So, there are two possibilities: you are misunderstanding and are incorrect, or all the technically competent members who are assuring you and providing mathematical proof of the inaccuracy of your position are misunderstanding you and are providing evidence that is not related to the topic at hand. I would suggest you consider the possibility of the former, as we consider the possibility of the latter and try and understand exactly what you're trying to convey here.
Title: What is "time resolution"?
Post by: ChiGung on 08 October, 2006, 03:28:17 PM
I would suggest you consider the possibility of the former, as we consider the possibility of the latter and try and understand exactly what you're trying to convey here.

Deal
Title: What is "time resolution"?
Post by: ChiGung on 08 October, 2006, 04:44:28 PM
I think that it is being claimed, almost unanimously that,  'conditions' (which would indicate 'events' or 'energy spikes') precise location in a PCM record, accurately informs us of their precise location in real time.
I have been trying to explain how this is untrue. That in real time, rather than the sampled approximation of it, the precise time of any condition can differ from what is idealy indicated by the record -by up to a sample interval (or maybe half a sample interval - I am not certain of the amount)

The correlation between the records indication of timing of instantaneous conditions (such as level= x) and the actual timing of indications would be something like this (loosely from intuition):

Indicated time is within 1 sample period of real time: odds ~1/1
Indicated time is within 1/2 sample period of real time: odds ~1/2
Indicated time is within 1/4 sample period of real time: odds ~1/3
Indicated time is within 1/8th sample period of real time: odds ~1/4

I have presented an intuitive guess of probability of accuracy there to drive through what I am generaly talking about - The uncertainty of PCM records, with regards to potential sources having significantly higher bandlimits. As is often the case with Redbook standard PCM (downsampled from production formats) and others.

It is the unknown frequencies above the samplerates implicit bandlimit which cause this uncertainty. We interprate the PCM record as though the frequnecies beyond the bandlimit must always have been flat, but in for example a production formats samplerate at 96kHz, they were not neccessarily flat (or else there would be little point in using those formats.)

The example of the 'tekkie' locating the spike with a record too precisely was a straight forward one. 
The rebuttal of the example that the spike could indicate any position therefore it must indicate the true position securely was invalid for the reason that to ensure the precise positioning of the spikes peak with the true peak, all the other samples would have to be employed to refine that single detail, and they cannot normaly be employed just to do that as they have to convey their own detail as well.
Revise the lumpy mattresse methaphor. It is not a silly one.

The situation I have been pointing out is very complex with great subtleties and many gotchas involved. I am very familiar with the technologies limitations because I have spent a great deal of time pondering it and programming for it, particularly over the past year. I have for example completed my own frequency analyser from first principles without reference to any text books or reported methods. It produces very fine output and the mechanics of it are now being employed in my own compression codec. Unfortunately it will be along time since Ill be able to talk about it in detail in public. But you see, (unless im lying  ) I am not wishfully lecturing in an area which I have no experience. I dont believe I have said anything unconfirmable or insensible in this thread (at least which is not transient to the arguement -everyones human), there may be certain mistakes or difficulties in expression to get caught up in, but the subject is outside of many peoples familiarity zone -even people involved here. If anyone reads my explainations open mindedly, and links the parts of the explainations which they can interprate and skips the bits they cant, there is a good chance they will acknowledge an under-reported aspect of PCM 'time resolution'.

I will leave this thread now, confident in the explaination Ive invested here.
If it really is a silly as everyone seems to think it is, I guess it will end up in the recycle bin but I do believe that it would be an uncommon shame on HA.org to do so. 

Sincerely.
twerpy' smartass' fat-tongued, Cheegunge
Title: What is "time resolution"?
Post by: legg on 08 October, 2006, 08:32:51 PM
I have presented an intuitive guess of probability of accuracy there to drive through what I am generaly talking about - The uncertainty of PCM records, with regards to potential sources having significantly higher bandlimits. As is often the case with Redbook standard PCM (downsampled from production formats) and others.

It is the unknown frequencies above the samplerates implicit bandlimit which cause this uncertainty. We interprate the PCM record as though the frequnecies beyond the bandlimit must always have been flat, but in for example a production formats samplerate at 96kHz, they were not neccessarily flat (or else there would be little point in using those formats.)


Preciselly that's why you must low pass the signal BEFORE sampling, otherwise the content above FS/2 will get mixed with the frequencies below FS/2 causing aliasing. On a bandlimited signal there's no "spike" that can not be represented in the sampled version, even if it lies within 2 samples. It isn't rocket science.

The straightforward solution to be able to capture your so called "spikes" is to increase the sample rate, but that by no means imply that the sampling theorem is flawed in any way. The theorem does imply that you must sample fast enough to have perfect reconstruction, at least from a mathematical point of view. In practice we all know that there's no ADC with a perfect delta dirac.

I'm still waiting to see your MATLAB code proving everyone wrong.
Title: What is "time resolution"?
Post by: ChiGung on 08 October, 2006, 09:16:37 PM

....snip vaguest part of my post....

Preciselly that's why you must low pass the signal BEFORE sampling, otherwise the content above FS/2 will get mixed with the frequencies below FS/2 causing aliasing. It isn't rocket science.

The straightforward solution to be able to detect "spikes" is to increase the sample rate, but that by no means imply that the sampling theorem is flawed in any way. It does imply that you must sample fast enough to have perfect reconstruction, at least from a mathematical point of view. In practice we all know that there's no ADC with a perfect delta dirac.

I'm still waiting to see your MATLAB code proving everyone wrong.

Another one tries to wriggle under the full case that has set on a plate for you and seasoned liberaly.
Dont say Im talking about detecting 'spikes' just after I have just described the uncertainty of detecting the realtime location of any 'conditions' -such as spikepeaks,  level values or waveform gradients -any conditions that could be locateable in an instant of time indicateable by a PCM record.

Ive never gone near MATLAB because I dont need it, I code in low level java/c syntax, and what I code ends up working sir.

Trying to drag it back to who was right or wrong like that is pathetic.
Title: What is "time resolution"?
Post by: legg on 08 October, 2006, 10:27:15 PM
Fine forget about the code and do try to provide mathematical proof of your statements instead of blabbering. I'm sure a person that names himself smart ass will be able to provide such proof.

FYI, java is NOT a low level language, it is actually FAR from being one. C is closer but it isn't considered low level either, the actual term to describe C is middle level.
Title: What is "time resolution"?
Post by: MedO on 09 October, 2006, 04:35:10 AM
If I understand you right, you are saying that the time when the signal reaches a certain level in the recorded PCM waveform may be different from the time in reality.

This is equivalent to saying that the recorded waveform is different from the real one. Which is true if you are sampling with less than twice the highest frequency which will occur in the source.

The signal will be reconstructable to great accuracy if it is bandlimited to half the sampling frequency. It won't if it isn't. Why make it so complicated?
Title: What is "time resolution"?
Post by: 2Bdecided on 09 October, 2006, 10:08:10 AM
The example of the 'tekkie' locating the spike with a record too precisely was a straight forward one. 
The rebuttal of the example that the spike could indicate any position therefore it must indicate the true position securely was invalid for the reason that to ensure the precise positioning of the spikes peak with the true peak, all the other samples would have to be employed to refine that single detail, and they cannot normaly be employed just to do that as they have to convey their own detail as well.


This is the heart of your misunderstanding.

A bandwidth limit (we agree there is such a thing in PCM) implies that, what you believe to be some kind of contradiction, is in fact the simple reality of the situation. Let me show you why with something less abstract...


For it to work properly, PCM requires two filters - one anti-alias at (before) the A>D, the other anti-image at (after) the D>A.


Forgetting PCM for a second, if those filters themselves cause an audible problem, then we have a problem. I don't think we do. However, you have expressed a wish to tackle this issue separately, so let us leave it to one side for now.


So, we have two filters. If _both_ filters block everything above fs/2, then the sampling stage itself will be transparent - lossless, if you like. In other words, these two systems would be identical...

1. input, filter1, filter2, output
2. input, filter1, sampling (no quantisation), filter2, output

Indeed, if you have two black boxes containing systems 1 and 2, there would be no way to tell these boxes apart (though number 2 may introduce a time delay in practice).

If you believe this to be false, you must bring something to disprove it. (This would disprove Nyquist, so good luck!).


Your example of non-adjacent samples having an impact on the apparent position of an inter-sample peak does not disprove it - this is just a consequence of the required filtering. Even a novice in filter design knows that output sample number N depends on the value of more than one input sample, unless the filter is a non-filter! This is all that is at work here. It's not magic. It's not a problem either.

Cheers,
David.
Title: What is "time resolution"?
Post by: 2Bdecided on 09 October, 2006, 10:24:37 AM
Here are some nice pictures...

[attachment=2591:attachment]

I worked at 16-bits throughout.

I started at 441kHz (i.e. 10x CD sample rate). I generated a single impulse. To prove the point, I also generated a second impulse one sample later on the other stereo channel. This is the left hand pair of plots.

I resampled to 44.1kHz (i.e. CD sample rate). The result is shown in the middle pair of plots. Interestingly, Cool Edit Pro's visual interpolation hints at what is represented by those samples - i.e. a 1/10th of a sample time delay between the two channels.

I resampled back to 441kHz. The result is shown in the right hand pair of plots. The peaks of the waveforms are clearly in the correct place relative to each other. Time resolution equivalent to 1/10th of a sample at 44.1kHz clearly survives this sample rate.


Of course the peaks are low amplitude (less energy) and longer (spread out in the time domain) - but this is just what happens when you low pass filter a click.


So, this is a simple, repeatable example proving the sub-sample accuracy of sampled systems, without a sine wave in sight!

Cheers,
David.
Title: What is "time resolution"?
Post by: cabbagerat on 09 October, 2006, 11:54:34 AM
It's not magic.
It's not? I suppose that explains why the FIR filter I designed with tarot cards didn't work.

Seriously, nice diagrams.
Title: What is "time resolution"?
Post by: Axon on 09 October, 2006, 12:30:02 PM
So I was mainly pissed off in my earlier post because it looked like this was about to turn into a rematch of ChiGung vs. the world. Which wound up happening, and it's not like I agree with him on much, but I already went through all of that on SH.tv.

The formula described by KikeG (and others) does help, but it doesn't really satisfy me. It seems to coincide well with what I've computed (with 1/20000 sample delays being feasible) - I suppose that the 1/(fs*2^n) number is a theoretical limit rather than an upper bound on period, and depending on the vagaries of the upsampling/downsampling implementations, the real testable interval may wind up being much higher. (In theory, I ought to be able to get a 1/65536 sample delay working?)

This gives a lot of wiggle room for audiophiles to claim that there could be large differences in performance based on how good the upsampling/downsampling filters are, resulting in numeric performance improvements to the minimum reproducible delay. However, one could pretty conclusively argue that even the implementation-tested periods are lower than the minimum audible delays by a wide margin. And it does give an exact definition to beat people over the head with, which is what I was wanting.
Title: What is "time resolution"?
Post by: Woodinville on 09 October, 2006, 01:00:41 PM
Yeah you did forget that. There is no downsample involved there, just a shifting of a record.


Now you're simply being evasive.

Since the signal in question will not be affected by any decent lowpass filter (it has no out-of-band components) your assertions are shown to be wrong.
Title: What is "time resolution"?
Post by: Woodinville on 09 October, 2006, 01:41:36 PM
The formula described by KikeG (and others) does help, but it doesn't really satisfy me. It seems to coincide well with what I've computed (with 1/20000 sample delays being feasible) - I suppose that the 1/(fs*2^n) number is a theoretical limit rather than an upper bound on period, and depending on the vagaries of the upsampling/downsampling implementations, the real testable interval may wind up being much higher. (In theory, I ought to be able to get a 1/65536 sample delay working?)


Well, consider this...

Let us take a sine wave at nearly half the sampling frequency...

It's slope (using +-1 for amplitude) is 2*pi*f at maximum (crossing zero).

You want to figure out when you can distinguish one LSB. That's when
2*pi*f > 2/(2**bits).

Give or take.  Since we have to dither, the numerator of the right side is bigger by some extent.

This is where the number comes from. It's a classic phase analysis problem.

Of course, when we dither, we can also average many cycles and get a better result.

Now, as strange as it seems, the single-cycle example is directly germane to the question at hand.

I leave it to ChiGung to explain to us how this completely controverts all of his assertions completely.
Title: What is "time resolution"?
Post by: ChiGung on 14 November, 2006, 07:16:35 PM
Hello all, I left this discussion in a tizz and have only just checked again to find these constructive replies.

A 'thought' experiment occured to me which would illustrate my point about PCMs 'time resolution' -which could be performed computationaly to generate precise data... Ill set it out hopefully:

I assume 'resolution' can refer to the ability to resolve discrete details of source material in pcm records. And there must be a difference in the potential of detail resolution in 'the source' and that in 'the record'.
eg if the source was just a CD, and the target record was 11kHz pcm,
- then their potential to have detail resolved in them would differ.
Fundamentaly the 11kHz pcm's potential to resolve detail 'should' seem to be 1/4 of the CDs 44kHz record.

That would go,
44kHz pcm 'time resolution' = 4* 11kHz pcm 'time resolution'

oddly, here and elsewhere this formula is eclipsed with not insubstantial excursions into test pattern replications and counter intuitive textbook quotations.

If i needed exact data on the capability of 'time resolution' in PCM records, here is how I would go about generating it:
Write a small program to read in pcm, and locate exact time of specifiable conditions in it. Conditions such as (level=0) or level=p(test),
or gradient =0, or gradient =p.
To avoid porting in or trying to write my own bandlimited solution of the pcm record, id write the code for simple linear interpolation and feed it high quality upsamples in order to achieve near 'bandlimited accuracy' in discernment of 'time location' of 'conditions'.

So a program can read in a bandlimited upsample of source pcm, and generates a list of times of all matching conditions which are found/resolvable within the upsample.

eg. hq upsample of cd track at 44kHz to ~192kHz
>list of times of peaks and troughs (gradient=0) found in 192kHz pcm rendering.

Next, high quality downsample the cd track to 11kHz (1/4 sample rate)
Then upsample to 192 again (for hq interpolation), and generate its list of (gr=0) times.
//(the upsample to 192 is only to facilitate high quality bandlimited interpolation)

At this stage in the thought experiment, I would note, that although both list of timings look for the same condition, there may be considerably less occurences of the condition (peaks or troughs) found in the predownsampled record, which would depend on the nature of the source material.

The two lists plotted on a graph should illustrate an observable time correlation between conditions found in each record, as well as 'orphaned' conditions represented only in the higher pcm.

Disregarding the orphaned conditions, the detail of 'time resolution' rests on how closely correlated the pairable condition times turn out to be.
A plot could be made of their distribution of correlation, perhaps it would tend to be a bell curve? for pink noise only? What would the limits of correlation be?

Additional explores: Compare accuracy of correlation of surviving details, in CD to 11kHz, then CD to various other rates. White noise, to some rates, then pink noise..etc.. Also do some comparisons in using different upsample rates, to discern the programs simpler linear discernments inherent innacuracy.

If we can spot a condition occuring at a time in a pcm record, with correlation data, we could indicate probabilities of that condition occuring within temporal distances in higher sampled records of the same kind of source material

It would be interesting to look at.

If I ever spend my sparse powers of collected concentration to generate the info myself, Ill post it here for all your troubles'

best'
cg
Title: What is "time resolution"?
Post by: kwwong on 15 November, 2006, 03:50:24 AM
44kHz pcm 'time resolution' = 4* 11kHz pcm 'time resolution'


For a fixed frame size,

44kHz pcm 'frequency resolution' = 4*11kHz pcm 'frequency resolution',

44kHz pcm 'time resolution' = 0.25*11kHz pcm 'time resolution'
Title: What is "time resolution"?
Post by: 2Bdecided on 15 November, 2006, 07:00:53 AM
ChiGung,

Your experiment wouldn't work. By knocking the sample rate down to 11kHz (and implicitly limiting the bandwidth to 5.5kHz) you would change the waveform dramatically. For simple synthetic waveforms, we could say correctly whether none, some, or all peaks would stay in the same place depending on the content of the original signal. However, for complex waveforms, we can't say anything sensible about what would happen to individual waveform peaks.

For example, if you have a bass drum and a high hat playing at the same time, most of the waveform excursion will be due to the bass drum (which will survive the 5.5kHz low pass filter), but the exact peak location will also depend on the "wiggles" in the waveform due to the high hat itself. These high frequency "wiggles" will be butchered by a 5.5kHz low pass filter, so the peak will move!

The only way you can be absolutely sure that it's a fair experiment, and that the low pass filter isn't significantly moving the peak by removing part of the signal that forms the peak itself, is to ensure that the low pass filter doesn't remove anything - i.e. that the original doesn't contain any frequencies above 5.5kHz, or, to put it another way, that the downsampled version still satisfies Nyquist with reference to the original content.

Nyquist is right yet again - what a surprise!



The basic problem is here:

Quote
Fundamentaly the 11kHz pcm's potential to resolve detail 'should' seem to be 1/4 of the CDs 44kHz record.

That would go,
44kHz pcm 'time resolution' = 4* 11kHz pcm 'time resolution'


You are implying that these two things are directly proportional in a real and limiting sense, whereas, until you get to the absolute limit, many orders of magnitude better than the limits of human hearing, and many orders of magnitude better than anything we expect the system to achieve, the two things are completely independent.


Rather than talking about sample rate and "time resolution", let's talk about the number of hours I'm awake in a day, and the number of bananas I eat that day.

Fundamentally, the number of bananas I eat if I'm awake for 8 hours "should" seem to be 1/2 of that if I'm awake for 16 hours.

What's wrong with this statement? On the face of it, it seems like intuition. However, the reality of the situation is that the number of bananas I eat in a day has nothing to do with how long I'm awake. I might not have any bananas in the house, and I might not go shopping. I might go to the market I buy a big bunch of bananas at a bargain price and eat several of them. I'll probably just have one a day for my lunch (I'm so boring and predictable) no matter how long I'm awake. The simple truth is that, whatever blind intuition may try to tell you, the practical real world truth is that the number of bananas I eat in a day is completely independent of how many hours I'm awake.


Similarly, the time resolution of a PCM system is independent of the sample rate!



Quote
oddly, here and elsewhere this formula is eclipsed with not insubstantial excursions into test pattern replications and counter intuitive textbook quotations.


"oddly"?! What's odd about reality not conforming to blinkered misguided uninformed intuition?!


As for "excursions into test pattern replications" - if you look carefully at my previous post, and the waveforms, I've performed your latest thought experiment already - but with the only type of waveform where it will work - a carefully controlled one!


Finally...
Quote
A plot could be made of their distribution of correlation, perhaps it would tend to be a bell curve? for pink noise only? What would the limits of correlation be?


In a suitably controlled version of your experiment (like mine) it wouldn't be a bell curve, it would be a single point! That would certainly be the case with the parameters you propose (44.1>192kHz).

If you try it with real music, it might be a bell curve, or it might be some other distribution (with a cut off corresponding to the point you decide the peaks don't match) - but that's got nothing to do with the temporal resolution of PCM, and everything to do with an experiment where you change something intentionally at random, and then measure how much you've changed it!

Cheers,
David.
Title: What is "time resolution"?
Post by: ChiGung on 15 November, 2006, 07:45:54 AM
......... For example, if you have a bass drum and a high hat playing at the same time, most of the waveform excursion will be due to the bass drum (which will survive the 5.5kHz low pass filter), but the exact peak location will also depend on the "wiggles" in the waveform due to the high hat itself. These high frequency "wiggles" will be butchered by a 5.5kHz low pass filter, so the peak will move!

The experiment cant not work, it is just designed to generate the surviving correlation distribution data, so that we can refer to data about different sample rates relative and absolute abilities to accurately record timings of discrete conditions in source. You restate the practical 'damage' done to 'time resolution' of isolateable conditions in natural sources (saying> the exact peak location will also depend on "wiggles" butchered by a 5.5kHz lowpass) Documenting the average degree of that 'butchery' is the purpose of the experiment, no more, no less.

Quote
The only way you can be absolutely sure that it's a fair experiment, and that the low pass filter isn't significantly moving the peak by removing part of the signal that forms the peak itself, is to ensure that the low pass filter doesn't remove anything.
- i.e. that the original doesn't contain any frequencies above 5.5kHz, or, to put it another way, that the downsampled version still satisfies Nyquist with reference to the original content.

That is plainly not fair. You are assuming preconditions which mean only informationaly lossless downsamples are considerable. I think you are unwilling to broaden your examination of 'reality' to a degree which would qualify the objections I have made about reported subsample 'time resolution' capabilities. I have been talking about reality. When we want to know what the timing resolution of a pcm record is, we would fundamentaly compare the capabilites of a record to the full potential of an ideal source.
The experiment would compare the capabilites of lower rates with higher rates. Presupposing all records in the higher rates must be additionaly bandlimited as lower rates, is not sensible. 

Quote
Quote
Fundamentaly the 11kHz pcm's potential to resolve detail 'should' seem to be 1/4 of the CDs 44kHz record.

That would go,
44kHz pcm 'time resolution' = 4* 11kHz pcm 'time resolution'


You are implying that these two things are directly proportional in a real and limiting sense, whereas, until you get to the absolute limit, many orders of magnitude better than the limits of human hearing, and many orders of magnitude better than anything we expect the system to achieve, the two things are completely independent.

Now you are talking of psychoacoustics. That is an entirely different matter, "what differences could we hear". I described a process to generate the correlation data of timing of surviving conditions between fully utilised (non extraneously bandpassed) pcm sample rate records. The data will "scale" according to simple principles. The time resolution of 1 Hz will be equal to 1/44100th of the time resolution of 44100 Hz - there is no doubt about that relationship.

Quote
Quote
A plot could be made of their distribution of correlation, perhaps it would tend to be a bell curve? for pink noise only? What would the limits of correlation be?


In a suitably controlled version of your experiment (like mine) it wouldn't be a bell curve, it would be a single point! That would certainly be the case with the parameters you propose (44.1>192kHz).


That would be the pointless version of the experiment - or rather one which just examines rounding error.

I have the code mostly written to perform (comparison of different sampling rates time resolution of conditions with various sources) I will hold off finishing it until it is acknowledged here that it presents a valid investigation (if done accurately enough and naturaly -without flattering extraneous bandpassing)

l8r,
cg
Title: What is "time resolution"?
Post by: 2Bdecided on 15 November, 2006, 08:29:08 AM
So, in short, you want to run an experiment to see what effect a low pass filter has?
Title: What is "time resolution"?
Post by: ChiGung on 15 November, 2006, 08:45:16 AM
So, in short, you want to run an experiment to see what effect a low pass filter has?

Yes.

As particular sample rates, do have implicit unavoidable lowpasses -the process of comparing the capabilites of different samplerates, refactors as comparing effects of different lowpasses. It is almost the same thing, although actualy doing the full downsample (as well its implied lowpass) investigates an attained quality of the full process, so would preferable for this charge for actual proof of subsample source/record ambiguity.
Title: What is "time resolution"?
Post by: cabbagerat on 15 November, 2006, 09:22:26 AM
It is almost the same thing, although actualy doing the full downsample (as well its implied lowpass) investigates an attained quality of the full process, so would preferable for this charge for actual proof of subsample source/record ambiguity.
There are two issues at stake here. The first is the question of audibility of low pass filters. This has been dealt with here and elsewhere at great length and could be easily rigourously tested. Such a test has been done before, but a repeat including filters with non-flat phase responses might offer some new information.

The second is that you seem to doubt whether lowpass->sample->reconstruct can be shown to have the same effect as just the lowpass. Without quantization, the theory says that the two processes are identical. If you wish to question this then a mathematical treatment will probably be necessary before your demonstration is accepted.
Title: What is "time resolution"?
Post by: ChiGung on 15 November, 2006, 09:51:38 AM
There are two issues at stake here. The first is the question of audibility of low pass filters. This has been dealt with here and elsewhere at great length and could be easily rigourously tested. Such a test has been done before, but a repeat including filters with non-flat phase responses might offer some new information.

Audibility of the timing capabilities has never been my interest here, so I have avoided refering to it and isolated it as extraneous to the empirical measurement or estimation of time resolution, whenever it has been brought up.

Quote
The second is that you seem to doubt whether lowpass->sample->reconstruct can be shown to have the same effect as just the lowpass.

That is not my contention, I have recently acknowledged these processes are potentialy identical. Their equivalence does nothing to invalidate the 'coupling correlation between sample rates' test described. Their equivalence only provides an accelerated to method of generating the data.

Quote
Without quantization, the theory says that the two processes are identical. If you wish to question this then a mathematical treatment will probably be necessary before your demonstration is accepted.

I havent questioned the equivalence of:
A high quality downsample followed by high quality upsample
= A high quality lowpass to the downsamples nyquist frequency

I have suggested that the locations of any isolatable conditions in a normaly utilised source record (ie with energy potentialy up to its own nyquist freq), can be correlated with the the best fitting locations of the same conditions in a downsampled (or equivalently lowpassed) record > to provide data (with bias towards best fits) on how accurately time of conditions can be resolved in an implicity bandlimited pcm record, against their actual potential placement in source material/records.
Title: What is "time resolution"?
Post by: 2Bdecided on 15 November, 2006, 10:18:05 AM
I wish you understood the theory CG, because without it, I can't begin to explain the complete and utter pointlessness of what you're suggesting.

It's a fair enough experiment to ask an undergrad to do in order to practice computer programming and audio processing, but in terms of what it actually tells you about anything, all I can do is just sit here slowly shaking my head!


FWIW, given a random selection of audio signals (real or synthetic) the lower the low pass filter, the further the peaks will move (and, to say the almost same thing differently, the more peaks will completely disappear). The major stumbling block to doing the experiment exactly as you propose will be in determining when a peak has moved vs when a peak has vanished - or, to put it another way, tracking the "same" peak between different versions. Various possible attempts to do this "correctly" (and it will be near-impossible) will mean your results might be unexpected!


The major problem is that every reasonable definition of time-resolution leads to a proof that PCM audio has no issues with time resolution - so now you've invented a new definition in order to prove the opposite. Your success here will not be down to your experiment (which will certainly show some change), but down to your strange definition of time resolution.

Cheers,
David.
Title: What is "time resolution"?
Post by: SebastianG on 15 November, 2006, 10:48:18 AM
I also don't see the point in checking the positions of zero crossings or peaks after lowpassing. This won't prove anything except that if you further limit the bandwidth of a signal these points may move, vanish, or appear at places where there previously havn't been any.

Assuming the lowpass filter's impulse response is symmetric the following is true: If your signal shows a certain symmetry within an interval with the same size of the lowpass' filter response a certain class of points within that interval will be at the exact same position.

Example signal:
first two harmonics of a square wave: you'll get 4 peaks within a cycle
after lowpassing (only the fundamental left): 2 peaks within a cycle (it's a sine)
The zero crossings are the same (two within a cycle) because there's a "point symmetry" at those points. (rotate the curve around the point 180° and it'll be the same)
Tell me what we have learned by that, ChiGung.

In the context of transform coding time resolution usually refers to the partition of the time/frequency plane that's done by a critically-sampled filterbank AFAIK. Without any noise shaping filter tricks this will effectivly limit how well we can control the quantization noise distribution in specific time/frequency regions only by choosing scalefactors. However, noise shaping filters can be and usually are used to improve this. (With "ANS" enabled Musepack can do better in terms of controling the noise's distribution in the frequency domain than what the filterbank suggests --one subband is 670 Hz wide, though ANS manages to shape the noise within a subband. With "TNS" enabled AAC can do better in terms controling the noise's distribution in the time domain than what the filterbank suggests.)
Title: What is "time resolution"?
Post by: ChiGung on 15 November, 2006, 11:01:00 AM
It's a fair enough experiment to ask an undergrad to do in order to practice computer programming and audio processing, but in terms of what it actually tells you about anything, all I can do is just sit here slowly shaking my head!

Yet you cant explain what is pointless about generating the data described, without indestinct reference to some 'theory' which you believe I dont understand.

Or is there an attempt here...
Quote
FWIW, given a random selection of audio signals (real or synthetic) the lower the low pass filter, the further the peaks will move (and, to say the almost same thing differently, the more peaks will completely disappear). The major stumbling block to doing the experiment exactly as you propose will be in determining when a peak has moved vs when a peak has vanished - or, to put it another way, tracking the "same" peak between different versions. Various possible attempts to do this "correctly" (and it will be near-impossible) will mean your results might be unexpected!

I dont need to be informed of possible surprises. I understand very well what you have written there, it is the very situation that I have described repeatedly in this thread re: the 'time resolution' of PCM. I understand what your prefered theoretical statements about 'time resolution' are, and because I have understood what they are not, I have brought the practical situation to your attentions - that the 'spike', the 'radar blip', the 'cymbal peak' etc. cannot be confidently estimated much beyond the sampling interval - precisely because[/i] of the unknown butchery of higher frequency information in the normaly utilised source - the true situation is as you, and as I have described.

Only you consider the true situation completely and utterly pointless to investigate.
And it seems many have felt patronised by my attempts to explain, that it is not utterly pointless to try to correlate actual conditions within record types - that it is in fact how you securely measure such accuracy of correlation. Measuring what is practicaly achieveable in real, normal (not extraneously bandpassed) records.

Quote
so now you've invented a new definition in order to prove the opposite. Your success here will not be down to your experiment (which will certainly show some change), but down to your strange definition of time resolution.

My invented definition of time resolution in pcm? - the ability to discern the times of conditions in a pcm record in contrast to the original (natural resolution) material which the pcm is merely a record of.

I think you guys have been mostly presenting the potential 'time resolution' of related partly analogous algebraic systems.
Title: What is "time resolution"?
Post by: ChiGung on 15 November, 2006, 11:16:14 AM
I also don't see the point in checking the positions of zero crossings or peaks after lowpassing. This won't prove anything except that if you further limit the bandwidth of a signal these points may move, vanish, or appear at places where there previously havn't been any.

It would just document our ability to compare time pin-pointable conditions in a waveform and provide a method of correlating conditions within different pcm records that fully utilise their sample rates.
It would document the confidence with which we can resolve such indicateable conditions in a waveform in comparision to what would be possible with a natural record of near infinite 'time resolution'
It would investigate actual data, rather than the isolated formula presented here which indicate 'algebraic resolutions' or 'time resolution of presumed lossless conversions' 

Quote
Example signal:
first two harmonics of a square wave: you'll get 4 peaks within a cycle
after lowpassing (only the fundamental left): 2 peaks within a cycle (it's a sine)
Tell me what we have learned by that, ChiGung.

Someone may learn, that downsampling can not only damage time resolution, but also the topology of the waveform.

Quote
In the context of transform coding time resolution usually refers to the partition of the time/frequency plane that's done by a critically-sampled filterbank AFAIK. Without any noise shaping filter tricks this will effectivly limit how well we can control the quantization noise distribution in specific time/frequency regions only by choosing scalefactors. However, noise shaping filters can be and usually are used to improve this. (With "ANS" enabled Musepack can do better in terms of controling the noise's distribution in the frequency domain than what the filterbank suggests. With "TNS" enabled AAC can do better in terms controling the noise's distribution in the time domain than what the filterbank suggests.)

I dont argue, you have a valid context there, but I have been explicity writing at length about the context of practical recovery of the source material from provided PCM records. There seems to be difficulties with getting the context of practical source reproduction examined.
Title: What is "time resolution"?
Post by: SebastianG on 15 November, 2006, 11:30:26 AM
I happened to code a subpixel detector for "x-corners" (checkerboard corners) for the purpose of calibrating cameras. Luckily it can be shown that the areas around these x-corners show the mentioned symmetries which enables me to accurately measure the subpixel position of those x-corners (=saddle points) by analysing an optically-low-passed-&-sampled image of a checkerboard. Simulations showed that the real bottleneck is the censor noise actually. Without (simulated) censor noise I got an accuracy of 1/300 pixel -- possibly restricted by a little bit of aliasing that's left in the image generation / subpixel-detector code.

The interesting part is: If you capture an image at high resolution with some censor noise and use a high quality resampler to reduce the image resolution you'll get pretty much the same locations for those x-corners -- meaning that the subpixel accuracy increased by the same factor I downsampled the image. In fact, lowpassing is an integral part of the detector to minimize the effect of noise it has on the estimated x-corner positions. So, it's not surprising that the subpixel detector's performance (measured in pixels) was better on the smaller image. By your definition of time resolition (spatial resolution for images) this would mean that the two images would have the same spatial resolution. But of course the 2nd one is a downsampled one which doesn't look as sharp. So what good is your definition?
Title: What is "time resolution"?
Post by: ChiGung on 15 November, 2006, 11:53:23 AM
I happened to code a subpixel detector for "x-corners" (checkerboard corners) for the purpose of calibrating cameras. Luckily it can be shown that the areas around these x-corners show the mentioned symmetries which enables me to accurately measure the subpixel position of those x-corners (=saddle points) by analysing an optically-low-passed-&-sampled image of a checkerboard. Simulations showed that the real bottleneck is the censor noise actually.

Interesting, in this case however you know what the checkboard looks like, unexpected deviations from a clean checkboard appearance, would introduce innaccuracy. It is a selective example not fully similar to resolving details in waveforms - which we can have few presumptions about.

Quote
However, if you capture an image at high resolution with some censor noise and use a high quality resampler to reduce the image resolution you'll get pretty much the same locations for those x-corners -- meaning that the subpixel accuracy increased by the same factor I downsampled the image. (I tested this and IMHO this is not surprising). By your definition of time resolition (spatial resolution for images) this would mean that the two images would have the same spatial resolution.

I dont fully agree with your case there, regard how you are locating nodes in a very ideal pattern (checkerboard). It will get complex to investigate fully, but the location of details when the source pattern is unpresumable (piano or violin, cymbal or triangle, square or saw or sine.. noise or not..) is a significant additional factor in recovering source material detail from pcm records.
Title: What is "time resolution"?
Post by: SebastianG on 15 November, 2006, 11:59:07 AM
It will get complex to investigate fully, but the location of details when the source pattern is unpresumable (piano or violin, cymbal or triangle, square or saw or sine.. noise or not..) is a significant additional factor in recovering source material detail from pcm records.

It seems nobody else than you interested in those "details" since it's very likely that our auditory system doesn't care about whether peaks have moved due to band limitation.
Title: What is "time resolution"?
Post by: 2Bdecided on 15 November, 2006, 12:06:12 PM

It's a fair enough experiment to ask an undergrad to do in order to practice computer programming and audio processing, but in terms of what it actually tells you about anything, all I can do is just sit here slowly shaking my head!

Yet you cant explain what is pointless about generating the data described, without indestinct reference to some 'theory' which you believe I dont understand.


OK, you're starting with any audio, aren't you? A signal picked up by a microphone, synthetic pink or white noise, etc - correct?

You won't accept pre-filtering of the signal, correct?

And you will low pass filter the signal at varying frequencies, and see how the peaks in the "original" change, correct?

Well think about this: You can start with a 10MHz sampled signal. Given the lack of a filter, there will be something (mainly noise) up to 5MHz. If you filter the signal at 1MHz, some peaks will move a little.

Thus you have proven that a 1MHz low pass filter does something.

So what?!?!?!?!

Cheers,
David.
Title: What is "time resolution"?
Post by: ChiGung on 15 November, 2006, 12:21:08 PM

It will get complex to investigate fully, but the location of details when the source pattern is unpresumable (piano or violin, cymbal or triangle, square or saw or sine.. noise or not..) is a significant additional factor in recovering source material detail from pcm records.

It seems nobody else than you interested in those "details" since it's very likely that our auditory system doesn't care about whether peaks have moved due to band limitation.

I dont care what they sound like, my interest in them is that they exist and cause real, measurable, examinable, innacuracy between waveform sources and pcm waveform records.

When there is negative interest in that practical circumstance here, in HAs Scientific/R&D Discussion forum, in a thread called "what is time resolution", and all my explainations of it are run around with... relentless indifference and absolutely no apparent solvent interest, does that make me the fool?

'who knows
Title: What is "time resolution"?
Post by: ChiGung on 15 November, 2006, 12:31:45 PM
You won't accept pre-filtering of the signal, correct?

No, it is clear in the process described, that all records of source can be suitably prefiltered to fit their format.
ie. we can assume the cd audio will be suitably prefiltered at 22kHz
only to compare that records time resolution to lower sampling rates, it is insensible to prefilter the higher sampling rates to the enforced bandlimit of the lower rate.

Quote
Well think about this: You can start with a 10MHz sampled signal. Given the lack of a filter, there will be something (mainly noise) up to 5MHz. If you filter the signal at 1MHz, some peaks will move a little.
Thus you have proven that a 1MHz low pass filter does something.
So what?!?!?!?!

So you will observe how the bandwidth limitations of samplerates damages timing and/or survival of time locatable conditions/events in waveform records vs waveform sources.
Title: What is "time resolution"?
Post by: Woodinville on 15 November, 2006, 01:42:45 PM

So, in short, you want to run an experiment to see what effect a low pass filter has?

Yes.

As particular sample rates, do have implicit unavoidable lowpasses -the process of comparing the capabilites of different samplerates, refactors as comparing effects of different lowpasses. It is almost the same thing, although actualy doing the full downsample (as well its implied lowpass) investigates an attained quality of the full process, so would preferable for this charge for actual proof of subsample source/record ambiguity.


So, if the lowpass filter is above the point where your ear captures information, then what have we found?

The second is that you seem to doubt whether lowpass->sample->reconstruct can be shown to have the same effect as just the lowpass. Without quantization, the theory says that the two processes are identical. If you wish to question this then a mathematical treatment will probably be necessary before your demonstration is accepted.



This mathematical treatment can be found in many places. I believe Taub and Shilling deal with it. Certainly  Jayant and Noll address it, but not quite in a form a novice will recognize.  Any good older book on modems will discuss it in great detail (PSK being exactly what would discover such differences, including quantization, noise, and distortion).

There is a lot of good mathematical treatment out there.

Interesting, in this case however you know what the checkboard looks like, unexpected deviations from a clean checkboard appearance, would introduce innaccuracy. It is a selective example not fully similar to resolving details in waveforms - which we can have few presumptions about.


So, do you LOOK at your audio, or do you listen to it?

So you will observe how the bandwidth limitations of samplerates damages timing and/or survival of time locatable conditions/events in waveform records vs waveform sources.


Once more, it is trivial to calculate this from first principles.

You DO understand that phase shift at a given frequency is a way of measuring time delay, yes?

Now, can you measure the phase shift (removing the ft, or pure delay, part) of your processing?

If you can't, it's not changing the in-band time resolution.

Now, a given level of quantization can be directly related to a given amount of phase uncertainty. Figure out for yourself what that equals at 16 bit quantization levels for a full-scale signal, now. Just go ahead and do it.
Title: What is "time resolution"?
Post by: ChiGung on 15 November, 2006, 01:56:07 PM
So, if the lowpass filter is above the point where your ear captures information, then what have we found?

I refer to previous replies on this matter such as:
Quote
What is 'accurate enough' is a different matter id not like to confuse the main investigation with.


Quote
The second is that you seem to doubt whether lowpass->sample->reconstruct can be shown to have the same effect as just the lowpass. Without quantization, the theory says that the two processes are identical. If you wish to question this then a mathematical treatment will probably be necessary before your demonstration is accepted.

This mathematical treatment can be found in many places. I believe Taub and Shilling deal with it. Certainly  Jayant and Noll address it, but not quite in a form a novice will recognize.  Any good older book on modems will discuss it in great detail (PSK being exactly what would discover such differences, including quantization, noise, and distortion).

There is a lot of good mathematical treatment out there.

Nice, it still doesnt make comparing waveforms encoded at different samplerates but bandlimited identicaly, any more informative of the realworld situation, where records usualy can utilise their samplerates implied full bandwidths.

Quote
So, do you LOOK at your audio, or do you listen to it?

I do all sorts of things with audio, but generaly pcm encoding and its limitations apply to much more material than just human audio.
Title: What is "time resolution"?
Post by: Woodinville on 15 November, 2006, 02:01:18 PM
Nice, it still doesnt make comparing waveforms encoded at different samplerates but bandlimited identicaly, any more informative of the realworld situation, where records usualy can utilise their samplerates implied full bandwidths.

Of course it does. Try it some time.
Quote
Quote
So, do you LOOK at your audio, or do you listen to it?

I do all sorts of things with audio, but generaly pcm encoding and its limitations apply to much more material than just human audio.


So, if you're dealing with other issues, why not state those issues? It seems to me that you have an investigation in search of a problem.
Title: What is "time resolution"?
Post by: ChiGung on 15 November, 2006, 02:14:35 PM
So you will observe how the bandwidth limitations of samplerates damages timing and/or survival of time locatable conditions/events in waveform records vs waveform sources.


Once more, it is trivial to calculate this from first principles.

The damage is trivial for you to calculate? Well, i wouldnt say that my method of actualy discerning it was trivial or too involved, but Im just the one who has pressed the issue to be acknowledged arent i?

Quote
You DO understand that phase shift at a given frequency is a way of measuring time delay, yes?

I dont accept phase shifts can be directly interprated as a 'time delay' because they applies to long multisample sinusoidal patterns (frequencies), phase shifts never alone detail any isolatable instants. Phase shifts are time relateable attributes of frequencies, not instant isolateable positions or durations in linear time.

Quote
Now, can you measure the phase shift (removing the ft, or pure delay, part) of your processing?
If you can't, it's not changing the in-band time resolution.
Now, a given level of quantization can be directly related to a given amount of phase uncertainty. Figure out for yourself what that equals at 16 bit quantization levels for a full-scale signal, now. Just go ahead and do it.

Im not interested in performing your excercises.
The resulting flaw of your own excercising, is that you neither can acknowledge that timing resolution of locateable conditions in real waveforms has significant 'subsample' uncertainty regarding the unknown frequencies which are unrepresentable at any given samplerate.
Title: What is "time resolution"?
Post by: Garf on 15 November, 2006, 02:18:23 PM
The resulting flaw of your own excercising, is that you neither can acknowledge that timing resolution of locateable conditions in real waveforms has significant 'subsample' uncertainty regarding the unknown frequencies which are unrepresentable at any given samplerate.


I don't understand a word of what you are saying there.

"unknown frequencies which are unrepresentable at any given samplerate"

Uh?
Title: What is "time resolution"?
Post by: ChiGung on 15 November, 2006, 02:30:53 PM
Nice, it still doesnt make comparing waveforms encoded at different samplerates but bandlimited identicaly, any more informative of the realworld situation, where records usualy can utilise their samplerates implied full bandwidths.

Of course it does. Try it some time.

I dont need to 'try' what you are saying. I know the difference between comparing two records with the same utilised bandwidth, and two records with different spectrums.

Quote
So, if you're dealing with other issues, why not state those issues? It seems to me that you have an investigation in search of a problem.

Why not read my contributions to the thread? The issue i am dealing with is the sensible value we can give for the ability of pcm records to record events in time accurately. "inaudible" is not such a value.




I don't understand a word of what you are saying there.
"unknown frequencies which are unrepresentable at any given samplerate"

Uh?

It is a tired rephrasing of an over repeated explaination:
The frequencies which are unrepresentable at any given samplerate, are of course, those above the nyquist for that samplerate, and being unrepresentable, they are usualy unknowable. Certainly in a downsample of cd audio to 22kHz, the frequency content of the origional CD track above 11kHz -is unknowable. Ok , in some cases we might know the source tracks frequency spectrum, generaly we shouldnt assume so should we?

Im feeling a little distrurbed again, that no one seems to be understanding anything that I have made efforts to explain.

edit: removed extraneous un, from "unusualy uknowable"
Title: What is "time resolution"?
Post by: AstralStorm on 15 November, 2006, 04:43:59 PM
It is a tired rephrasing of an over repeated explaination:
The frequencies which are unrepresentable at any given samplerate, are of course, those above the nyquist for that samplerate, and being unrepresentable, they are unusualy unknowable. Certainly in a downsample of cd audio to 22kHz, the frequency content of the origional CD track above 11kHz -is unknowable. Ok , in some cases we might know the source tracks frequency spectrum, generaly we shouldnt assume so should we?

Im feeling a little distrurbed again, that no one seems to be understanding anything that I have made efforts to explain.


You know... air is a good lowpass filter too and there's a good deal of dither in it. (thermal noise, ~-20 bits, that is ~-120 dB)
Not to count interference from other sound waves.

Other than that, the eardrum/microphone has some known temporal resolution. Then, the neural analysis system has to react (much slower). Also mostly known.
What's more: those "errors" stack.

Nothing is perfect. So you can't even notice such a tiny temporal change, unless you're a robot. Then, it goes back to square one: the microphone and electrical noise.

Go figure.
If you ever build an infinite precision machine, go for the Nobel prize.
Title: What is "time resolution"?
Post by: Woodinville on 15 November, 2006, 05:35:01 PM
Im not interested in performing your excercises.

Then you're not interested in the answer to your question.
Quote
The resulting flaw of your own excercising, is that you neither can acknowledge that timing resolution of locateable conditions in real waveforms has significant 'subsample' uncertainty regarding the unknown frequencies which are unrepresentable at any given samplerate.



The exercises I provided you allow you to do exactly what you want to do. 

If you don't want to do them, you aren't going to get your answers.

I dont accept phase shifts can be directly interprated as a 'time delay' because they applies to long multisample sinusoidal patterns (frequencies), phase shifts never alone detail any isolatable instants. Phase shifts are time relateable attributes of frequencies, not instant isolateable positions or durations in linear time.


Actually, given an amount of phase shift at any given frequency, you have precisely specified duration in time.

But this seems to suggest you're stuck in a larger problem. You do realize that all physically realizable waveforms (we're talking audio here, not cosmology, after all) can be represented by an integral of sine waves, do you not?  You do realize that you can decompose any physically realized waveform into its sinusoidal components, yes?

Your failure to understand that phase shift and time delay are DEFINED to be related would suggest, as well, that you "don't accept" the language of the field. This is not a good place to start.  Perhaps you could start by accepting the language, and then state what your problem is in terms of generally accepted language. Language, after all, is no good for communication if you use different meanings, and if you are using the same meaning as everyone else, a phase shift of x at a given frequency is exactly, precisely specifying a given amount of time.
Title: What is "time resolution"?
Post by: ChiGung on 15 November, 2006, 07:20:07 PM
The exercises I provided you allow you to do exactly what you want to do. 
If you don't want to do them, you aren't going to get your answers.

i'm scheduled to dip my head in a clow clap and sprinkle ants in my pants just before i get your answers prof 

The positions have been stated, time may clarify.....
Title: What is "time resolution"?
Post by: kwwong on 16 November, 2006, 04:24:26 AM

44kHz pcm 'time resolution' = 4* 11kHz pcm 'time resolution'


For a fixed frame size,

44kHz pcm 'frequency resolution' = 4*11kHz pcm 'frequency resolution',

44kHz pcm 'time resolution' = 0.25*11kHz pcm 'time resolution'


Sorry I was wrong..

For a fixed frame size,

44kHz pcm 'frequency resolution' = 0.25*11kHz pcm 'frequency resolution',

44kHz pcm 'time resolution' = 4*11kHz pcm 'time resolution' 
Title: What is "time resolution"?
Post by: 2Bdecided on 16 November, 2006, 08:22:55 AM
Im feeling a little distrurbed again, that no one seems to be understanding anything that I have made efforts to explain.


No, I think I get it perfectly.

When you low pass filter a signal, the positions of the peaks will move (and some peaks will vanish).

You seem to think this is important, and want to perform an experiment to determine how far the peaks move, and then relate this quantity to the low pass filter cut-off frequency. You believe the peak location is related to time resolution, and thus hope to show the relationship between low pass filter cut-off frequency (or bandwidth, or sample rate, etc) and time resolution.

That's your position, isn't it?


No one is doubting that the peaks will move and/or vanish with most signals.

I personally am doubting you can perform the experiment on arbitrary samples, because you won't be able to track the peaks.

More generally, I think everyone (including me) is failing to see the point of the experiment.


I tried, intuitively, so show why I think it's pointless with the 10MHz example...

Well think about this: You can start with a 10MHz sampled signal. Given the lack of a filter, there will be something (mainly noise) up to 5MHz. If you filter the signal at 1MHz, some peaks will move a little.
Thus you have proven that a 1MHz low pass filter does something.
So what?!?!?!?!

So you will observe how the bandwidth limitations of samplerates damages timing and/or survival of time locatable conditions/events in waveform records vs waveform sources.


...but you just re-iterated that the peaks would move/vanish, and the amount may be related to bandwidth. I know. I said that too!

My "So what?!?!?!" wasn't facetious - it was a serious (albeit exasperated  ) question. Having done your experiment, what have you proven? What conclusion can you draw? What relevance does this conclusion have to anything?


The thing is, I think your experiment is impossible, so we're never going to get trustworthy results from it. That is why I am trying to move things on; Since the fact that the peaks move isn't disputed by anyone, what we want to know is: what conclusion do you draw from that?

(because I suspect its a vastly different conclusion from the one drawn by everyone else!!!)

Cheers,
David.
Title: What is "time resolution"?
Post by: ChiGung on 16 November, 2006, 11:10:57 AM
My "So what?!?!?!" wasn't facetious - it was a serious (albeit exasperated  ) question. Having done your experiment, what have you proven? What conclusion can you draw? What relevance does this conclusion have to anything?

Hi 2B, thanks for going through what you understand of the investigation I presented. I think we have similar expectations of the outcome of the investigation, although I find the 'best matching' stage (of nodes) less troublesome, because the innacuracy introduced by missed and imaginary matches only tends to increase the appearance of accuracy and i am satisfied to look at flatteringly skewed best case data from practice, rather than isolated formulations or none at all.

The investigation was designed to give us a most optimistic reckoning, of our ability to match the location of instantaneous features apparent in PCM records, to their potential position in their original source material.
The findings could apply to eg, estimating the location of percussive attacks in human audio from audio pcm, or (perhaps fancifully) estimating the edges of a region of different luminousity and/or spectroscopy in an image of space.
As a thought experiment, we are reminded that timings (or positions) derived from pcm, are often/normaly unknowable estimations of the timings occuring in the recordings source.
I believe this relationship of uncertainty and innacuracy between PCM and its potential source is central to the issue of achieved time resolution @ sample rate, and makes claims of confident subsample time resolution highly misleading -misreadings of the fundamental algebraic systems useable to most consistently process PCM.

I appreciate you taking my position head on. I am satisfied that my point is explicit enough now for readers to draw their own conclusions.

cheers'
cg

Sorry I was wrong..

For a fixed frame size,
44kHz pcm 'frequency resolution' = 0.25*11kHz pcm 'frequency resolution',
44kHz pcm 'time resolution' = 4*11kHz pcm 'time resolution' 

Thanks kwwong, I should try and make less typos really 
Title: What is "time resolution"?
Post by: SebastianG on 16 November, 2006, 12:22:02 PM
The findings could apply to eg, [...] or (perhaps fancifully) estimating the edges of a region of different luminousity and/or spectroscopy in an image of space.

See? You usually have a model for the kind of thing you search for. For example: Edge = curve that joins dark and bright areas in an image. Usually the signal you recorded is distorted in some ways (noise, nonlinear transfer, ...), so you have to account for that via preprocessing and stuff (oftentimes even a lowpass with Gaussian-like response is used for that, actually).

What you can determine through simulation is that detector algorithm A locates feature type B (eg. edges) with accuracy C (eg. +/-0.2 pixels) when given a signal with distortion D (eg. SNR of 20 dB).

In these cases where the location of features is interesting (like the position of an x-corner for camera calibration or peaks of a cross-correlation to detect movements and stuff) zero-phase-lowpassing (to some extent) hardly affects the accuracy that can be achieved. Most changes you encounter after lowpassing is due to the noise that has been filtered out so it can't disturb the estimated location anymore. Usually the parameter that is directly related to the accuracy that can be achieved is a combination of noise power and sampling rate. But increasing the sampling rate doesn't necessarily imply that the accuray you get with "detector A" will improve because you also collect more high frequency noise that isn't filtered out anymore ...

Anyhow ... I guess I can say that most of us don't agree with you that a definition of "time resolution" based on how peaks will move around, vanish or appear due to band-limitation makes much sense/is any practical.
Title: What is "time resolution"?
Post by: ChiGung on 16 November, 2006, 12:51:32 PM

The findings could apply to eg, [...] or (perhaps fancifully) estimating the edges of a region of different luminousity and/or spectroscopy in an image of space.

See? You usually have a model for the kind of thing you search for. For example: Edge = curve that joins dark and bright areas in an image. Usually the signal you recorded is distorted in some ways (noise, nonlinear transfer, ...), so you have to account for that via preprocessing and stuff (oftentimes even a lowpass with Gaussian-like response is used for that, actually).

I understand you are talking about knowledge of the artifacts/condtions searched for - and I recognise if the artifact is known to span several samples and has its own consistent reliable form through a period or periods of time, its form can be traced throughout multiple samples, allowing increased accuracy of placement. This is the case i see with calculating phase delays, or checkerboard positioning - not so much with uncertain appearances in space, where we cant be sure of eg. a nebulas form or objects' edge consistency.

Quote
What you can determine through simulation is that detector algorithm A locates feature type B (eg. edgex) with accuracy C (eg. +/-0.2 pixels) when given a signal with distortion D (eg. SNR of 20 dB).

In these cases where the location of features is interesting (like the position of an x-corner for camera calibration or peaks of a cross-correlation to detect movements and stuff) zero-phase-lowpassing (to some extent) hardly affects the accuracy that can be achieved. Most changes you encounter after lowpassing is due to the noise that has been filtered out so it can't disturb the estimated location anymore. Usually the parameter that is directly related to the accuracy that can be achieved is a combination of noise power and sampling rate (something like the ratio of sampling rate to the square root of the noise power). But increasing the sampling rate doesn't necessarily imply that the accuray you get with "detector A" will improve because you also collect more high frequency noise that isn't filtered out anymore ...

This is an informative account of a practical situation but it should not detract from the case presented that in many applications, most relevantly -the selection of sample rates for human audio, the practical rates selected 44,32,24 etc.. do differ in bandwidth from potential sources, and that reduction in bandwidth does affect accurate recording of timeable events/conditions/features, which within audio are not usualy suitable for extra interpolations for locating knowable formations (some instruments might be predictable enough to try experimentaly, but in practice this isnt done). 

Quote
Anyhow ... I guess I can say that most of us don't agree with you that a definition of "time resolution" based on how peaks will move around, vanish or appear due to band-limitation makes much sense/is any practical.

I believe if that is so, you are all kidding yourselves, because the situation that "peaks will move around, vanish or appear due to band-limitation" is unavoidably present at such audio ranges considered, and when you accept 'subsample accurate' reproduction at those ranges, you are simply deciding to dismiss the highlighted matter - that the pcm record cannot indicate any instantaneous condition's presence in their potential sources with 'subsample accuracy'.

Why people should wish to ignore such practical uncertainty of source timing (in R&D discussion) -i do not know.

regards'

edit: tpyos & phrasing
Title: What is "time resolution"?
Post by: Woodinville on 16 November, 2006, 04:48:11 PM
I believe if that is so, you are all kidding yourselves, because the situation that "peaks will move around, vanish or appear due to band-limitation" is unavoidably present at such audio ranges considered, and when you accept 'subsample accurate' reproduction at those ranges, you are simply deciding to dismiss the highlighted matter - that the pcm record cannot indicate any instantaneous condition's presence in their potential sources with 'subsample accuracy'.

Once again, a simple test using a gaussian pulse will show that you can trivially resolve subsample intervals. Ergo, your assertion is defeated directly.
Quote
Why people should wish to ignore such practical uncertainty of source timing (in R&D discussion) -i do not know.

regards'

edit: tpyos & phrasing


Allow me to point something else out, since you said "record". Peaks in the record (vinyl) playback will move around and vanish with record wear, stylus pressure, the difference in phase between the turntable rumble and the "peak", and furthermore, distortion mechanisms will create peaks (very sharp ones) here and there.

Of course, said peaks have no frequency content inside the range of hearing, but that's a separate issue.

The position of such error peaks can be distinquished easily to sub-sample accuracy in PCM, as well. Been there, done that.

The thing, and the only thing, you can't see in the PCM representation, is the part of the peak that has frequency content OUTSIDE the pcm range.

Now, I notice that you've refused to try the basic experiments I've suggested earlier, and instead engaged in personal abuse. Don't engage in abuse again. 

If you ever do finally try a few real-life experiments you will discover immediately that a phase shift at a given frequency precisely specifies a time delay. I'll await your admission of that.
Title: What is "time resolution"?
Post by: ChiGung on 16 November, 2006, 05:32:22 PM
....the situation that "peaks will move around, vanish or appear due to band-limitation" is unavoidably present...

Once again, a simple test using a gaussian pulse will show that you can trivially resolve subsample intervals. Ergo, your assertion is defeated directly.

"woosh", (thats the sound of the practical matters which ive brought brought up and Seb and 2B have finaly acknowledged as real (though not yet central)

- flying over over your head.

Quote
Allow me to point something else out, since you said "record".

As in pcm "record" - 'nice smoke screen.

Quote
Now, I notice that you've refused to try the basic experiments I've suggested earlier, and instead engaged in personal abuse.
 
Which person?
I said i'd abuse myself before taking you seriously again Woody.
Quote
Don't engage in abuse again.

Aww i thought you liked it - stop scratching my back, and i wont scratch yours then.

always'
cg
Title: What is "time resolution"?
Post by: Woodinville on 16 November, 2006, 05:44:34 PM
"woosh", (thats the sound of the practical matters which ive brought brought up and Seb and 2B have finaly acknowledged as real (though not yet central)

- flying over over your head.


Since I've said the same thing they have, in different words, I think that perhaps you're just handing out abuse again.

Ciao.
Title: What is "time resolution"?
Post by: ChiGung on 16 November, 2006, 06:15:32 PM
Since I've said the same thing they have, in different words, I think that perhaps you're just handing out abuse again.

You are very sensitive for someone who posts in such a critical manner.

2B confirmed:
Quote
When you low pass filter a signal, the positions of the peaks will move (and some peaks will vanish).

Seb stated:
Quote
Anyhow ... I guess I can say that most of us don't agree with you that a definition of "time resolution" based on how peaks will move around, vanish or appear due to band-limitation makes much sense/is any practical.

-he does seem to confirm here that "peaks will move around, vanish or appear due to band-limitation" - only for some reasons denies relevance to 'time resolution'

But i think Seb understands that the investigation I described would confirm that "peaks* will move around, vanish or appear due to band-limitation" It would at least measure, with a flattering bias, the shifts in temporal position we can expect to result from a given downsample and source track type.
(not only "peaks" but troughs, zero crossings, slopes, every shape and form in the record can be distorted by the necessary lowpassing involved in hq downsampling) Because that point seem to be accepted and partly because Im a lazy so, I stopped writing the program to do the investigation.

Although ive had no encouragement, when i get round to finishing it, ill post the results here.

So Woody, your prediction is on record that no differences in timing (especialy in hand crafted gaussian pulses etc) will be observed.
Title: What is "time resolution"?
Post by: MoSPDude on 16 November, 2006, 06:21:02 PM
I've been trying to follow this as well, and especially reading 2Bdecided post which I think summarises primarily what ChiGung wants to test, this is how I understand the issue.

A lot of this seems to not have much to do with PCM but more sampling theorem in general, as a quick reference I've been using my books and notes, for an online reference - wikipedia (Nyquist–Shannon sampling theorem) as it provides the mathematic descriptions accordingly. Theoretically, a band-limited signal sampled at greater than twice the highest frequency component when reproduced through the sinc interpolation, which requires knowledge of all samples over all time, is a perfect representation. Practically, we don't know all samples across all time and DACs use various methods to reproduce the signal, but not perfectly.

If we do these tests digitally, and the real-world source is band limited below the Nyquist frequency, then the Nyquist–Shannon sampling theorem will hold and values representing that signal will theoretically reproduce an exact perfect signal, including any sub sample shifts in peaks due to filtering. Quantisation will have an effect in terms of increasing noise. If the source signal was not band-limited, aliasing will occur - and the sampled signal will certainly not represent the original signal.

In terms of the peaks moving after a low pass filter etc, I was taught these such things were due to the phase characteristic of the filter where indeed the phase change specified at a specific frequency will give an exact definable time shift. As 2Bdecided said, it would be difficult to track EXACT peaks, but I imagine you could compare magnitude/phase plots of a set period of time with an arbitrary signal before and after an LPF or whatever filter, along with the magnitude/phase plot of the transfer function of the filter. What people are saying when they mention 'records' etc. is that a communication medium also has a transfer function and an appropriate magnitude/phase response - eg age/wear changes these responses.
Title: What is "time resolution"?
Post by: Woodinville on 16 November, 2006, 06:40:20 PM
If the source signal was not band-limited, aliasing will occur - and the sampled signal will certainly not represent the original signal.

Very, very true.

And, as a dual, a signal that is reconstructed without a reconstruction filter will also mean that the resulting nonlinear system has worse time resolution than the system with the reconstruction filter.
Quote
In terms of the peaks moving after a low pass filter etc, I was taught these such things were due to the phase characteristic of the filter where indeed the phase change specified at a specific frequency will give an exact definable time shift.

That entirely depends on the signal. Suppose we have a gaussian pulse centered at time t1 whose substantial frequency components are above the cutoff, and another much smaller one at time t2 that is entirely in-band as far as the filter is concerned..

Doesn't matter what kind of filter you use there.
Quote
As 2Bdecided said, it would be difficult to track EXACT peaks,

Or, even define what an "exact peak" means, really, in the presence of noise, which is something that we always have, all the time, in the real workd.
Quote
but I imagine you could compare magnitude/phase plots of a set period of time with an arbitrary signal before and after an LPF or whatever filter, along with the magnitude/phase plot of the transfer function of the filter. What people are saying when they mention 'records' etc. is that a communication medium also has a transfer function and an appropriate magnitude/phase response - eg age/wear changes these responses.


You could go beyond that, and simply plot the Hilbert envelope of the signal at different bandwidths. I think you'd find that extraordinarily useful in this discussion.


So Woody, your prediction is on record that no differences in timing (especialy in hand crafted gaussian pulses etc) will be observed.


No, that's not my prediction.  You can abuse this, as I have already explained.
Title: What is "time resolution"?
Post by: ChiGung on 16 November, 2006, 06:41:39 PM
Hi MoSP' Ill try not to confuse things with my ..deviances..
but just add a few carefull comments
If we do these tests digitally, and the real-world source is band limited below the Nyquist frequency, then the Nyquist–Shannon sampling theorem will hold and values representing that signal will theoretically reproduce an exact perfect signal,

Its not clear which 'Nyquist frequency' you mean there, that of the recording, or that of the target samplerate. To be clear -i acknowledge that when they are the same, we have very great, potentialy lossless accuracy of reproduction of each (to each other).

Quote
In terms of the peaks moving after a low pass filter etc, I was taught these such things were due to the phase characteristic of the filter....

This issue of filters which change phases of frequencies is a different one.

Peaks can move after bandwidth filtering, because the whole employed spectrum contributes to every observable detail in a waveform, so if we remove a portion of the frequency spectrum, every peak, trough, slope and level in the waveform is suspectable to being affected. Its not a case of 'one' peak shifting like an isolated part of a sinusoid changing phase, its 'one' peak (along with all the other instants) being rendered by a bundle of different superimposed sinusoids, and then how a peaks rendering might change, when sines' are removed from the origional bundle.

hth,
regards'
cg
Title: What is "time resolution"?
Post by: MoSPDude on 16 November, 2006, 07:11:41 PM
All good comments and corrections. 

@ChiGung, the Nyquist frequency I was referring to was the one of half the target sample rate. And again, the source signal would have to be band-limited to below this frequency. I'm interested in what you are saying, but in the heat of the argument in previous posts you were offering some confusing comments.

In terms of the posts original question at the top, " what is "time resolution"? ", I don't believe that sample rate conversion would affect the continuous time position of peaks and troughs of any arbitrary signal if, again, the signals you are up/down sampling are contained below the Nyquist frequency of the lower sample rate, the interpolation was theoretically ideal and subject to suitable filtering bringing in no mag/phase changes.

As a side interest that I might play with, I wonder about upsampling a file by loading in all the samples and performing a sinc interpolation per sample across "all time" would yield an improved sample rate converter for pre-recorded files?? - I wonder how long such a calculation would take??

Its all good stuff, just hard to read with the heated debate going on.
Title: What is "time resolution"?
Post by: saratoga on 16 November, 2006, 07:16:24 PM
As a side interest that I might play with, I wonder about upsampling a file by loading in all the samples and performing a sinc interpolation per sample across "all time" would yield an improved sample rate converter for pre-recorded files?? - I wonder how long such a calculation would take??


O(n^2) time.

In practice you'd have problems with precision since after enough samples the contribution from the next sample would be less then the smallest number your CPU could do.
Title: What is "time resolution"?
Post by: Garf on 16 November, 2006, 07:17:24 PM
I would have thought it goes without saying that ad hominem attacks are way out of bounds in the Science/R&D forum, but unfortunately, it seems a reminder is required. Don't let it happen again.
Title: What is "time resolution"?
Post by: MoSPDude on 16 November, 2006, 07:30:09 PM
@Mike Giacomelli,  it was only a passing thought 
Title: What is "time resolution"?
Post by: ChiGung on 16 November, 2006, 07:44:45 PM
but in the heat of the argument in previous posts you were offering some confusing comments.

I understand that, but ive lost my cool over 'various attack' here and.... i dont speak fluent 'text' either  I do try though.

Quote
In terms of the posts original question at the top, " what is "time resolution"? ", I don't believe that sample rate conversion would affect the continuous time position of peaks and troughs of any arbitrary signal if, again, the signals you are up/down sampling are contained below the Nyquist frequency of the lower sample rate, the interpolation was theoretically ideal and subject to suitable filtering bringing in no mag/phase changes.

But that is a rare condition.
For instance, i like lowpassed music, i prefer listening to music sampled at 24k than 44k - because its more comfortable to my ears. But the time resolution of the 24k isnt the same as the 44k cd track. I dont care, i listen to what sounds nice. i dont need to tell myself the 'time resolution' is a magic quality beyond the samplerate - to enjoy the results.

Potential reductions in frequencyband / timeresolution
(resulting from samplerate.)
Natural Source
> Original recording/mastering formats
> CD
> 32,24,22,8..khz wav

Each has its own limits on ...frequencyband / timeresolution.
Im feeling more comfortable with using those terms interchangeably now

Quote
As a side interest that I might play with, I wonder about upsampling a file by loading in all the samples and performing a sinc interpolation per sample across "all time" would yield an improved sample rate converter for pre-recorded files?? - I wonder how long such a calculation would take??

Sounds like Sebs area of finesse'

Quote
Its all good stuff, just hard to read with the heated debate going on.
Cheers I appreciate your comments, I hope it does cool down here.



No one is doubting that the peaks will move and/or vanish with most signals.

I personally am doubting you can perform the experiment on arbitrary samples, because you won't be able to track the peaks.

Thats not a problem. I will simply loop through all the nodes in the lowersampled record and try to match each against any node in the highersampled record. If a matching node is not found within small distance of a partner in the other record, it will be discounted. It represents a flattering measure of temporal consistency between samples.

Why would I do this? Well it started with this quote in an otherwise great article on Vinyl Myths (http://wiki.hydrogenaudio.org/index.php?title=Myths_%28Vinyl%29) in the HA wiki:
"PCM can encode time delays to any arbitrarily small length. Time delays of 1us or less - a tiny fraction of the sample rate - are easily achievable. The theoretical minimum delay is 1ns or less."

or

PCM can encode "time delays" to any arbitrarily small length. "Time delays" of 1us or less - a tiny fraction of the sample rate - are easily achievable. However, actual locatable conditions such as zero crossings, gradients or levels are only located semi-reliably within 1/2 sample at a given sample rate...
Title: What is "time resolution"?
Post by: cabbagerat on 17 November, 2006, 01:19:38 AM
As a side interest that I might play with, I wonder about upsampling a file by loading in all the samples and performing a sinc interpolation per sample across "all time" would yield an improved sample rate converter for pre-recorded files?? - I wonder how long such a calculation would take??
As Mike says, it's O(n^2) - every sample must be looped over for every other sample. Many resamplers (such as libsamplerate, SoX and others) use the windowed sinc interpolation algorithm described by Julius O Smith - you can see the details on his resampling page (http://www-ccrma.stanford.edu/~jos/resample/). Performing the entire bandlimited interpolation calculation (http://www-ccrma.stanford.edu/~jos/resample/Theory_Ideal_Bandlimited_Interpolation.html) would be extremely prohibitive for any decent number of samples (for example 1 minute of 44100 sound would require 1.4x10^13 multiplies). The solution they choose is to window the interpolation function to a certain number of zeros.

The length of the trunctation and the window used effects the parameters of the resampler - width of it's passband and SNR. For sound applications Smith chose the Kaiser window with a relatively high Beta. I am using a similar calculation for other means (doppler simulation) and am busy evaluating the Nutall window to give the trade between passband and SNR I want.
Title: What is "time resolution"?
Post by: 2Bdecided on 17 November, 2006, 06:03:50 AM
Let me consider this most practical of issues first...

No one is doubting that the peaks will move and/or vanish with most signals.

I personally am doubting you can perform the experiment on arbitrary samples, because you won't be able to track the peaks.

Thats not a problem. I will simply loop through all the nodes in the lowersampled record and try to match each against any node in the highersampled record. If a matching node is not found within small distance of a partner in the other record, it will be discounted. It represents a flattering measure of temporal consistency between samples.


It may be flattering, but it could simply be so wrong as to hide any "useful" (I use that word in a very lose sense!) data. A given peak could vanish as soon as you apply your first (highest) low pass. However, for a random signal, the chance of finding the wrong peak within a given "small distance" will be roughly proportional to the low pass filter cut-off frequency, since the higher the cut-off, the more peaks will remain. (The lower the cut off, the fewer peaks will remain). This you can probably prove - but it tells you nothing about that specific original peak.



Hi MoSP' Ill try not to confuse things with my ..deviances..
but just add a few carefull comments
If we do these tests digitally, and the real-world source is band limited below the Nyquist frequency, then the Nyquist–Shannon sampling theorem will hold and values representing that signal will theoretically reproduce an exact perfect signal,

Its not clear which 'Nyquist frequency' you mean there, that of the recording, or that of the target samplerate. To be clear -i acknowledge that when they are the same, we have very great, potentialy lossless accuracy of reproduction of each (to each other).


That's good. It means you accept that the signal from any microphone (which is inherently band-limited by simple mechanics), or any analogue recording (which is inherently band-limited by mechanics, electronics, particle properties etc depending on the type of recording) can be (potentially) losslessly reproduced using PCM sampling, given a sufficiently high sampling rate.

That's handy, isn't it? Especially when you look at the bandwidths of some of these things, and realise that 192kHz sampling is enough, even for your definition of "enough"!

Cheers,
David.
Title: What is "time resolution"?
Post by: 2Bdecided on 17 November, 2006, 07:25:20 AM
To go back to the beginning...

This is what I think: The peaks move, not because you've done anything to the "time resolution", but because you've removed spectral components that contributed to the exact peak position. This is not the same as time resolution.


This is what you think: What really changes is time resolution. Maybe the time resolution really is about 1/2 a sample. The "moving peaks" show this.


Let me show you why this "works", but is silly. (This is long - casual readers might like to skip to the conclusion!)

Arbitrary content could have peaks anywhere.

Here is statement 1 (feel free to disprove it): "For a peak to move (but not vanish) due to low pass filtering, that peak must have been "built" from at least two spectral components, at least one below the filter cut off, and at least one above."

The statement holds for any number of spectral components, even infinite, so don't complain we're not talking about real signals here! What it really says is (a) that if low pass filtering a signal changes the signal, there was something above the low pass filter, which was removed (obvious), and (b) that if we really are correctly considering the same peak, then that peak must have been formed by spectral components which overlapped in time. (A bad explanation, but I think you know what I mean.)


You can separate the signals above and below the cut off frequency using complementary low pass and high pass filters. Adding these two resulting signals together would give the original signal. If you hate the idea of complementary filters, just have a low pass filter, then subtract the result from the original to give the high pass version.

Let us consider the high pass output (or the part we're throwing away by low pass filtering, if you like). The lowest possible frequency component in the high pass section would have peaks spaced by just less than 1 over the filter cut off frequency. Higher frequencies would have more closely spaced peaks, but there can be no lower frequencies with more widely spaced peaks. Adding this signal back to the low pass version can, at most, move an existing peak by this inter-peak distance. It can't move it any further if the signal meets statement 1, since any further and you are looking at a new peak, not the original one.


Magic! Thus we "prove" (though it's more of a hand waving explanation!) your +/- 1/2 sample "time resolution", but we see it's really about frequency resolution. To move a peak, what you remove in the frequency domain must contrive to move the peak in the time domain. If it does not (e.g. it's co-timed, or there's nothing above the frequency cut-off anyway), the peak won't move.


So you come down to proving something rather trivial: "if I do something that I know will change the shape of the waveform, then the shape of the waveform will change".

Genius!

It tells you nothing about anything. Why? Because the peak could start anywhere, and could end up anywhere. You are only proving that it could move by up to that amount - you are not proving that it is "quantised" by that amount (which would prove a limit in time resolution), since a peak whose location was entirely due to a frequency component below the filter cut-off could have its position at the same point as the "original" signal.


Conclusion...

Let me give an example of something that is a limit in resolution: quantisation. Quantisation limits the amplitude resolution. The amplitude at that instant can be one quantisation step, or the next, but it cannot be any value in between. (If you dither before quantisation, this error becomes random-like noise, but it is still an error, and still a limit in instantaneous amplitude resolution).

Similarly, low pass filtering introduces a limit in bandwidth. For an ideal brick wall filter, we can have any frequency up to the cut off frequency, but none of the ones above.

So with the +/- 1/2 sample example from CG, are we looking at a limit in time resolution?

Consider this: Signal A has a peak at position A, and frequency components above some arbitrary frequency F. Removing those frequency components moves the peak to position A2, which is slightly different from A.
(Look, says CG, a limit in time resolution. Hold on! says DR...)

However a different signal, signal B, which has no frequency component above frequency F, can have a peak at exactly position A, and that peak will not be moved by removing frequency components above frequency F.

Thus we show that suggesting "the move from A to A2 demonstrates some limit of time resolution due to low pass filtering" is factually incorrect. A low pass filtered signal can have a peak at A, A2, or anywhere else.

All you have shown is that frequency components in signal A contributed to the position of peak A, and these have been removed, thus moving the peak. However, there is no limit to where peaks can occur. It is not like the quantisation amplitude resolution limit at all! It is not a time resolution limit, just a predictable effect of low pass filtering a signal.



I don't think I can put it any clearer than that!

(I shall not be giving up my day job  )

Cheers,
David.
Title: What is "time resolution"?
Post by: bhoar on 17 November, 2006, 10:29:19 AM
I'm treading into an area I know nothing about, but I'll make a short comment anyway:

The location of a single mathematical sample peak should not be assumed to be the defined location of
the attack of particular instrument.  Just because filtering leads to a peak slightly
before or after the original peak does not mean the location of the attack has changed
temporally.

I would think that what we audibly hear as an attack would be more precisely defined as a zone, or
perhaps the middle of a series of PCM peaks and troughs of a certain nature.  I suspect using these
sorts of definitions, you would find that there is no temporal movement of the instrument's attack
due to quality low-pass filtering above the typical human hearing range before digitization or
in the digital domain.

Summary: PCM peak != attack

Meta-Summary: I might be completely wrong.  Or I might be stating the completely obvious.

-brendan
Title: What is "time resolution"?
Post by: ChiGung on 17 November, 2006, 01:02:05 PM
To go back to the beginning...

This is what I think: The peaks move, not because you've done anything to the "time resolution", but because you've removed spectral components that contributed to the exact peak position. This is not the same as time resolution.

That is like saying: "the tin can crumples, not because you are doing anything to its form, but because you are destroying its structural integrety"

The difficulties displayed here by those "in the know" in admitting anything is being done to "time resolution" -as sample rate is reduced (!) - is an odd phenomenon.

Explicity - sample rate is the rate of provided instances through time. 

Quote
Maybe the time resolution really is about 1/2 a sample. The "moving peaks" show this.
Let me show you why this "works", but is silly. (This is long - casual readers might like to skip to the conclusion!)

hmmm, "works" but is silly.... getting a bit obscure, it feels like you are erecting a wall of denial....

Quote
Arbitrary content could have peaks anywhere.
Here is statement 1 (feel free to disprove it): "For a peak to move (but not vanish) due to low pass filtering, that peak must have been "built" from at least two spectral components, at least one below the filter cut off, and at least one above."
This is not difficult for me to visual, Ive made such points all throughout this thread.... ill cut to the chase.
Quote
Magic! Thus we "prove" (though it's more of a hand waving explanation!) your +/- 1/2 sample "time resolution", but we see it's really about frequency resolution. To move a peak, what you remove in the frequency domain must contrive to move the peak in the time domain. If it does not (e.g. it's co-timed, or there's nothing above the frequency cut-off anyway), the peak won't move.

What I like about this is the honesty of your description, and it makes the logic quite clear.
But your present feeling that you can simply declare what 'results' are 'about' is wrong.
Saying 'in a way' 'it is like' ..time resolution, but really "its about" frequency resolution -its insubstantial, a whimsical fig leaf. How you choose to approach a circumstance conceptualy is your choice, but if you want to invalidate an approach such as dealing with the "time domain", you cant simply anounce you find it 'silly' or not the same as your approach which seems now to be exclusively the "frequency domain" These things are sides of a coin.

Quote
So you come down to proving something rather trivial: "if I do something that I know will change the shape of the waveform, then the shape of the waveform will change".

If i reduce the number of provided samples throughout time, the potential accuracy of placement of detail throughout time will decrease, the potential resolution of detail through time will decrease > time resolution is decreased.

I have to snip, because although involved, the objections you are providing here cant be argued against because they are ruleless.

Quote
All you have shown is that frequency components in signal A contributed to the position of peak A, and these have been removed, thus moving the peak. However, there is no limit to where peaks can occur. It is not like the quantisation amplitude resolution limit at all! It is not a time resolution limit, just a predictable effect of low pass filtering a signal.

If there is no limit to where the peaks can occur, how come they cant be arranged to occur in the correct place between records of differing sample rates? Why must they be susceptable to unknown distortions during downsamples with your "no limitations" arguement? Because their precise subsample positions are limited - by every other sample in the record which they are a part of. Thats why you cant normaly use the "unlimited" resolution which you can infer - without distorting all other samples to create the subsample details. (done to provide some limited demostrations in this thread, but not possible in practice where all samples must be treated equally)

Quote
I don't think I can put it any clearer than that!
(I shall not be giving up my day job  )

Theres no need to bring professional pride into this. These matters are similarly misreported by many professionals. Anyway we are all professionals.

I should be able to post the data tonight on the actual accuracy of reproduction possible of event timings between well utilised sample rates.

regards'
cg
Title: What is "time resolution"?
Post by: Woodinville on 17 November, 2006, 01:59:55 PM
Thats why you cant normaly use the "unlimited" resolution which you can infer - without distorting all other samples to create the subsample details. (done to provide some limited demostrations in this thread, but not possible in practice where all samples must be treated equally)



You can't have unlimited resolution without unlimited bandwidth.

This does not mean that peaks move.

As I pointed out in the discussion of the sum of two gaussians, peaks will move if and only if you remove frequency components that contribute to the envelope in a way that moves it.

Again, look up "Hilbert Envelope".  You're doing nobody any good by failing to read up on the field you're talking about before you work.

As to your experiments, they prove nothing until you specificially produce the ***exact*** equations, and explain your reasoning.
Title: What is "time resolution"?
Post by: ChiGung on 18 November, 2006, 01:04:37 PM
You can't have unlimited resolution without unlimited bandwidth.
Of course, that has been my point.
Quote
This does not mean that peaks move.
Your criticisms are not consistent. When I quoted you as implying peaks would not move due to lowpassing, you said I misquoted you while crying 'abuse'. So you have me warned while berating my lack of contemporary study and making inconsistent demands to perform various pet excercises.
Im not your student.
Quote
You're doing nobody any good by failing to read up on the field you're talking about before you work.
Untrue. I limit my research to protect my originality. Education is to Innovation what Masterbation is to Procreation  I have learned adequate tools at home, school and university and beyond to suit my own designs. Ive never been forced to research previous solutions to computational problems -except for a while when I began learning to program  -quite intensively, around the age of 9.

Quote
As to your experiments, they prove nothing until you specificially produce the ***exact*** equations, and explain your reasoning.
You demand exact equations and provide only irrelevant ones. To suggest I have not explained my reasoning in this thread is absurd.

@all,
I have only been trying to defend sensible, intuitive, practical use of terminology here by argueing against the idea forwarded - that "time resolution" of pcm is practicaly finer than the samplerate.
As explained previously, i understand that processes can maintain timing details in source which is suitably limited to particular samplerates bandwidth. But processes cannont recover timing details once bandwidth is limited. This means downsampling potentialy and normaly does damage 'time resolution'.

Despite a heavy bias to not examine the practical limitations on time resolution of samplerate, some expert contributers in this thread, have acknowledged that measureable timing details will be routinely distorted by downsampling at normal audio rates. I am not concerned with the audibility of such distortion, only its existence and its limits.

It has been much work trying to have it fairly examined in such a heated and onesided discussion. I do suspect others have better experience to estimate the situation than myself, but seem ideologicaly unwilling to do so.

I have tried to rise to the groups challenge and do some work to illustrate the situation,
heres a scrappy program, not quite finished, but I hope some might appreciate my input so far...

The central chunks of code are:

Code: [Select]
  int nodi=1;                            //count of node found 
  int pregrad,pstgrad;                  //approximate derivatives

  for( int ndfi=0; ndfi<samsGet; ndfi++)              //ndfi = time index( samples loop )
  { smx2=smx1; smx1=smx0; smx0=retSam[ndfi];
   pregrad=smx1-smx2;
   pstgrad=smx0-smx1;

   if((pregrad*pstgrad<-1)&&(Math.abs(pregrad-pstgrad)>100))
   {  nodes[nodi++]=(ndfi<<8)+( (512*pstgrad+1) / ( ((pstgrad-pregrad)*2)+1) ); }
     //record simple linear solution of 1st derivative=0
     //expression: (( (512*pstgrad+1) / (((pstgrad-pregrad)*2)+1) )) produces ~ 0-255
     //node units are samplesize/256 (1/256th of sample interval)
   }//end for(ndfi)


This finds 'nodes' in pcm, approximately the presence and position of major peaks and troughs

and
Code: [Select]
      for(int aninx=1; aninx<=endnodea; aninx++)    //ninx is node index
     { int findtime=anodes[aninx];                //next node to find (units of sample*256)
       findfit=maxoff;                        //Maximum distance for fit         
       paired=false;
      
       for(int findnode=lastfind; (findnode<endnodeb)&&(bnodes[findnode]<(findtime+maxoff)); findnode++)
       { if(Math.abs(findfit)>Math.abs(findtime-bnodes[findnode]))
         { findfit=findtime-bnodes[findnode];
           lastfind=findnode; paired=true;
           }
         }
       if(paired){ discreps[nndi++]=findfit; paired=false; }
       else{ missnode++; }

       }//end looping through 1 buffer
This finds a nodes nearest neighbour in parallel track and records its descrepancy

whole program (warning spaghetti/frankenstien)
Code: [Select]
import java.io.*;

class nodecouple
{ //int[] series = new int[80000];

  public static void main(String[] args) /* main */
  { nodecouple nodecoup = new nodecouple(args);    //creates instance of self for javas nonstatic context hooha
   System.exit(1); }                    //graceless exit better than hang

  public nodecouple(String[] args)
  { int chnksize=1024;  //what length
   int chnkread=1000;  //how many
   int srcsamx=4;      //?
   int maxoff=128;      //maximum distance between pairings
   int mgfy=1;          //magnify record

   System.out.println("Reading in"+args[0]+"\n");
   getNodesWave tookWav1 = new getNodesWave(args[0], chnksize/mgfy);
   //int[] test0=tookWav1.getnodes(0);
   System.out.println("And Reading "+args[1]+"\n");
   getNodesWave tookWav2 = new getNodesWave(args[1], chnksize);
  
   if(tookWav1.totlFrames<chnksize*chnkread)
   { chnkread=tookWav1.totlFrames/chnksize; };

   long ThScnds=((chnksize*chnkread)*1000/tookWav1.Samprate);
  
   System.out.print("Only reading first "+ThScnds/1000+"."+(ThScnds%1000)/100+""+(ThScnds%100)/10+""+(ThScnds%10));
   System.out.print(" seconds");
   if(tookWav1.channels>1)
   { System.out.print(" (of 1 channel)"); }
   System.out.println("(Change chnkread for more)");

   int[] discreps= new int[(chnksize*chnkread)]; //(impossible maximum size for discreps)
   int nndi=0;                                  //count of nodes found
   int missnode=0;
   int endnodea=0,endnodeb=0;
   int endnodeSuma=0,endnodeSumb=0;
  
   System.out.println("\nLocating Nodes...");

   for(int chnk=0; chnk<chnkread; chnk++)  //refresh chunks to read
   { int[] anodes=tookWav1.getnodes(0);  //nodes in a's chunk
     int[] bnodes=tookWav2.getnodes(0);  //nodes in b's chunk
    
     endnodea=anodes[0];    //length of array is stored in first position (lowsampled one)
     endnodeb=bnodes[0];  //length of array is stored in first position
    
     endnodeSuma+=endnodea;
     endnodeSumb+=endnodeb;
    
     /*debout("a:"+endnodea, 9); debout("b:"+endnodeb, 6); 
     if(chnk%6==5){ debout("\n", 0); } */
    
     int timedif;
     int lastfind=1;          //to be remind of position of previous couple
     boolean paired = false;
     int findfit;

     for(int aninx=1; aninx<=endnodea; aninx++)    //ninx is node index
     { int findtime=anodes[aninx]*mgfy;            //next node to find (units of sample*256)
       findfit=maxoff;                            //Maximum distance for fit         
      
       paired=false;
      
       //note: sign of nodetime could be bodged to reflect peak or valley.
       for(int findnode=lastfind; (findnode<endnodeb)&&(Math.abs(bnodes[findnode])<(findtime+maxoff)); findnode++)
       { if(Math.abs(findfit)>Math.abs(findtime-Math.abs(bnodes[findnode])))
         { findfit=findtime-bnodes[findnode];
           if(findfit==-1){ debout("!",2); }
           lastfind=findnode; paired=true;
           }
         }
       if(paired){ discreps[nndi++]=findfit; paired=false; }
       else{ missnode++; }

       }//end looping through 1 buffer
    
     }//end looping through all buffers
  
   System.out.println("\nTotal nodes in: "+args[0]+":"+endnodeSuma);
   System.out.println("Total nodes in: "+args[1]+":"+endnodeSumb);
   System.out.println("\nMissednodes="+missnode+", discreps="+nndi+", Searchednodes="+endnodeSuma+"\n");

   /*System.out.println("\nTime differences List..."); //dump all discreps       
   for(int tal=0; tal<nndi; tal++)
   { debout(""+discreps[tal],5); if(tal%16==15){ System.out.println(); }
     }*/

   int maxtallie=1;
   int histbars=25;
   int histrange=maxoff*2;
   int[] tallie = new int[histbars];
   int budge=histrange/((histbars-1)*2);

   for(int npair=0; npair<nndi; npair++) //do tallie count
   { int valo=discreps[npair];
    
     if(valo>-histrange/2)
     { for(int talo=1; talo<=histbars; talo++)
       { if (valo<(histrange*talo/histbars-histrange/2))
         { tallie[talo-1]++; talo=histbars+1; }
         }
       }
     }     
   for(int x=0; x<histbars; x++)
   { if(tallie[x]>maxtallie){ maxtallie=tallie[x]; } }
      
   debout("\n",0);
  
   int histhigh=16;
   for( int g=histhigh; g>0; g--)
   { debout(""+(maxtallie*g/histhigh)+":  ",9);
     for(int i=0; i<histbars; i++)
     { if(tallie[i]<(maxtallie*g/histhigh))
       { debout(" ",3);}
       else
       { debout("**",3);}
       }//i
    
     debout("\n",0);
     }//g
    
    
   for(int x=0; x<histbars-3; x++)
   { System.out.print("----"); } 
   System.out.print("\n Sums:  ");
   for(int x=0; x<histbars; x+=2)
   { deboutm(""+tallie[x], 6); } 
   System.out.print("\n Devs: <");
   for(int x=-histbars/2; x<(histbars+1)/2; x+=2) //printing hist headers
   { deboutm(""+Math.abs((int)( (x+0.5)*histrange)/histbars), 6); }
  
   System.out.print(">");
   System.out.println("\n\nDistribution chart, range="+histrange+"n (256n=1 sample)\n");
  }
 private void debout(String deb, int size)  //writing to size, for debug output
 { size=size-deb.length();
  for(int o=0; o<size; o++) { System.out.print(" ");}
  System.out.print(deb);
  }//end debout method

 private void deboutm(String deb, int size)  //writing to size, for debug output
 { size=size-deb.length();
   int pesize=size/2;
   int posize=size-pesize;

  for(int o=0; o<pesize; o++) { System.out.print(" ");}
  System.out.print(deb);
  for(int o=0; o<posize; o++) { System.out.print(" ");}
  }//end debout method

}//end nodecouple

class getNodesWave {
/**
 * Wavfile gurgitor
 *
 * Casual version - it only understands simple wav file formats
 *
 * This utility is written in private as part of a study
 * portfolio in developement.
 *
 * neutron.soupmix@ntlworld.com */

/* Public discernables are channels, sampling rate, timeframes, (samples/channels).... */

private int hdChnkSz,fmt,dmt,wavFrmtTag; //metaMetas
public  int channels, rawPcmByts, totlFrames, bitsPerSample, Samprate; //stream details

byte[] loaded;
byte[] bpass= new byte[0]; //possibly bugged tweak! -appears to work
private int samsGet, framPerGet, FrmsBfd, rdIn, bytsRd, bytLft;

private int[] samsGvn;
private short[] retSam;
private short[][] samRng;
private byte samStep;
private int ndfi; //node find index
private int smx0,smx1,smx2;

public FileInputStream wavIn;
public File wavFile;

public static void main(String[] args)/* main */
{ System.out.println("getNodesWave has no main");
  System.exit(1); }                //graceless exit better than hang

public getNodesWave(String wvName, int samsPerGet){ //bytbffa is sampls per modwork area

System.out.println("  Opening "+wvName);
try
{ wavFile = new File(wvName);
  FileInputStream wavIn = new FileInputStream(wavFile);

  byte[] hdrz = new byte[44];
  int hdrzlen = wavIn.read(hdrz);
  byte hdrzi  = 12; //wavIn.skip(12);
 
  fmt                          // header should be fmt, fmt 4 bytes
  = ((hdrz[hdrzi++]&0x00ff)<<24) | ((hdrz[hdrzi++]&0x00ff)<<16)
  | ((hdrz[hdrzi++]&0x00ff)<<8) | ( (hdrz[hdrzi++]&0x00ff));

  if (fmt!=0x666D7420)
  { System.out.println("  fmt sig not encountered - Failure Likely...");
   System.out.println("  fmtsig val="+fmt+"\n");}

  hdChnkSz                    //size in bytes of a header chunk
  = ((hdrz[hdrzi++]&0x00ff) | ((hdrz[hdrzi++]&0x00ff)<<8)
  | ((hdrz[hdrzi++]&0x00ff)<<16) | ((hdrz[hdrzi++]&0x00ff)<<24));
  if (hdChnkSz!=16)
  { System.out.println("  Complex wav header - Failure Possible..."); }

  wavFrmtTag = (hdrz[hdrzi++]&0x00ff)|((hdrz[hdrzi++]&0x00ff)<<8 );

  channels  = (hdrz[hdrzi++]&0x00ff)|((hdrz[hdrzi++]&0x00ff)<<8 ); //channels

  Samprate
  = ((hdrz[hdrzi++]&0x00ff) | ((hdrz[hdrzi++]&0x00ff)<<8)          //samprate
  | ((hdrz[hdrzi++]&0x00ff)<<16) | ((hdrz[hdrzi++]&0x00ff)<<24));
  System.out.println("  SampleRate:"+Samprate);
 
  hdrzi+=6;                          //skip byterate and blockalign
  bitsPerSample = (hdrz[hdrzi++]&0x00ff)|((hdrz[hdrzi++]&0x00ff)<<8 );

  //data chunk
  dmt                              // header should be dmt, 4 bytes
  = ((hdrz[hdrzi++]&0x00ff)<<24) | ((hdrz[hdrzi++]&0x00ff)<<16)
  | ((hdrz[hdrzi++]&0x00ff)<<8) | ( (hdrz[hdrzi++]&0x00ff));

  if (dmt!=0x64617461)
  { System.out.println("  No data signature found in wav - Abort! Abort! ");
   System.out.println("  dmtsig val="+dmt+"\n");}

  rawPcmByts                                        //size in bytes of pcm data
  = ((hdrz[hdrzi++]&0x00ff) | ((hdrz[hdrzi++]&0x00ff)<<8)
  | ((hdrz[hdrzi++]&0x00ff)<<16) | ((hdrz[hdrzi++]&0x00ff)<<24));

  //hdrzreading finished
  //hopefuly wav chunk headers overwith

  totlFrames=rawPcmByts/(2*channels);

  if (channels==0){ System.out.println("  No Channels Arrrgh! Abort! Abort!"); channels=1; }
  if (channels==1){ System.out.println("  Mono input"); }
  if (channels==2){ System.out.println("  Stereo input"); }
  if (channels>=3){ System.out.println("  "+channels+" channels (weird, trying as mono)"  ); channels=1; }

  long ThScnds=(rawPcmByts)/(2*Samprate*channels/1000);
  System.out.println("  Samples "+(rawPcmByts)/(2*channels));
  System.out.println("  Trackime at "+Samprate+"Hz :"+ThScnds/1000+"."+(ThScnds%1000)/100+""+(ThScnds%100)/10+""+(ThScnds%10)+"\n");
  wavIn.close();
 
  samStep=0;
  retSam=new short[samsPerGet];
  samRng=new short[channels][4096];
  samsGvn=new int[channels];
  samsGet=samsPerGet;
  FrmsBfd=0;
  bytsRd=0;
  smx0=0;smx1=0;smx2=0;
  rdIn=6144*channels; //reading in 6k a time per channel,
                       //6144 samples fitting into 4096wide ringbuffs
                       //1024 sample was safe get for two channel access

 
  }//end io try

catch(FileNotFoundException fnfe)
{ System.out.println("File Not Found, " + wvName);
  return; }// end catch FileNotFoundException

catch(IOException ioe)
{ System.out.println("IO Error: " + ioe);
  return; }// end catch IOException*/

finally
{ } // end LoadArray

return;
}//end constructor (open wav, get header details)

private void debout(String deb, int size)  //writing to size, for debug output
{ size=size-deb.length();
  for(int o=0; o<size; o++) { System.out.print(" ");}
  System.out.print(deb);
  }//end debout method
  
private void debout(String deb)  //writing to size, for debug output
{ System.out.println(deb);
  }//end debout method

public void setStep(byte set)
{ samStep = set; return; }

public int[] getnodes( int chnnel )
{ if( (samsGvn[chnnel]+samsGet)>=(totlFrames) )
  { samsGet=totlFrames-samsGvn[chnnel];      //check if last get
   if(samsGet==0){ System.out.println("wavin buffer empty"); }
   retSam = new short[samsGet]; }

  if(FrmsBfd<(samsGvn[chnnel]+samsGet)) { movebf(); } //check if ringbuff needs moved

  for(int samsOut=0; samsOut<samsGet; samsOut++)
  { retSam[samsOut]=samRng[chnnel][(samsGvn[chnnel]++)%4096]; }

  //** review channel returned.
                                         //retSam is series of pcm levels
  int[] nodes= new int[2008];            //fairly safe sized node list
  int nodi=1;                            //count of node found
  int pregrad,pstgrad;                  //approximate derivatives

  for( int ndfi=0; ndfi<samsGet; ndfi++)              //ndfi = time index( samples loop )
  { smx2=smx1; smx1=smx0; smx0=retSam[ndfi];
   pregrad=smx1-smx2;
   pstgrad=smx0-smx1;

   if((pregrad*pstgrad<-1)&&(Math.abs(pregrad-pstgrad)>100))
   {  nodes[nodi++]=(ndfi<<8)+( (512*pstgrad+1) / ( ((pstgrad-pregrad)*2)+1) ); }
     //record simple linear solution of 1st derivative=0
     //expression: (( (512*pstgrad+1) / (((pstgrad-pregrad)*2)+1) )) produces ~ 0-255
     //node units are samplesize/256 (1/256th of sample interval)

//What was producing the central spike in
//an approxomated but balanced (equally distributed error) measure of a peaks intensity/accuteness,
//is a simple discernment of the second derivative (change of change) =
//the method used to select peaks strength, peaks in the middle had to be less powerful to
//be selected than peaks at the sides, (of the considered sample length)
//this then allowed nodes to be matched more often coincidentaly close, tahn not)
//the new expression used has no such bias

   }//end for(ndfi)


  nodes[0]=nodi-1; //first in nodelist stores length of nodelist

  return nodes;  //return list of nodes to analysis director
  }// end getsams method

public void movebf() //fetch next load of samples
{
  try
  { FileInputStream wavIn = new FileInputStream(wavFile);
   wavIn.skip(44+bytsRd);
   if((bytsRd+rdIn)>rawPcmByts){ rdIn=rawPcmByts-bytsRd; }

   if(bpass.length!=rdIn){ bpass= new byte[rdIn]; }
   bytsRd+= wavIn.read(bpass);
   loaded=bpass;
   wavIn.close();
   }
   catch(IOException ioe){ System.out.println("IO Error: " + ioe); return; }// end catch IOException
   finally{ } // end LoadArray
 
  if(channels==1)
  { for( int loadi=0; loadi<rdIn ; FrmsBfd++)
   { samRng[0][FrmsBfd%4096] = (short)( (loaded[loadi++]&0x00ff)|((loaded[loadi++]<<8)&0xff00) );
     loadi+=samStep*2; } }
  else
  { for( int loadi=0; loadi<rdIn ; )
   { samRng[0][FrmsBfd%4096] = (short)( (loaded[loadi++]&0x00ff)|((loaded[loadi++]<<8)&0xff00) );
     samRng[1][(FrmsBfd++)%4096] = (short)( (loaded[loadi++]&0x00ff)|((loaded[loadi++]<<8)&0xff00) );
     loadi+=samStep*4; } }
 
  return;
  }//end eatWav

}//end getNodesWave

Here is a current output:
Code: [Select]
---------- Run java ----------
Reading innofun22176.wav
  SampleRate:176400
  Stereo input
  Samples 1850146
  Trackime at 176400Hz :10.497

And Reading nofun176400.wav
  SampleRate:176400
  Stereo input
  Samples 1850134
  Trackime at 176400Hz :10.497

Only reading first 1.160 seconds (of 1 channel) (Change chnkread for more)

Locating Nodes...

Total nodes in: nofun22176.wav:1132
Total nodes in: nofun176400.wav:1444

Missednodes=127, discreps=1005, Searchednodes=1132

   253                                                                    ***          
   237                                                                    ***          
   221                                                                    ***          
   205                                                                    ***          
   189                                                                    ***          
   173                                                                    ***          
   158                                                                    ***          
   142                                                                    ***          
   126                                                                    ***          
   110                                                               ***  ***          
    94                  ***  ***                                     ***  ***          
    79                  ***  ***                                     ***  ***  ***    
    63             ***  ***  ***  ***                                ***  ***  ***    
    47             ***  ***  ***  ***  ***                           ***  ***  ***    
    31             ***  ***  ***  ***  ***                      ***  ***  ***  ***    
    15        ***  ***  ***  ***  ***  ***  ***  ***            ***  ***  ***  ***  ***
 Sums:     3   28   76  102  103   67   50   22   22    5    9   36  125  253   83   21
 Devs:  1920 1664 1408 1152  896  640  384  128  128  384  640  896 1152 1408 1664 1920

Distribution chart, range=4096n (256n=1 sample)

Output completed (0 sec consumed).

-This is a curious output that cant be trusted at this stage of the programs developement.
It compares a clip of cd audio upsampled x4, with one downsampled x2 and then upsampled x8
by ssrc_hp.exe
A 176400 (44100*4) Hz sample length in the chart is 256,
a 44100 Hz sample length in the chart is 1024
( these relate to the distribution bands )
more investigation/developement may follow..

Its obviously troublesome to start interprating unsecurely tested/debuged programs, but if some recognise the effort ive put into it (the code ended up taking some valuable hours to get to this stage).
- Maybe they could give me the benefit of their prediction of the best distribution possible of detectable conditions in a waveforms pairing between different samplerates/bandwidths.

regards'
cg

edit: inserted smaller chart
Title: What is "time resolution"?
Post by: ExUser on 18 November, 2006, 03:15:23 PM
Education is to Innovation what Masterbation(sic) is to Procreation


That is quite a ridiculous claim, especially in the context of computer science. Yes, you can probably come up with some silly sort algorithm that works, but in real life, experienced coders use the best sort algorithm for the expected data by researching the sort algorithms and selecting the best. These sort algorithms were not devised by some unschooled hack, these sort algorithms were designed by highly-educated and talented individuals, working in academic settings with other highly-educated and talented individuals.

Whether you believe it or not, education has the benefit of saving everyone time on meaningless missteps such as this thread. The concept of a "peak" holds little relevance to anything in electrical engineering; any form of frequency filtration changes all these peaks anyhow. Lowpass filter a Dirac pulse and instead of a single peak, you get a repeating set of peaks, with the highest peak potentially moving depending on the structure of the filter. A single peak, when lowpassed, can result in multiple peaks, all offset by some factor.

Your issue is trying to perceive frequency domain effects while visualizing the effects solely in the time domain. "Peaks" are time-domain phenomena that do not have any meaning in the frequency domain. All your down- and upsampling is affecting the frequency domain. Changes in the frequency domain imply changes in the time domain, but the way in which the two are related is less trivial to understand than you seem to think it is.

As you no doubt notice, your program does not simply show that changing spectral content shifts peaks, it shows that there is not a single peak that remains unaffected (if I am understanding the output correctly).

The time and frequency domains are mathematically identical, but are very different to conceptualize. If you wish to discover the ways in which a frequency domain transform affects audio, you must look at it from a frequency domain perspective if you wish to understand well. What you are doing is looking at a frequency domain transformation from a time domain perspective, and are getting complex results that you don't really understand. Because you don't understand them, you assume there's something weird happening there. There isn't. You're just not looking at it correctly.
Title: What is "time resolution"?
Post by: ChiGung on 18 November, 2006, 03:55:21 PM
As you no doubt notice, your program does not simply show that changing spectral content shifts peaks, it shows that there is not a single peak that remains unaffected (if I am understanding the output correctly).

If you had the capability to run the program, you could check such a conclusion on other tracks -trying different methods of lowpassing/downsampling.
And you might have noticed that the tracks compared there where of slighlty different lengths due to ssrc's particulars.

Quote
The time and frequency domains are mathematically identical......What you are doing is looking at a frequency domain transformation from a time domain perspective, and are getting complex results that you don't really understand. Because you don't understand them, you assume there's something weird happening there. There isn't. You're just not looking at it correctly.

That is your misunderstanding - that "looking at a frequency domain transformation from a time domain perspective" is problematic. As both domains are equaly valid perspectives on the same data, they can be considered in parallel. To consider time resolution without reference to the time domain is folly, if not impossible.

In the frequency domain a downsample manifests as a reduction in bandwidth. In the time domain a downsample manifests as a reduction in resolution of level through time.
These statements are simply not sensibly refutable.
Title: What is "time resolution"?
Post by: Woodinville on 18 November, 2006, 04:20:06 PM
You can't have unlimited resolution without unlimited bandwidth.
Of course, that has been my point.


And, nobody has argued otherwise.
Quote
Quote
This does not mean that peaks move.
Your criticisms are not consistent. When I quoted you as implying peaks would not move due to lowpassing, you said I misquoted you while crying 'abuse'. So you have me warned while berating my lack of contemporary study and making inconsistent demands to perform various pet excercises.
Im not your student.


My statements are absolutely consistant.

I think that it is telling that you will not try a trivial, simple experment, one that requires much less code than you already appear to have posted, that will show you some of the errors implicit in your complaint.

In the frequency domain a downsample manifests as a reduction in bandwidth. In the time domain a downsample manifests as a reduction in resolution of level through time.
These statements are simply not sensibly refutable.



And, that does not mean that peaks must move. The question of a peak moving or not, using a linear-phase (constant delay) filter, is strictly a question of what frequency content is removed. No more, no less.

As phase and frequency are absolutely equal to a time delay, I think you'll need to readjust your thinking here quite a bit, and simply accept the reality.

I'll say it again.

Generate two gaussian pulses, one of amplitude .1 centered at 10kHz with bandwidth of 1 kHz (just for simplicity's sake. Center it at the third sample.  Add to that sequence a gaussian pulse of amplitude 10, bandwidth 1kHz, at 30kHz, centered at the 5th sample.

Do this at a sampling rate of 96kHz.

Downsample this to 48 and back up.  Use linear phase filters.

Wait. You don't even have to downsample. Just filter the 96kHz stream at 20kHz with a 192 tap FIR. Look at the results.

You didn't change the sampling rate. You DID move the peak. Why? Because you filtered out some frequency bands. That's all. No more, no less. Nothing special here.

Do the work.
Title: What is "time resolution"?
Post by: ChiGung on 18 November, 2006, 04:49:54 PM

You can't have unlimited resolution without unlimited bandwidth.
Of course, that has been my point.
And, nobody has argued otherwise.

Not quite, but 'abilities' to locate details at "arbitrarily small" times in pcm samples, keep being presented to me, to counter my claims that "pcm cannot reliably record the times of real events/conditions with subsample accuracy" nor can it maintain such accuracy with further downsampling/lowpassing.

Quote
This does not mean that peaks move.....
Quote
Your criticisms are not consistent....

My statements are absolutely consistant.

Quote
When I quoted you as implying peaks would not move due to lowpassing, you said I misquoted you

Well I dont know what your position is, maybe thats fault of your expression or my comprehension, or combination of both, it happens.

Quote
I think that it is telling that you will not try a trivial, simple experment, one that requires much less code than you already appear to have posted, that will show you some of the errors implicit in your complaint.

Maybe I shall some day, or you could just explain how it would turn out, as ive tried to do with my 'experiments'. But the thing is, I have already devised a valid grasp of comparing timeable details between samplerates/bandwidth, and im tired of your attempts to tutor me. Im sure you are an excellent tutor, surely better than I am an attentive student

Im very interested to hear about other & better methods of locating any sort of conditions in time in a waveform, and we might be able to implement them here to improve our real world study of pcms time resolution.

regards'
cg
Title: What is "time resolution"?
Post by: ChiGung on 18 November, 2006, 05:05:33 PM
Quote
And, that does not mean that peaks must move. The question of a peak moving or not, using a linear-phase (constant delay) filter, is strictly a question of what frequency content is removed.

I have also restated this relationship throughout this thread.
But it follows that if frequency content is removed, ( and this is normaly the case when transfering between common rates, such as 44kHz > 22kHz )
Then timings of waveform conditions - such as peaks, all throughout the waveform will be distorted.

This claim wasnt accepted, so I have started a programming project to not only prove it, but record approximately how much conditions can move when their bandwidth/samplerate is reduced.

Quote
I'll say it again. You didn't change the sampling rate. You DID move the peak. Why? Because you filtered out some frequency bands. That's all. No more, no less. Nothing special here.


Thanks for that description. You have shown that a waveform will distort in time and level when its bandwidth is reduced. This is the very same mechanism that distorts waveforms when their sampling rate is reduced.
Observing the situation as you did there, you should acknowledge the same occurs from 96>44 or 44>24. 

That was basicaly an experiment which proves the existence the effect which I wrote the program to measure.
Quote
Do the work.

I have been.
Title: What is "time resolution"?
Post by: ExUser on 18 November, 2006, 05:10:34 PM
That is your misunderstanding - that "looking at a frequency domain transformation from a time domain perspective" is problematic. As both domains are equaly(sic) valid perspectives on the same data, they can be considered in parallel. To consider time resolution without reference to the time domain is folly, if not impossible.


I don't disagree. There's a blend of phenomena going on here, and I don't blame you for getting lost and confused. Try follow this: You have data. You understand the meaning of this data in time-domain format. You apply a frequency-domain transform. You re-analyze the data and notice that the representation has changed quite markedly. From here, you are coming to the invalid conclusion that as the representation has changed, there's some loss of "time resolution", a term that is nigh meaningless.

The problem is simple: after the frequency transform, the form of the time-domain data is going to be completely different looking and cannot be sensibly compared to the original time-domain data. In order for the initial and final set of data to be comparable, you must use a representation that allows for comparison. In particular, "peaks" or "nodes" are completely meaningless comparisons. Like myself and many others mentioned before, when a Dirac pulse is lowpassed, you get a time offset and multiple new peaks. The initial and final forms of the data are completely different, and comparisons using "peaks"  are no longer valid. This is all due to the frequency-wise transformation. This transformation also can introduce a calculable, constant delay to the signal. These are known phenomena, but do not imply that "time resolution" as I understand it has changed at all.

Quote
In the time domain a downsample manifests as a reduction in resolution of level through time.


Could you restate this in other terms, please? I'm not understanding what you mean by this. I understand what downsampling does to time-domain data, but the way in which you state this is ambiguous. I suspect that by elaborating on this point, we may be able to get to the bottom of your misunderstanding.
Title: What is "time resolution"?
Post by: ChiGung on 18 November, 2006, 05:19:22 PM
That is your misunderstanding - that "looking at a frequency domain transformation from a time domain perspective" is problematic. As both domains are equaly(sic) valid perspectives on the same data, they can be considered in parallel. To consider time resolution without reference to the time domain is folly, if not impossible.


I don't disagree. There's a blend of phenomena going on here, and I don't blame you for getting lost and confused.

You are incredible...... 
I do have to laugh, even if it might get me in more trouble here.
I have to be honest. Im not gonna be anyones doormat.

Quote
Quote
In the time domain a downsample manifests as a reduction in resolution of level through time.

Could you restate this in other terms, please?

Afraid not, it should be easy to interprate if you are in a position to guide this thread.
Title: What is "time resolution"?
Post by: ExUser on 18 November, 2006, 05:30:24 PM
Ignoring the objective elements of my comments and focusing on the subjective ones will not advance your position here, I am afraid. If my position is so flawed and I am so clueless, then my statements should be absolutely child's play to refute.

Quote
Afraid not, it should be easy to interprate(sic) if you are in a position to guide this thread.


All I was asking for was something simple. Your phrasing was ambiguous and non-rigorous. I was hoping to gain insight into your position by having you restate it in other terms. But go ahead, disregard whatever you like. Your character is showing.
Title: What is "time resolution"?
Post by: ChiGung on 18 November, 2006, 05:39:01 PM
Ignoring the objective elements of my comments and focusing on the subjective ones will not advance your position here,

Im sorry but ill have to pass. I refer others to the rest of my multitudious replies replies amounting to thousands of words now, several illustrations and runnable statistics program. Whatever clarifications you would like to present to others you are of course free to do so without my consideration.

bye
Title: What is "time resolution"?
Post by: ExUser on 18 November, 2006, 05:44:01 PM
Quote
I refer others to the rest of my multitudious replies...
...all of which have been refuted quite thoroughly insofar as they present "new" ideas.

Quote
several illustrations...
...none of which prove anything new.

Quote
and runnable statistics program...
...which again proves nothing new.

So, at the end, you step away, having proven nothing other than that you like to talk about things that other people seem to think you don't really understand.
Title: What is "time resolution"?
Post by: ChiGung on 18 November, 2006, 06:34:44 PM
I think this thing might be working
Code: [Select]
Here is sample nofun examined at 96kHz (bandlimited interpolation) >with frequency response to 22kHz
Compared to itself just relowpassed at 22kHz (for experimental control) -
sox.exe was used for lowpassing (sinc windowed),
and lowpass was checked in a frequency spectrum to be good, but a slighlty gradual cutoff...

---------- Run java ----------
Reading innofun9622.wav
  Opening nofun9622.wav
  SampleRate:96000
  Stereo input
  Samples 1006876
  Trackime at 96000Hz :10.488

And Reading nofun96.wav
  Opening nofun96.wav
  SampleRate:96000
  Stereo input
  Samples 1006877
  Trackime at 96000Hz :10.488

Only reading first 2.133 seconds (of 1 channel)(Change chnkread for more)
Locating Nodes...

Total nodes in: nofun9622.wav:10078
Total nodes in: nofun96.wav:10129

Missednodes=297, discreps=9781, Searchednodes=10078

  9776                                           ***                                  
  9165                                           ***                                  
  8554                                           ***                                  
  7943                                           ***                                  
  7332                                           ***                                  
  6721                                           ***                                  
  6110                                           ***                                  
  5499                                           ***                                  
  4888                                           ***                                  
  4277                                           ***                                  
  3666                                           ***                                  
  3055                                           ***                                  
  2444                                           ***                                  
  1833                                           ***                                  
  1222                                           ***                                  
   611                                           ***                                  
Sums:     0    1    0    1    0    0    0    0 9776    0    0    1    0    1    0    1
Devs:   480  416  352  288  224  160   96   32   32   96  160  224  288  352  416  480

Distribution chart, range=1024n (256n=1 sample)

Normal Termination

>> Here is 22kHz lowpassed, compaired to 11kHz lowpass (simulating 22kHz downsample)

---------- Run java ----------
Reading innofun9622.wav
  Opening nofun9622.wav
  SampleRate:96000
  Stereo input
  Samples 1006876
  Trackime at 96000Hz :10.488

And Reading nofun9611.wav
  Opening nofun9611.wav
  SampleRate:96000
  Stereo input
  Samples 1006876
  Trackime at 96000Hz :10.488

Only reading first 2.133 seconds (of 1 channel)(Change chnkread for more)

Locating Nodes...

Total nodes in: nofun9622.wav:10078
Total nodes in: nofun9611.wav:7807

Missednodes=3320, discreps=6758, Searchednodes=10078

  3280                                           ***                                  
  3075                                           ***                                  
  2870                                           ***                                  
  2665                                           ***                                  
  2460                                           ***                                  
  2255                                           ***                                  
  2050                                           ***                                  
  1845                                           ***                                  
  1640                                           ***                                  
  1435                                           ***                                  
  1230                                           ***                                  
  1025                                      ***  ***                                  
   820                                      ***  ***                                  
   615                                      ***  ***                                  
   410                                      ***  ***                                  
   205        ***  ***                 ***  ***  ***  ***                 ***  ***    
Sums:    34  226  271  189   96   72  247 1166 3280  297   51   75  177  286  250   41
Devs:   480  416  352  288  224  160   96   32   32   96  160  224  288  352  416  480

Distribution chart, range=1024n (256n=1 sample)

Normal Termination

>> Here is lp 22 compared to lp 5.5kHz.... (@96k bndlimint)


---------- Run java ----------
Reading innofun9622.wav

  Opening nofun9622.wav
  SampleRate:96000
  Stereo input
  Samples 1006876
  Trackime at 96000Hz :10.488

And Reading nofun9605.wav

  Opening nofun9605.wav
  SampleRate:96000
  Stereo input
  Samples 1006876
  Trackime at 96000Hz :10.488

Only reading first 2.133 seconds (of 1 channel)(Change chnkread for more)

Locating Nodes...

Total nodes in: nofun9622.wav:10078
Total nodes in: nofun9605.wav:1455

Missednodes=9046, discreps=1032, Searchednodes=10078


   161                                           ***                                  
   150                                           ***                                  
   140                                           ***                                  
   130                                           ***                                  
   120                                           ***                                  
   110                                           ***                                  
   100                                           ***                                  
    90                                           ***                                  
    80                                           ***            ***                    
    70                                      ***  ***            ***                    
    60             ***  ***  ***  ***  ***  ***  ***       ***  ***  ***              
    50        ***  ***  ***  ***  ***  ***  ***  ***  ***  ***  ***  ***  ***          
    40        ***  ***  ***  ***  ***  ***  ***  ***  ***  ***  ***  ***  ***  ***    
    30        ***  ***  ***  ***  ***  ***  ***  ***  ***  ***  ***  ***  ***  ***    
    20   ***  ***  ***  ***  ***  ***  ***  ***  ***  ***  ***  ***  ***  ***  ***    
    10   ***  ***  ***  ***  ***  ***  ***  ***  ***  ***  ***  ***  ***  ***  ***  ***
Sums:    26   57   64   67   66   68   63   70  161   56   69   84   69   52   44   16
Devs:   480  416  352  288  224  160   96   32   32   96  160  224  288  352  416  480

Distribution chart, range=1024n (256n=1 sample)

Normal Termination


It does strike me that a central spike persists.
Ill have to go through the code again before I can be sure that is not a buggy artifact of the prog.
Food for thought though.

cheers'
cg
Title: What is "time resolution"?
Post by: Woodinville on 18 November, 2006, 08:18:54 PM
Im very interested to hear about other & better methods of locating any sort of conditions in time in a waveform, and we might be able to implement them here to improve our real world study of pcms time resolution.

regards'
cg



Then how come you won't accept them when they are offered?  Try it. Learn.

It does strike me that a central spike persists.
Ill have to go through the code again before I can be sure that is not a buggy artifact of the prog.
Food for thought though.

cheers'
cg



I have a suggestion, go load Cygwin, Xserver, and Octave.

It will save you lots of time and eventually you'll understand that phase shift and time delay are the same thing, that you can build any real-world waveform out of continuous sine waves, etc.
Title: What is "time resolution"?
Post by: ChiGung on 18 November, 2006, 09:23:43 PM
Im very interested to hear about other & better methods..............

Then how come you won't accept them when they are offered?

It depends partly on the manner of offering and partly on the excercises potential to distract, - because i am making cases here which you are opposing.
At this stage im trying to measure distortion in time done to various waveform types, due to simulated resampling with lowpasses. Once measured, the expected distortion for different simulated samplerates will define the uncertainty of temporal placement of events within the waveforms source.
A task which is synonymous to me as quantifying 'time resolution'

btw, i confirmed that the spike in the preceeding plots is a bug, throwing much uncertainty on the programs performance at the moment, but ill get it fixed (the toil is in the assembling). In the meantime i expect honest estimates to be made here of the temporal resolution of pcm records. Because the proof will follow

Quote
Try it. Learn.
Thankyou for encouraging me to learn, may you also continue to learn

^I expect that you do know a better expression to use to locate the maxima and minima or other time pin-pointable conditions in waveforms, that i have used. If you could provide something i could use in this investigation - 'great 

Quote
I have a suggestion, go load Cygwin, Xserver, and Octave.
Octave is a good processing suite? I havent had time to try it, thanks for the tip though.

Quote
It will save you lots of time and eventually you'll understand that phase shift and time delay are the same thing,
maybe if you didnt save time, and built your own codebase, you just might realise that "phase shift and time delay" are different....

Phase shift's 'dimension' is tightly cyclic, time's dimension is not normaly considered so, most commonly an infinite line. The geometry of phase differs from the geometry of time, phase has a finite distribution through its own 'time' (loop) and an infinite distribution throughout 'real' time. This makes phase detail imperfect for locating finite positions in 'real' time. If I could recall Euclid as well as others i could say it better -but basicaly time delay and phase shift are different.

Although i supposed they might be used synonymously in some professional contexts. 

rgrds'
cg
Title: What is "time resolution"?
Post by: Woodinville on 19 November, 2006, 12:14:23 AM
maybe if you didnt save time, and built your own codebase, you just might realise that "phase shift and time delay" are different....

I see you're resorting to insuts again.
Quote
Phase shift's 'dimension' is tightly cyclic,

No, it's not. 2 pi is not the same phase shift as 4 pi, although sometimes measuring which is which requires good understanding, or in some cases even the use of time delay to disambiguate between 2 pi and 4 pi.

The fact that they can be disambiguated in relevant contexts shows fully your mistake.

I would suggest, again, that you go back and learn the basic definitions for what you seek.
Title: What is "time resolution"?
Post by: cabbagerat on 19 November, 2006, 04:20:14 AM
Phase shift's 'dimension' is tightly cyclic, time's dimension is not normaly considered so, most commonly an infinite line. The geometry of phase differs from the geometry of time, phase has a finite distribution through its own 'time' (loop) and an infinite distribution throughout 'real' time. This makes phase detail imperfect for locating finite positions in 'real' time. If I could recall Euclid as well as others i could say it better -but basicaly time delay and phase shift are different.
Euclid? If you want to have a scientific discussion perhaps following the standard of scientific publications would be a good idea. Either put up a proof or a reference to a published document containing a proof.
Title: What is "time resolution"?
Post by: Garf on 19 November, 2006, 04:54:41 AM
btw, i confirmed that the spike in the preceeding plots is a bug, throwing much uncertainty on the programs performance at the moment, but ill get it fixed (the toil is in the assembling)


Quote
maybe if you didnt save time, and built your own codebase, you just might realise that "phase shift and time delay" are different....


One wonders how you can make these two statements and keep a straight face.

If you are going to try arguing based on the implication that results from Octave would somehow be flawed, compared to your own software, then I think there is absolutely no point in continuing this argument further.
Title: What is "time resolution"?
Post by: SebastianG on 19 November, 2006, 08:17:44 AM
It looks like we're going in circles. I see you, ChiGung, posted some Java code that estimates the positions of peaks (quite badly I might add -- but since the signal you used is oversampled at least 4 times it doesn't hurt that much). But what was the point of doing it? You didn't have to "prove" that bandlimitation changes something. Nobody questioned it.

It's merely your notion of "time resolution", "timing detail" and your obsession about peaks. I mentioned a real practical example where one is interested in the location of a saddle point which is a center of a highly symmetric region (checkerboard corner) and that detectors exist which are reliable even when noise is present (I got an accuracy of +/- 0.05 pixels at an SNR of 20 dB). The theoretical limit of accuracy that can be achieved when no noise is present and aliasing didn't take place during the sampling is infinitely fine.

Why should we accept your definition of time resolution? Is there any practical reason for it? Who cares about how peaks may move on arbritrary signals due to band limitation? In all interesting cases those features don't move when band limiting due to symmetries (Try a smooth Gaussian pulse for example). Your "definition" (we've yet to see an good formulation) of time resolution is just a vague statement about how peaks may move. Your "time resolution" is what? An attribute to describe the accuracy of what? An instance of the PCM format? The way peaks may move certainly depends on the type of signal. So, is "time resolution" something you use to describe a type of signal? It's just vague nonsense. Again, nobody questions that peaks may move but you seem to be overly concerned about it. Regardless of how one should measure this and assign a number to describe the accuracy of something.... Why should we care?

Lemme say that I think I know what situation you are in. I wouldn't be honest if I denied that I've never been in a similar situation (me being sure about something and thinking everybody was wrong). Hopefully one realizes what's going on and feels only a little embarressed -- instead of really ashamed because of name calling, arrogant behaviour or whatever...
Title: What is "time resolution"?
Post by: ChiGung on 19 November, 2006, 12:25:30 PM
Quote
Euclid? If you want to have a scientific discussion perhaps following the standard of scientific publications would be a good idea. Either put up a proof or a reference to a published document containing a proof.
I roughly recall Euclid doing some early explorations into the 'geometry of space" You guys need references to remind you that "phase" and "delay" exist in different dimensions? perhaps compare "phase space" with "space time"
Quote
It looks like we're going in circles.
a bit like phase space -infinite cycles

SebastianG:"I see you, ChiGung, posted some Java code that estimates the positions of peaks (quite badly I might add"
- Its just an approximation to get the ball running. Like i said im interested if you might describe a better method. We could also see how the methods compare. When ive tidied the code up a bit,it will be quite easy to modify.

SebastianG:"but since the signal you used is oversampled at least 4 times it doesn't hurt that much). But what was the point of doing it? You didn't have to "prove" that bandlimitation changes something. Nobody questioned it."
- Ive had to respond to a great deal of dismissals and missreports, but here are some quotes about youre claim that "nobody questioned it" :
Quote
If you are saying that, in PCM, distortion is introduced by the impulse response of the system, then please demonstrate that this distortion is even plausibly audible.
Note the sly attempt to shift context from detectability to "audibility"

Quote
Resolution refers about the smallest time event that can be resolved.
KikeG never questioned its existence, just dismissed its relevance. I am attempting resolve events and observe their timing differences throughout different bandwidths/samplerates, to inform claims about pcm time resolution.

@SebastianG
- you might have a better appreciation of my efforts if you were more familiar with the content of this thread:

Quote
Chigung wrote: "Detail of any time localisable events, will be distorted by the implicit lowpass of conversion by an unknowable amount (post conversion) by upto a sample-period-width of difference."

This is completely incorrect. Please do not state it as a fact, and please do not reproduce this myth where it may confuse others.
(not just "incorrect" but completely incorrect - followed by an order to desist saying so(!)

Do people read HA to learn? How well is sense defended here?

Quote
So, we have two filters. If _both_ filters block everything above fs/2, then the sampling stage itself will be transparent - lossless, if you like. In other words, these two systems would be identical...
I have never disagreed with this, but this is the fact which has been repeatedly put forward to show the futility of examining timing differences between different samplerates/bandwidths of the same potential source. Because it only considers sources with the same bandwidth - it is an irrelevant, disruptive case -especialy when repeated often throughout this thread as something i 'dont get'

SebastianG:"Why should we accept your definition of time resolution? Is there any practical reason for it? Who cares about how peaks may move on arbritrary signals due to band limitation?"
- 'Arbitrary' is a dismissive term to use there, this an investigation of practical time resolution in pcm of various kinds of source including music tracks. Who cares? The thread is "what is time resolution", this is the R&D section of an audio forum. But hey it might be true,that no one but me really cares about the subject.

SebastianG:"Lemme say that I think I know what situation you are in. I wouldn't be honest if I denied that I've never been in a similar situation (me being sure about something and thinking everybody was wrong). Hopefully one realizes what's going on and feels only a little embarressed -- instead of really ashamed because of name calling, arrogant behaviour or whatever..."
- Sincerely thanks, but i dont think you have appreciated the thrust of this debate, or how my ultimately trivial situation in this thread might relate to my circumstances outside of it.

I am self critical and acknowledge my faults, i percieve that you all too should perform some critical introspection.

Quote
ChiGung:"btw, i confirmed that the spike in the preceeding plots is a bug, ....
maybe if you didnt save time, and built your own codebase, you just might realise that "phase shift and time delay" are different...."

One wonders how you can make these two statements and keep a straight face.
They arent related. If you develope your understanding from first principals you are more likely to spot fundamental differences between different entities like "phase shift" and "time delay" - than if you prematurely seek the meanings of the terms as reported by other peoples studies.

Garf: "If you are going to try arguing based on the implication that results from Octave would somehow be flawed, compared to your own software, then I think there is absolutely no point in continuing this argument further."
- Ive no idea why you suspect that. Please do present comparable results from Octave if you get the time.

---

Im not over the moon, that my program is not working completely yet, but it will when I get an hour or so to concentrate on fixing it. Its not complex compared to my other projects, just a quick throwing together of a couple of parts. I could just await more accurate data on the matter from you guys and your own tools, but suspect that might never materialise.

If i dont bother finishing the program, who has contributed less? Me, or those who simply refered the great job their own favourite tools could do?

Quote
chigung: "maybe if you didnt save time, and built your own codebase, you just might realise that "phase shift and time delay" are different...."

I see you're resorting to insuts again.
I didnt mean for that to be insulting to you.
Please examine your own manners of expression.
(I attempt to fairly return the respect i recieve)

Quote
chigung:Phase shift's 'dimension' is tightly cyclic,

No, it's not. 2 pi is not the same phase shift as 4 pi, although sometimes measuring which is which requires good understanding, or in some cases even the use of time delay to disambiguate between 2 pi and 4 pi.
This reported subtlety does not make phase shifts dimension equivalent to realtime's. However you arrange it, you cant show these things are equal. But you do often half report a theoretical contention, before handwaving towards further neccessary 'studies'

Woodinville:"I would suggest, again, that you go back and learn the basic definitions for what you seek."
- I gather if i suggested that to you, you would report insult.

--
'fair regards to you all,
cg
Title: What is "time resolution"?
Post by: MoSPDude on 19 November, 2006, 03:03:51 PM
@ChiGung, A phase shift at a given frequency is equal to a time shift. As you said, a phase shift on its own doesn't really have any meaning. The time shift in seconds for a frequency 'f' in Hz, and phase shift 'p' in radians is equal to p/(2*pi*f) for a straight sinusoid. This can be extended and applied to any form of signal, for any duration, by realising that any waveform is a composite sum of sines and cosines - hence why the fourier transform returns both magnitude and phase plots.

When you perform the up-sampling, perhaps adding a small sample shift manually and taking the FFT would help to illustrate the phase-time relationship.
Title: What is "time resolution"?
Post by: MedO on 19 November, 2006, 03:22:59 PM
Woodinville:"I would suggest, again, that you go back and learn the basic definitions for what you seek."
- I gather if i suggested that to you, you would report insult.


Well, you have to admit that this quote of you kind of suggests that you didn't read up on the definitions of the terms used in the textbooks:

Quote
Untrue. I limit my research to protect my originality. Education is to Innovation what Masterbation is to Procreation. I have learned adequate tools at home, school and university and beyond to suit my own designs.


A main problem through this discussion is that there is a lot of misunderstanding going on. Most notably, the term "time resolution" is used a lot, and interpreted as a different concept by different people here.

As far as I understand it, what you're trying to show is that certain conditions (like "level=x" or peak positions) shift in time when the signal is lowpassed. Big deal. This is completely equivalent to saying that the waveform has changed. Why? Because if the waveform was different in one place, you could construct a condition that was fulfilled in this place in the source signal but not in the result.

Conclusion: Lowpassing changes the waveform, so some or all of your conditions might not be fulfilled anymore (or will be fulfilled in different positions) in the result. Please note that this is probably not what most other people here understand as "time resolution".

The question now asked is, how much will those conditions move. I (and other people following this thread) fail to see the point in this question. Maybe you could give an example where this information would be relevant?
Title: What is "time resolution"?
Post by: ChiGung on 19 November, 2006, 03:30:40 PM
As you said, a phase shift on its own doesn't really have any meaning.

Yes, i would say an individual 'phase shift' is an incomplete value, without refering to a (potential) period which resides within a phase space. A 'time delay' is an incomplete value without refering a (potential) instant within 'time'.
When phase space is mapped onto time, it fills time with unending repetitions of its periodic content (ie frequencies are theoreticaly infinite in duration). So a value which is interprated as a phase shift, cannot locate any finite point in time,  only a theoreticaly infinite amount of finite points described with reference to the 'phase shifts' accompaning period.

Quote
- hence why the fourier transform returns both magnitude and phase plots.

I'm normaly interested in discussing such, but am weary from the previous reactions and charges made against my outlooks and character here.

may you fair better here'

cg
Title: What is "time resolution"?
Post by: ChiGung on 19 November, 2006, 03:45:45 PM
Maybe you could give an example where this information would be relevant?

It would be relevant to knowing how accurately times of conditions which are indicatable in PCM records can predict the conditions true time of occurence in source material.

Such as this simple example brought up pages ago:
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techie: "captain we have located a 'spike' event on the PCM sensor"
captain:"what is the position of the spikes peak teki?"
techie:"324.37643 sampling intervals exactly captain"
captain:"how can you be so precise?"
techie:"because time delays are quite precisely encodable in PCM"

But a natural spike, will have an unknown frequency spectrum, the tools (information) to locate the true peak with certainty had to be removed before the downsample, so we can make the best guess by assuming the 'subsample deviators' (frequencies beyond nyquist) were all flat anyway but thats just a guess, the true peak could have been anywhere in the sample interval. If it was actualy somewhere other than the record suggests most likely, that information was contained in the lowpassed higher frequencies which now manifest as the unrecorded gaps between samples.


Responses to this example included, refutations that the true spikes subsample position was insecure at all. The case can also be applied to any use of pcm, where the source is not known to be suitably bandlimited to the bandwidth of the employed samplerate. Such as master audio > CD audio, CD audio> less, seismology, radio astronomy... astrology...nope not quite astrology

Imagine it was an examine question: what applications of pcm records do you think are susceptable to timing uncertainties caused by samplerate enforced bandlimitation ? How does the concept and common usage of the term 'time resolution' contrast with practicaly introduced distortions?

cheers,
cg

edit: added clarifications to over saturated language used in the quote
Title: What is "time resolution"?
Post by: MoSPDude on 19 November, 2006, 04:09:07 PM
I agree a reference point is needed, a phase shift at a specified frequency does not specify an exact time, as does a time delay not specify an exact time - but both a phase shift at a specified frequency and a time delay are equivalent in these terms, and it's possible to have a phase shift of greater than 2*pi allowing any duration to be specified. Phase shifts tend to be measured relative to the input to a transfer function - so could be used to locate exact positions if you know those of the input. Again, comparing input mag/phase plots to output mag/phase plots would help to illustrate this.

Perhaps looking at it from a different angle is needed, I think in the end we're interested in if PCM can follow its analogue band-limited source counterpart exactly. Quantization will add a noise error signal so 'exact' won't be fully achievable. At the moment, the movement of peaks haven't be attributed to anything other than removal of frequencies. Just a thought.

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Imagine it was an examine question: what applications of pcm records do you think are susceptable to timing uncertainties caused by samplerate enforced bandlimitation ? How does the concept and common usage of the term 'time resolution' contrast with practicaly introduced distortions?


These questions are only valid to the extent that they question the use of ANY form of sampling, not only PCM. Again, all the ideal theoretical mathematical explainations of sampling I've read don't indicate any such timing uncertainties - only problems caused by causality and the knowledge of all samples and the like. Practically I've not tested this but again, in the physical world things are a bit different!
Title: What is "time resolution"?
Post by: ChiGung on 19 November, 2006, 04:21:28 PM
I agree a reference point is needed, a phase shift at a specified frequency does not specify an exact time, as does a time delay not specify an exact time - but both a phase shift at a specified frequency and a time delay are equivalent in these terms,

I dont think so -
A phase shift is an 'orphaned' value without reference to a period and a mapping onto time (reference point to)
A time delay, just needs a reference point in time, as a time value just needs a reference point to time=0

The difference is, with knowledge only of time, a time value is complete.
With knowledge only of time, a phase-shift value is incomplete (until we have reference to its period)
Then, when a phase shift value is employed as a phase shift value, it details the  location of an infinite periodic conditions throughout realtime. It cant detail a finite condition without meaning something other than "phase shift"

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and it's possible to have a phase shift of greater than 2*pi allowing any duration to be specified.

I admit i dont know how the particulars of that are theoreticaly employed, though i could make guesses at options. In practice i interprate things circumspectly for the task at hand.

Its not absolutely clear to me how his subject applies to showing that my investigation of how lowpass distortion affects timing is uninformative,
besides it being arguement presented for me to answer - "time delays and phaseshifts are exactly the samething"

rgrds'
cg

Perhaps looking at it from a different angle is needed, I think in the end we're interested in if PCM can follow its analogue band-limited source counterpart exactly. Quantization will add a noise error signal so 'exact' won't be fully achievable. At the moment, the movement of peaks haven't be attributed to anything other than removal of frequencies. Just a thought.

Its a good point about the situation in practice which i wondered about while putting together my 'great unfinished' program.

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These questions are only valid to the extent that they question the use of ANY form of sampling, not only PCM.

I dont know, question get asked about particular things all the time, without needing to encompass all of creation 

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Again, all the ideal theoretical mathematical explainations of sampling I've read don't indicate any such timing uncertainties - only problems caused by causality and the knowledge of all samples and the like. Practically I've not tested this but again, in the physical world things are a bit different!

I will try to generate data about it unhurredly over the next while... (read >days)

cheers'
cg
Title: What is "time resolution"?
Post by: MoSPDude on 19 November, 2006, 04:26:40 PM
I think we are deviating from the point, but totally disagree with the phase shift requiring a mapping onto an exact period in time, the period is found from the frequency which is given and as we mentioned before a reference point in time is needed - which is usually given by the input to the transfer function.

In terms of your exact study, of how low pass filtering affects timing, what kind of lowpass filter are you studying? I'd be interested in this filters transfer function. Is this filter being applied in the digital domain or analogue before sampling?

I don't disagree with anyone who performs any study or investigation, as I find it helps to perform these things to allow a clear view of why things work.
Title: What is "time resolution"?
Post by: ChiGung on 19 November, 2006, 04:34:14 PM
I think we are deviating from the point, but totally disagree with the phase shift requiring a mapping onto an exact period in time,

That wasnt quite what i meant to describe, but can put it on hold.

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In terms of your exact study, of how low pass filtering affects timing, what kind of lowpass filter are you studying? I'd be interested in this filters transfer function. Is this filter being applied in the digital domain or analogue before sampling?
I would be studying relevant available lowpasses to simulate the effect on event timing of high quality downsampling.

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I don't disagree with anyone who performs any study or investigation, as I find it helps to perform these things to allow a clear view of why things work.
I bow to your standards of intrest

cheers'
cg
Title: What is "time resolution"?
Post by: SebastianG on 19 November, 2006, 06:20:01 PM
Quote

...You didn't have to "prove" that bandlimitation changes something. Nobody questioned it."

Ive had to respond to a great deal of dismissals and missreports, but here are some quotes about youre claim that "nobody questioned it":
cabbagerat> If you are saying that, in PCM, distortion is introduced by the impulse response of the system, then please demonstrate that this distortion is even plausibly audible.
Note the sly attempt to shift context from detectability to "audibility"

Actually band limitation is generally not considered distortion (as in "non-linear" distortions). You both were just talking about different kinds of distortion.

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Resolution refers about the smallest time event that can be resolved.
KikeG never questioned its existence, just dismissed its relevance. I am attempting resolve events and observe their timing differences throughout different bandwidths/samplerates, to inform claims about pcm time resolution.

Then what are "timing events"? This discussion seems pointless because we don't seem to have a common ground concerning many (pseudo-) technical terms. Everybody knows what a peak is. <rethorical>But what is "timing event"?</rethorical>

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Chigung wrote: "Detail of any time localisable events, will be distorted by the implicit lowpass of conversion by an unknowable amount (post conversion) by upto a sample-period-width of difference."
This is completely incorrect. Please do not state it as a fact, and please do not reproduce this myth where it may confuse others.
(not just "incorrect" but completely incorrect - followed by an order to desist saying so(!)

That's probably because Woodinville interprets "timing event" differently. This only shows the need for a common vocabulary with precisly defined terms. ("timing event" is not part of it!)
Note that I was talking about peaks. Nobody claimed that peaks remain at the exact same position in general when you lowpass a signal (even with a zerophase lowpass). This is only the case when the filter's impulse response and the signal (locally) have certain properties. But of course we all know that already.
However, if you talk about "time events" this is a different story. Then it's up to interpretation. Or perhaps you should have just included the word "may" in there. Quote:"Any time localisable event" is pretty much anything and also includes the "events" whose location won't be altered during bandlimiting. <splitting hairs>These exist. So you're wrong.</splitting hairs>

One could also think of "time event" as a specific energy distribution in time (Woodinville's example: gaussian pulse). This (or the lower spectrum part that's left after lowpassing/sampling) can be located perfectly if the signal has been properly sampled. The only thing that'll mess things up here is noise (eg quantization noise).

...Who cares? The thread is "what is time resolution", this is the R&D section of an audio forum. But hey it might be true,that no one but me really cares about the subject.

Again: I was talking about peaks and their possible movement. It's you not me nor 2B nor Woodinville that connects peaks and their possible movement to "time resolution" -- a term whose notion we havn't agreed upon. After all the "who cares"/"so what"-talk I was kind of expecting you to mention a case where a possible movement of peaks poses an actual problem. I still can not understand your obsession about those things on arbitrary signals ("arbitrary" = those that may show different locations of those points you look for after bandlimiting).

Cheers!
SG
Title: What is "time resolution"?
Post by: ChiGung on 19 November, 2006, 07:46:10 PM
cabbagerat> "If you are saying that, in PCM, distortion is introduced by the impulse response of the system, then please demonstrate that this distortion is even plausibly audible."
chigung: Note the sly attempt to shift context from detectability to "audibility"

Actually band limitation is generally not considered distortion (as in "non-linear" distortions). You both were just talking about different kinds of distortion.

The type of distortion i was talking about, was already described (ie that which occurs in the "tekkie's spike" example which preceeded it and elsewhere besides).
It is also possible to be over pedantic about terminology.

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chigung:"KikeG never questioned its existence, just dismissed its relevance. I am attempting resolve events and observe their timing differences throughout different bandwidths/samplerates, to inform claims about pcm time resolution."

Then what are "timing events"? This discussion seems pointless because we don't seem to have a common ground concerning many (pseudo-) technical terms. Everybody knows what a peak is. <rethorical>But what is "timing event"?</rethorical>


Firstly, I did not use the term "timing event" there, though i may have used loose phrases elsewhere. I apologise for my over occasional errors in spelling grammar and terminology, but i shouldnt apologise for the diversity or ambitiousness of my expression, which may also challenge those not especialy fluent in my dialect of english.
Regarding 'timeable events' I use such terms as a broad set of which 'peaks' are a member.
I simply wished to refer to any kind of detail which might be identified and pinpointed in time within waveforms. Basicaly anything you might think of which might be precisely locateable in time (in a prcm record)  -( which peak of level is an example of).

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That's probably because Woodinville interprets "timing event" differently. This only shows the need for a common vocabulary with precisly defined terms.

Again, I did not use the term 'timing event' in the statement which woodinville expressed great objection to.

This statement i used:
"Detail of any time localisable events, will be distorted by the implicit lowpass of conversion by an unknowable amount (post conversion) by upto a sample-period-width of difference."

-Is very explicit english. "time localisable events" are> [events] [which are possible to locate in] [time].

I do use complex and varied english (in order to be as descriptive as possible) Some of my posts contain more grammatical errors than others, but most are not too bad, and some are carefuly composed. I think you suspect my english is worse than it actualy is, because it is not your own first language and i attempt to describe concepts in complex english, rather than employing the terminology which you are familiar with.

There is a similar problem with the phrase "time resolution" here. "Resolution" has a common meaning, and "time" does to. If a technical usage of the term 'time resolution' conflicts with the plain english translation, that can certainly cause confusion.

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"Any time localisable event" is pretty much anything and also includes the "events" whose location won't be altered during bandlimiting.

Yes that term is meant to mean anything time-locatable. I am interested to hear any event-types (conditions) which are not susceptable to being altered by bandlimitation - or other types which are.

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One could also think of "time event" as a specific energy distribution in time (Woodinville's example: gaussian pulse). This (or the lower spectrum part that's left after lowpassing/sampling) can be located perfectly if the signal has been properly sampled. The only thing that'll mess things up here is noise (eg quantization noise).
Yes as i wrote before, when patterns spanning multiple samples are known to be present, their solution in time can be refined by involving all the samples they affect.

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It's you not me nor 2B nor Woodinville that connects peaks and their possible movement to "time resolution" -- a term whose notion we havn't agreed upon.

I think you eventualy will understand how the movement of measureable occurences in time which might result from lowpassing, informs 'time resolution' @ pcm samplerates.

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After all the "who cares"/"so what"-talk I was kind of expecting you to mention a case where a possible movement of peaks poses an actual problem. I still can not understand your obsession about those things on arbitrary signals ("arbitrary" = those that may show different locations of those points you look for after bandlimiting).


My obsession here, has simply been to defend my reputed understanding of the topic.
The quote which started it all, was in the otherwise great "vinyl myths" article in the HA wiki.

cheers'
andy
Title: What is "time resolution"?
Post by: ExUser on 19 November, 2006, 08:38:47 PM
The common definition of "time resolution" is not sufficient. Mathematical and common definitions are usually quite different. If mathematical language is too much for you, give an example in which "time resolution" is defined. We may be able to do something with that.

If you use the Techie example, it is obvious that the a spectral component of the measured peak is significantly below the sampling frequency. However, where is this "spike" defined? Any similar definition I've seen tends to be the length of time a signal is above a certain value. The "Techie"'s language is woefully inadequate and is not at all descriptive. "The signal was 20dB above the noise floor for 324.37643 sampling frequencies with the rising edge located at a system time stamp of X." That would be a more scientific statement. Noise is interfering with precise temporal placement. The precise location of the rising edge is lost in the noise. Statistics can then give you an idea of the location and a level of certainty that you can apply to the measurement.

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"Detail of any time localisable(sic) events, will be distorted by the implicit lowpass of conversion by an unknowable amount (post conversion) by upto(sic) a sample-period-width of difference."

-Is very explicit english. "time localisable(sic) events" are> [events] [which are possible to locate in] [time].


Very explicit English, sure. It is not, however, very precisely defined English. What is an event? Likewise what is a detail? A peak? A zero-crossing? Both are affected by low-pass and are therefore unsuited for defining time resolution. What does this leave? Not a lot, I'm afraid. Until you can pick out some detail that actually withstands low-passing and allows for some measurement before and after, you're going to be in trouble.

The single detail I could think of for experimental use would be for a signal to go from 0 to 1 in some set time. Then the detail becomes your zero-crossing, and it should resist low-pass. "Time resolution" as I understand it is very well defined in this context.
Title: What is "time resolution"?
Post by: SebastianG on 19 November, 2006, 08:57:09 PM
The type of distortion i was talking about, was already described

Yeah, I was aware of that. I just pointed out that there was a possible misunderstanding between you and him.

Regarding 'timeable events' I use such terms as a broad set of which 'peaks' are a member.
I simply wished to refer to any kind of detail which might be identified and pinpointed in time within waveforms. Basicaly anything you might think of which might be precisely locateable in time (in a prcm record)  -( which peak of level is an example of).

Yeah, I was aware of that. I just tried to point out a possible misunderstanding between you and him.

I think you eventualy will understand how the movement of measureable occurences in time which might result from lowpassing, informs 'time resolution' @ pcm samplerates.

We can agree so far that lowpassing can move those things you mean (this is nothing new. we've been there already). However, I refuse to use the term "time resolution" for that. This is something you just made up and serves no purpose.

My obsession here, has simply been to defend my reputed understanding of the topic.

So, you bring up possible peak movement just to tell us about your notion of "time resolution"?
I would have loved to hear from you about application examples where this does matter.
Title: What is "time resolution"?
Post by: 2Bdecided on 20 November, 2006, 07:17:52 AM
Im not your student.


Ah, that's where you're going wrong!

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Quote
You're doing nobody any good by failing to read up on the field you're talking about before you work.
Untrue. I limit my research to protect my originality. Education is to Innovation what Masterbation is to Procreation


Einstein stood on the shoulders of giants, and you're standing on quicksand?

I wonder who will see further!

Cheers,
David.


The time and frequency domains are mathematically identical, but are very different to conceptualize. If you wish to discover the ways in which a frequency domain transform affects audio, you must look at it from a frequency domain perspective if you wish to understand well. What you are doing is looking at a frequency domain transformation from a time domain perspective, and are getting complex results that you don't really understand. Because you don't understand them, you assume there's something weird happening there. There isn't. You're just not looking at it correctly.


You put that very well.

I tried to give an example that was so "simple" this became obvious, but CG felt that I was trying to hide something or use specific examples to back my view point.

The problem is that CG doesn't believe that some of us have both an intuitive and mathematical understanding of the relationship between time and frequency, and so actually understand what's happening to his peaks. (And it's not very interesting!(.

He is mistaking our disinterest in the "answers" he's generating with this program for a lack of understanding of his "big question". The problem is that we do understand it - that's why it's not very interesting!

Never mind the fact that there isn't an algorithm that will "work" even for what he's trying to prove.

Cheers,
David.
Title: What is "time resolution"?
Post by: 2Bdecided on 20 November, 2006, 07:35:23 AM
In the meantime i expect honest estimates to be made here of the temporal resolution of pcm records. Because the proof will follow


I already did that, and provided a worked example.

With your completely bizarre definition of "time resolution", which in fact means "how far will the peaks move" - it's up to + or - 1/2 the wavelength of the low pass filter cut-off.

WRT resampling to a lower sample rate, that's up to +/- 1 sample at the new sample rate.

I could be wrong. It's such a pointless question that I doubt anyone will bother to point it out if I am!


The distribution is the sum of some random process, but I'm not entirely sure what.

The actual results are confounded by the impossibility of "identifying and tracking the same peak". You're trying to see how far the peaks moves, but you have to make some assumption about how far they could move in order to track them!

Cheers,
David.
Title: What is "time resolution"?
Post by: 2Bdecided on 20 November, 2006, 07:59:42 AM
All you have shown is that frequency components in signal A contributed to the position of peak A, and these have been removed, thus moving the peak. However, there is no limit to where peaks can occur. It is not like the quantisation amplitude resolution limit at all! It is not a time resolution limit, just a predictable effect of low pass filtering a signal.

If there is no limit to where the peaks can occur, how come they cant be arranged to occur in the correct place between records of differing sample rates? Why must they be susceptible to unknown distortions during downsamples with your "no limitations" argument? Because their precise subsample positions are limited - by every other sample in the record which they are a part of. Thats why you cant normally use the "unlimited" resolution which you can infer - without distorting all other samples to create the subsample details. (done to provide some limited demonstrations in this thread, but not possible in practice where all samples must be treated equally)


So (presumably) it's OK to look at multiple samples when discussing the position of a peak in the frequency domain, it's acceptable to talk about the time and frequency domains being linked, but its suddenly voodoo and/or cheating to look at multiple samples when discussing the position of a peak in the time domain?

Glad we got that cleared up!


I still don't get the obsession or difficulty. If a peak moves when low pass filtering, it's because you are deleting the part of the signal that put the peak there - how could it not move? It's not a limit in resolution because, if the peak was supposed to be there ("there" being absolutely anywhere), it could and would be. Nothing fake, clever or contrived. PCM audio allows a peak to exist absolutely anywhere - on samples, and anywhere between samples. What it doesn't allow is audio above fs/2. It's a frequency domain phenomena, not a time domain phenomena.


Let me draw a parallel. Try performing a time domain analysis on a nice linear-phase graphic equaliser with the bass at +6dB and the treble at -6dB. Would it change the time domain signal? Of course! It must change the time domain - you can't change one domain without affecting the other! But what we have is very much a frequency domain phenomena, any anyone who tries to analyse solely in the time domain is going to look very stupid - especially if they say they're going to do it for a random set of audio signals. Think about it - what on earth would it tell you?

Cheers,
David.
Title: What is "time resolution"?
Post by: ChiGung on 20 November, 2006, 12:07:24 PM
I still don't get the obsession or difficulty. If a peak moves when low pass filtering, it's because you are deleting the part of the signal that put the peak there - how could it not move? It's not a limit in resolution because, if the peak was supposed to be there ("there" being absolutely anywhere), it could and would be.

Imagine sampling something at a very high sampling rate, so all the peaks are nearly exactly where they should be. Then downsample; if the peaks move are they where they 'should' be anymore? When we read a pcm record, how close can we say the peaks are to where they could/should be in the source material?
If we have knowledge of the source materials frequency distribution we can estimate the discrepancies we are likely to find.
(Peaks are just examined here as one example of waveform conditions which can be detected and precisely located in time.)

The statement i made earlier that ~"all peaks are susceptable to moving up to a samplewidth..." was speculative, it may be close to the exact situation, it may not be. There is only a question of detail to resolve -"how far are peaks susceptable to move?"

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Nothing fake, clever or contrived. PCM audio allows a peak to exist absolutely anywhere - on samples, and anywhere between samples. What it doesn't allow is audio above fs/2. It's a frequency domain phenomena, not a time domain phenomena.

This is a commonly overread situation. - Just because a peak level created by any combination of frequencies can occur at any subsample location in time, does not imply that a peak represented in pcm as a neccessarily bandlimited frequency spread (limited by the nyquist f), can have its temporal position in the source predicted absolutely precisely.

When you suppose 'resolution' is dependant on the smallest values with which a record can confidently resolve itself Then with pcm, resolution of time and level is effectively infinite because the 'resolution' of algebra is effectively infinite. With such a flattering use of the term 'resolution' (which has been relied on here) the amount of information in a record has almost no contribution at all to its reportable resolution - all you really need are 2 samples in order to have a record which you can say you can resolve with infinite resolution.

Put another way, there have been great objections put forward to my report that unless we have secure knowledge of the frequency distribution of the source, time resolution is practicaly around 1/2 the sample interval.
What is "level resolution" then? Doesn't a pcm record of 8bit words differ in 'level resolution' from one of 16bit words? Or do you all contend that to a properly educated engineer, both records resolution of level are effectively infinite as well?
Title: What is "time resolution"?
Post by: 2Bdecided on 20 November, 2006, 12:15:59 PM
Put another way, there have been great objections put forward to my report that unless we have secure knowledge of the frequency distribution of the source, time resolution is practicaly around 1/2 the sample interval.
What is "level resolution" then? Doesn't a pcm record of 8bit words differ in 'level resolution' from one of 16bit words? Or do you all contend that to a properly educated engineer, both records resolution of level are effectively infinite as well?


So you didn't even bother to read, never mind understand, that part where I contrasted quantisation (which does limit amplitude resolution) to sampling (which does not limit time resolution)?


Or comment on the part where I ask just how stupid it would be to perform time domain analysis on the output of a graphic equaliser?

Cheers,
David.
Title: What is "time resolution"?
Post by: ChiGung on 20 November, 2006, 12:26:06 PM
So you didn't even bother to read, never mind understand, that part where I contrasted quantisation (which does limit amplitude resolution) to sampling (which does not limit time resolution)?

Or comment on the part where I ask just how stupid it would be to perform time domain analysis on the output of a graphic equaliser?

Of course I read those parts, but choose other parts to attach clear comments to.
You decided to complain about 'the parts' i commented on rather than make any response to any of the answers put to you.

Ok then, ill take another look at the parts you would most like me to respond to,
maybe then you will honour me with a response to any of my points.....
Title: What is "time resolution"?
Post by: ChiGung on 20 November, 2006, 12:41:03 PM
Let me draw a parallel. Try performing a time domain analysis on a nice linear-phase graphic equaliser with the bass at +6dB and the treble at -6dB. Would it change the time domain signal? Of course! It must change the time domain - you can't change one domain without affecting the other!
But what we have is very much a frequency domain phenomena,
any anyone who tries to analyse solely in the time domain is going to look very stupid - especially if they say they're going to do it for a random set of audio signals. Think about it - what on earth would it tell you?

Check the veracity of your focus here, you confirm "you can't change one domain without affecting the other" but then anounce that "we have a frequency domain phenomenon" (only modified conviently with the words "very much")
This is like bending a piece of steel, and anouncing "what we have is 'very much' a structural phenomenon" - therefore, anyone who wishes to observe how the structural phenomenon affects temperature is going to look very stupid.

I admit, i cant locate the comments on quantisation which you asked me to respond to. Generaly i would expect issues regarding quantisation will only reinforce limits on resolution of time & level detail within pcm records.....

@SebastianG
I would have loved to hear from you about application examples where this does matter.

An example application where real-world 'time resolution' would matter would be in rangefinding. Imagine a very accurate visual sensor records a flash, and a sound sensor records a shock wave following it. Employing knowledge of the speed of light, and the speed of sound, we can estimate the distance of the cause of the flash and the shockwave (assuming the same event produced both).

[speed of sound] * [time interval] (between the flash and the shockwave)
=[distance of sensor] (from the cause)

or more accurately,
distance from event =observed time between sight and sound/(1/soundspeed-1/lightspeed)

This example is basicaly a filling out of the 'tekkie's spike' example.
If rangefinding processing used pcm, wouldnt 'time resolution' be one factor that limits its maximum "range resolution"?

It surely is an odd thing to hear engineers report that they cant think of any applications where practical 'time resolution' of an employed encoding format, might matter.
Title: What is "time resolution"?
Post by: 2Bdecided on 21 November, 2006, 05:51:00 AM

Let me draw a parallel. Try performing a time domain analysis on a nice linear-phase graphic equaliser with the bass at +6dB and the treble at -6dB. Would it change the time domain signal? Of course! It must change the time domain - you can't change one domain without affecting the other!
But what we have is very much a frequency domain phenomena,
any anyone who tries to analyse solely in the time domain is going to look very stupid - especially if they say they're going to do it for a random set of audio signals. Think about it - what on earth would it tell you?

Check the veracity of your focus here, you confirm "you can't change one domain without affecting the other" but then anounce that "we have a frequency domain phenomenon" (only modified conviently with the words "very much")
This is like bending a piece of steel, and anouncing "what we have is 'very much' a structural phenomenon" - therefore, anyone who wishes to observe how the structural phenomenon affects temperature is going to look very stupid.


Oh come on. The frequency and time domains are mathematically related. Of course you can't change one without changing the other.

However, there is little practical use or sense in trying to analise certain changes in one domain, when all the important stuff is hidden in that domain, but apparent (obvious) in the other.


That's why I gave the example I did, because it's analogous to what you're doing. Let me put it like this:

I give you a black box to test. You decide the way you're going to test it by taking a random selection of audio signals (e.g. tracks off commercial CDs), and looking at the time domain output.

If that black box is a linear phase graphic equaliser, with the bass at +6dB and the treble at -6dB, you're really going to struggle to understand that with your time domain analysis! Whereas if you do a frequency domain analysis and/or if you use some suitable test signals, you can find out what's happening almost immediately.


You're probably thinking "but I want to know what's happening in both domains" - that's fair enough, but those of us who understand audio know that we can grab the data in whichever domain it makes most sense, and then know exactly what is happening in the other domain.


To put it really simply, we already know all the stuff you're trying to demonstrate, and more importantly we understand why it happens, and why it's not very interesting or important. That, in a nutshell, explains the "attitude" you've been getting over these 6 pages!

Quote
I admit, i cant locate the comments on quantisation which you asked me to respond to. Generaly i would expect issues regarding quantisation will only reinforce limits on resolution of time & level detail within pcm records.....


Post 109 - after the word "conclusion". I explain why quantisation does represent a limit in amplitude resolution, while low pass filtering does not represent a limit in time resolution.

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@SebastianG
I would have loved to hear from you about application examples where this does matter.

An example application where real-world 'time resolution' would matter would be in rangefinding. Imagine a very accurate visual sensor records a flash, and a sound sensor records a shock wave following it. Employing knowledge of the speed of light, and the speed of sound, we can estimate the distance of the cause of the flash and the shockwave (assuming the same event produced both).

[speed of sound] * [time interval] (between the flash and the shockwave)
=[distance of sensor] (from the cause)

or more accurately,
distance from event =observed time between sight and sound/(1/soundspeed-1/lightspeed)

This example is basicaly a filling out of the 'tekkie's spike' example.
If rangefinding processing used pcm, wouldnt 'time resolution' be one factor that limits its maximum "range resolution"?

It surely is an odd thing to hear engineers report that they cant think of any applications where practical 'time resolution' of an employed encoding format, might matter.


I think Sebastian has already explained and demonstrated precisely how low pass filtering does not reduce the accuracy in such real word experiments, and is often used as a simple way of removing noise and improving accuracy.

It's precisely because it works in the real world, as well as in theory and all the examples given here, that your continued objection is so funny.

If you were right, we'd have to stick with analogue electronics and timers for no end of things which have been digital for decades!!!

Cheers,
David.
Title: What is "time resolution"?
Post by: MoSPDude on 21 November, 2006, 08:44:34 AM
@ChiGung, are you actually performing your analysis in both domains or purely in the time domain? As everyone has stated previously, low pass filtering effects are easily visible in the frequency domain - and awkward/impossible to visualise in the time domain especially if your working with complex signals. Can you show both the phase and magnitude characteristics of the low pass filters you've been examining? Is it a linear phase filter etc.?
Title: What is "time resolution"?
Post by: ChiGung on 21 November, 2006, 10:22:41 AM
If that black box is a linear phase graphic equaliser, with the bass at +6dB and the treble at -6dB, you're really going to struggle to understand that with your time domain analysis! Whereas if you do a frequency domain analysis and/or if you use some suitable test signals, you can find out what's happening almost immediately.

Whatever the black box does, if you want to find out how it affects details in the time domain, you need to examine the time domain. It is irrelevant that the black boxes process might be more difficult to discover in the time domain, its affect on the time domain is apparent in the time domain.

Quote
You're probably thinking "but I want to know what's happening in both domains" - that's fair enough, but those of us who understand audio know that we can grab the data in whichever domain it makes most sense, and then know exactly what is happening in the other domain.

Not really, here in this thread, the issue examined is 'time resolution', not 'frequency resolution'. "Those of you who understand audio" should understand that just because you can only make sense of a proccess in one domain, does not mean its affects on another are insignificant.

Quote
To put it really simply, we already know all the stuff you're trying to demonstrate, and more importantly we understand why it happens, and why it's not very interesting or important.

That is a simple account which you keep presenting, yet you continue to also present explicity falacious arguements against the investigation, and no there have not been any confident predictions made about the results you might expect, only attempts to colour the results as somehow irrelevant to 'time resolution'


Quote
Post 109 - after the word "conclusion". I explain why quantisation does represent a limit in amplitude resolution, while low pass filtering does not represent a limit in time resolution.

I see, then the comment i made on it generaly, stands then.

A pity you again choose to try and explain your untouchable understandings, instead of commenting on any of the very accessible points I made to you earlier.

Quote
Quote
It surely is an odd thing to hear engineers report that they cant think of any applications where practical 'time resolution' of an employed encoding format, might matter.

I think Sebastian has already explained and demonstrated precisely how low pass filtering does not reduce the accuracy in such real word experiments, and is often used as a simple way of removing noise and improving accuracy.

That is not another 'get out' clause. You are saying, that innacuracy of the input signal usually eclipses the capabilities of the record. You are saying that practical time resolution of pcm is even lesser than the limit i am investigating.
(That is what you are saying there) And elsewhere you present the claim that pcms time resolution is near infinite as algebra's, and leave my contentions about that unanswered.

As long as you all maintain a united front of experte denial, no one need feel silly right?

Quote
@ChiGung, are you actually performing your analysis in both domains or purely in the time domain? As everyone has stated previously, low pass filtering effects are easily visible in the frequency domain - and awkward/impossible to visualise in the time domain especially if your working with complex signals.

I am not studying effects of filters in the frequency domain, in the same way as if i wanted to measure how bending steel changed its temperature, i wouldnt need to bring a protractor....well, yes, to measure the bend, but here the filters have a set 'bend' which we can double check if we want, but its the temperature change that is being investigated.
I can look at things in 'a' frequency domain, with a frequency renderer ive made myself, but it would only be useful for looking into details of how the filters work, not what how they affect time domain information.

Quote
Can you show both the phase and magnitude characteristics of the low pass filters you've been examining? Is it a linear phase filter etc.?

I will try to contrast results from some differently implemented lowpass filters. I dont have a raft of tools available to investigate the particulars of the filters i use, so others might be able to scrutinise them better. But i will mostly use the best i get my hands on such as sox, and ssrc. Or if anyone could provide prefiltered samples that would be great.

Ive made a couple of refinements to nodecouple.java, fixed a problem with the 'nodeselection' clause which was unfairly selecting nodes towards the middle of sample intervals, and fewer towards edges. And a few other fixes.
I should get time to generate some data with it, within a day or two.

i also thought of imposing a minimum distance between nodes to attempt to correlate, in order to make extra sure that closer nodes arent 'misplaced'
There is the potential to select between many thousands of accute nodes in source tracks, so employing an unbiased subselection of them will not lead to sparse results. 

Here is what im thinking of examining:

First a correlation between two different tracks of white noise, as a control to check the degree and evenness of correlation between random sources.

Then a correction between two different tracks of pink noise, to double check same.

Then a correlation between a pink noise track and itself upsampled x4, but with the unupsampled track internaly scaled to fit the upsampled one.
This is to observe the difference between the simple node locating formula used by the code, and improvements possible with high quality upsampling.

I also want to check, the evenness of intersample node location (not coupling), so ill output a distribution of intersample node locations (-0.5 to +0.5) of a sample, for pink noise, and then for the music track which will be used.

That will all be for pretesting of the program, and of the source material.

Then I can proceed to outputing distributions of correlated timing of detectable conditions between tracks lowpassed at different levels, to simulate different samplerates.....

so, in a couple of days hopefuly.

cheers'
cg
Title: What is "time resolution"?
Post by: 2Bdecided on 21 November, 2006, 12:17:48 PM
[quote name='ChiGung' date='Nov 21 2006, 16:22' post='451177']
[quote name='2Bdecided' post='451141' date='Nov 21 2006, 10:51']If that black box is a linear phase graphic equaliser, with the bass at +6dB and the treble at -6dB, you're really going to struggle to understand that with your time domain analysis! Whereas if you do a frequency domain analysis and/or if you use some suitable test signals, you can find out what's happening almost immediately.[/quote]
Whatever the black box does, if you want to find out how it affects details in the time domain, you need to examine the time domain. It is irrelevant that the black boxes process might be more difficult to discover in the time domain, its affect on the time domain is apparent in the time domain.

Quote
You're probably thinking "but I want to know what's happening in both domains" - that's fair enough, but those of us who understand audio know that we can grab the data in whichever domain it makes most sense, and then know exactly what is happening in the other domain.

Not really, here in this thread, the issue examined is 'time resolution', not 'frequency resolution'. "Those of you who understand audio" should understand that just because you can only make sense of a proccess in one domain, does not mean its affects on another are insignificant.
[/quote]

No one said that had to be the case.

However, for a linear system, simply knowing the frequency+phase response tells you the impulse response, and therefore everything there is to know about the system. Simply knowing the impulse response tells you the frequency+phase response, and therefore everything these is to know about the system.

Quote

Quote
To put it really simply, we already know all the stuff you're trying to demonstrate, and more importantly we understand why it happens, and why it's not very interesting or important.

That is a simple account which you keep presenting, yet you continue to also present explicity falacious arguements against the investigation, and no there have not been any confident predictions made about the results you might expect, only attempts to colour the results as somehow irrelevant to 'time resolution'


I have given you exact numerical predictions twice now!


Quote

Quote
Post 109 - after the word "conclusion". I explain why quantisation does represent a limit in amplitude resolution, while low pass filtering does not represent a limit in time resolution.

I see, then the comment i made on it generaly, stands then.

A pity you again choose to try and explain your untouchable understandings, instead of commenting on any of the very accessible points I made to you earlier.


?!

Quote
Quote
Quote
It surely is an odd thing to hear engineers report that they cant think of any applications where practical 'time resolution' of an employed encoding format, might matter.

I think Sebastian has already explained and demonstrated precisely how low pass filtering does not reduce the accuracy in such real word experiments, and is often used as a simple way of removing noise and improving accuracy.

That is not another 'get out' clause. You are saying, that innacuracy of the input signal usually eclipses the capabilities of the record. You are saying that practical time resolution of pcm is even lesser than the limit i am investigating.
(That is what you are saying there)


That's not what myself or seb are saying. We've both said very clearly you can downsample to low sample rates (or just low pass filter), and use the sub-sample accuracy very easily. In the real world.

Quote
And elsewhere you present the claim that pcms time resolution is near infinite as algebra's, and leave my contentions about that unanswered.

Oh no - I've just said it again! You've had the proofs several times over.


Quote

As long as you all maintain a united front of experte denial, no one need feel silly right?


I'm trying to get my head around ChiGung world, and it's a very strange place!

Cheers,
David.
Title: What is "time resolution"?
Post by: ChiGung on 21 November, 2006, 01:36:05 PM
Quote
Quote
2Bdecided: "You're probably thinking "but I want to know what's happening in both domains" - that's fair enough, but those of us who understand audio know that we can grab the data in whichever domain it makes most sense, and then know exactly what is happening in the other domain."
Not really, here in this thread, the issue examined is 'time resolution', not 'frequency resolution'. "Those of you who understand audio" should understand that just because you can only make sense of a proccess in one domain, does not mean its affects on another are insignificant.

No one said that had to be the case.
However, for a linear system, simply knowing the frequency+phase response tells you the impulse response, and therefore everything there is to know about the system. Simply knowing the impulse response tells you the frequency+phase response, and therefore everything these is to know about the system.

I said it had to be the case, that statements about time resolution must inform us of details expressed in the time domain. Details expressed in the time domain are most securely derivable from the time domain.(ie by discerning timings)

Quote
I have given you exact numerical predictions twice now!

Of how details will be susceptable to move/change in the time domain for different source material types and levels of bandlimitation?
Sorry, this thread is rather long now, and I missed that. Could you recall them for me?

Quote
Quote
A pity you again choose to try and explain your untouchable understandings, instead of commenting on any of the very accessible points I made to you earlier.
?!


Here is an example of most recent fundamental explainations which you have avoided responding to:
Quote
Just because a peak level created by any combination of frequencies can occur at any subsample location in time, does not imply that a peak represented in pcm as a neccessarily bandlimited frequency spread (limited by the nyquist f), can have its temporal position in the source predicted absolutely precisely.

When you suppose 'resolution' is dependant on the smallest values with which a record can confidently resolve itself Then with pcm, resolution of time and level is effectively infinite because the 'resolution' of algebra is effectively infinite. With such a flattering use of the term 'resolution' (which has been relied on here) the amount of information in a record has almost no contribution at all to its reportable resolution - all you really need are 2 samples in order to have a record which you can say you can resolve with infinite resolution.

Put another way, ....
What is "level resolution" then? Doesn't a pcm record of 8bit words differ in 'level resolution' from one of 16bit words? Or do you all contend that to a properly educated engineer, both records resolution of level are effectively infinite as well?


Quote
Quote
'2B':"I think Sebastian has already explained and demonstrated precisely how low pass filtering does not reduce the accuracy in such real word experiments, and is often used as a simple way of removing noise and improving accuracy."
cg:"That is not another 'get out' clause. You are saying, that innacuracy of the input signal usually eclipses the capabilities of the record. You are saying that practical time resolution of pcm is even lesser than the limit i am investigating."

That's not what myself or seb are saying. We've both said very clearly you can downsample to low sample rates (or just low pass filter), and use the sub-sample accuracy very easily. In the real world.

My summarisation of your points there, was straightforward and accurate.
You respond that you can "use the sub-sample accuracy very easily"
I am aware that you can only do this when you are not significantly bandlimiting the frequency distribution of the source material. Which may often be true for CD audio, but does not hold for pcm generaly.
To force you to deal with the practical reality which you denied, and you and most others collectively riddiculed my understanding of, I have devised and begun an investigation of actual uncertainty of time domain details caused by bandlimitation. Amongst you, because of your own concerns, none can even acknowledge the relevance of the investigation to the topic.
I contend - very certainly, that good, unaffected engineers, could acknowledge the veracity of my investigation and what it is designed to prove to you all.

Quote
cg:"And elsewhere you present the claim that pcms time resolution is near infinite as algebra's, and leave my contentions about that unanswered."
Oh no - I've just said it again! You've had the proofs several times over.

You are saying that time and level resolution are infinite in practice, and that you have defended this claim effectively somewhere. It is an impossible claim to defend, the best attempt so far, has been to deny the relevance of the common meaning of the term "resoltuion"

Quote
cg:"As long as you all maintain a united front of experte denial, no one need feel silly right?"

I'm trying to get my head around ChiGung world, and it's a very strange place!

Fair enough, i dont argue with that really.
The whole world is a strange place too, i dont try and deny it.

when the fog of war lifts, the country will be revealed 
'cg
Title: What is "time resolution"?
Post by: krabapple on 22 November, 2006, 12:18:50 AM
You should be made aware, ChuGung, that your rhetoric resembles that of a crackpot.  I suggest you try to explain your theories and data in reference to current norms, to avoid such rhetoric.
Title: What is "time resolution"?
Post by: 2Bdecided on 22 November, 2006, 05:04:51 AM
You should be made aware, ChuGung, that your rhetoric resembles that of a crackpot.  I suggest you try to explain your theories and data in reference to current norms, to avoid such rhetoric.


I guess the clue is in the name. Google for ChiGung.
Title: What is "time resolution"?
Post by: 2Bdecided on 22 November, 2006, 06:07:47 AM
[quote name='ChiGung' date='Nov 21 2006, 19:36' post='451227']
Quote from: '2B'
Quote from: 'cg'
2Bdecided: "You're probably thinking "but I want to know what's happening in both domains" - that's fair enough, but those of us who understand audio know that we can grab the data in whichever domain it makes most sense, and then know exactly what is happening in the other domain."
Not really, here in this thread, the issue examined is 'time resolution', not 'frequency resolution'. "Those of you who understand audio" should understand that just because you can only make sense of a proccess in one domain, does not mean its affects on another are insignificant.

No one said that had to be the case.
However, for a linear system, simply knowing the frequency+phase response tells you the impulse response, and therefore everything there is to know about the system. Simply knowing the impulse response tells you the frequency+phase response, and therefore everything these is to know about the system.

I said it had to be the case, that statements about time resolution must inform us of details expressed in the time domain. Details expressed in the time domain are most securely derivable from the time domain.(ie by discerning timings)
[/quote]

Thanks for fixing the quotes.

This is a side issue, but if you don't accept that you can analyse in one domain, and then perfectly transform the results into the other domain, then you're denying well known and proven maths, and the FFT function itself!


Quote
Quote
I have given you exact numerical predictions twice now!

Of how details will be susceptable to move/change in the time domain for different source material types and levels of bandlimitation?
Sorry, this thread is rather long now, and I missed that. Could you recall them for me?


Post 109 (http://www.hydrogenaudio.org/forums/index.php?s=&showtopic=49043&view=findpost&p=450207) was the long explanation (though I wrote "sample" when I meant "cycle")
Post 145 (http://www.hydrogenaudio.org/forums/index.php?s=&showtopic=49043&view=findpost&p=450893) was the correcy summary


Quote
Quote from: "2bdecided"
Quote
A pity you again choose to try and explain your untouchable understandings, instead of commenting on any of the very accessible points I made to you earlier.
?!


Here is an example of most recent fundamental explainations which you have avoided responding to:
Quote from: chigung
Just because a peak level created by any combination of frequencies can occur at any subsample location in time, does not imply that a peak represented in pcm as a neccessarily bandlimited frequency spread (limited by the nyquist f), can have its temporal position in the source predicted absolutely precisely.



No one has argued that the waveform peaks in a signal with spectral content above arbitrary frequency f will always remain in the same location after removing all content above frequency f using a low pass filter. Everyone has agreed with you that the peaks will move.


Quote
When you suppose 'resolution' is dependant on the smallest values with which a record can confidently resolve itself Then with pcm, resolution of time and level is effectively infinite because the 'resolution' of algebra is effectively infinite. With such a flattering use of the term 'resolution' (which has been relied on here) the amount of information in a record has almost no contribution at all to its reportable resolution - all you really need are 2 samples in order to have a record which you can say you can resolve with infinite resolution.


It's got nothing to do with the resolution of algebra. It has always been and continues to be a disagreement about the definition of time resolution.

No one has ever doubted that, in "your" definition of time resolution (which is basically about what happens to waveform peaks when a low pass fitler is applied) it is, at worst, +/- 1/2 a wavelength at the cut-off frequency.


Quote

Put another way, ....
What is "level resolution" then? Doesn't a pcm record of 8bit words differ in 'level resolution' from one of 16bit words? Or do you all contend that to a properly educated engineer, both records resolution of level are effectively infinite as well?[/color]


8-bit audio has 256 different possible quantisation levels. 16-bit audio has 65536 different possible quantisation levels.

Any instantaneous amplitude will be quantised (rounded, truncated, etc) to the nearest available level.

This is an easily measurable error. Without dither, this causes distortion, and a discrete "level resolution" limit.

With dither, the error is noise-like, rather than distortion-like, and it makes much more sense to talk about the noise floor.


With dither, if the signal is known to be stationary, then averaging successive samples can indeed increase the resolution. (It works, try it. It becomes just a standard noise-averaging calculation). However, audio signals aren't stationary, so that doesn't strictly apply. Despite this, there is a perceptual effect in frequency analysis (in the ear, in paper, or on a PC!) which works rather well to average the noise in any frequency bands of interest. Just basic filtering and/or frequency analysis really, but the results in dB terms can be surprising.


The similar argument with "time resolution" is that, with correct filtering (anti-alias and anti-image), inter-sample peaks do survive. Without correct filtering, they don't (and you don't know what or where they are).


So the "original" signal must be changed in two ways to survive sampling without further corruption: filter at or below the Nyquist frequency before sampling to prevent aliasing, and add noise at the least significant bit level before quantisation to prevent distortion. The signal that is preserved perfectly in the digital domain is the filtered, noisy signal. You simply select a suitable sampling frequency and bit depth such that the filter cut off and noise level does not perceptibly degrade the signal. No one would claim that the digital version is any better than its parameters allow, and infinite precision is not possible without infinite data.



If you compare the "correct" digital signal (i.e. the one from a filtered, dithered source) with the original analogue signal, then yes - at each instant the amplitude error may be up to +/- 2 least significant bits; the position of individual waveform peaks may have moved by up to +/- 1 sample.

Interestingly, if you do not dither, and do not filter, then the amplitude error is only +/- 1/2 a least significant bit, and the position of individual waveform peaks which survive will only move by up to 1/2 a sample.

Slightly interestingly, if you use noise shaped dither, then the raw amplitude errors get worse, but perceived noise gets less.

However in the first and third examples, the amplitude errors are "just" noise at a pre-defined level, and the waveform peak movements are "just" due to bandlimiting at a pre-defined level. In the second example, the amplitude errors are nasty distortion, and the waveform peaks can be lost entirely (even if they are due entirely to in-band signals), and spurious ones can be created (which have nothing to do with in-band signals).


That's why it's pointless defining amplitude and timing errors in the way you're trying to.

When the digital system is set up properly (filter, dither), then you have a noise floor and a bandwidth limit, not a level or temporal resolution limit.


You can try to argue that the noise floor represents a resolution limit, but that is a misuse of the word resolution.

You can try to argue that the bandwidth limit represents a resolution limit, but that is a misuse of the word resolution.


The resolution is infinite (or "complete", if you like) within the noise and bandwidth limits, and non-existent outside of it.


Quote
Quote
Quote
'2B':"I think Sebastian has already explained and demonstrated precisely how low pass filtering does not reduce the accuracy in such real word experiments, and is often used as a simple way of removing noise and improving accuracy."
cg:"That is not another 'get out' clause. You are saying, that innacuracy of the input signal usually eclipses the capabilities of the record. You are saying that practical time resolution of pcm is even lesser than the limit i am investigating."

That's not what myself or seb are saying. We've both said very clearly you can downsample to low sample rates (or just low pass filter), and use the sub-sample accuracy very easily. In the real world.

My summarisation of your points there, was straightforward and accurate.
You respond that you can "use the sub-sample accuracy very easily"
I am aware that you can only do this when you are not significantly bandlimiting the frequency distribution of the source material. Which may often be true for CD audio, but does not hold for pcm generaly.


The example already raised, rangefinding, works perfectly well.

If I though you would learn anything from it, I'd provide some examples, but you've shown yourself almost uniquely unwilling to learn anything.


Quote
To force you to deal with the practical reality which you denied, and you and most others collectively riddiculed my understanding of, I have devised and begun an investigation of actual uncertainty of time domain details caused by bandlimitation. Amongst you, because of your own concerns, none can even acknowledge the relevance of the investigation to the topic.
I contend - very certainly, that good, unaffected engineers, could acknowledge the veracity of my investigation and what it is designed to prove to you all.


Anyone with any "engineering" knowledge, experience, or even qualification, would laugh at you.

I think you underestimate the high standard of HA's members (and I'm not talking about myself). HA isn't full of idiots who waffle about things they don't understand - the founding members were and are experts in their field who actually do this stuff, either for a living, or for enjoyment. The widespread use of Lame mp3, Nero AAC etc, the developers of which are regular posters on this board, speaks volumes.

This isn't some audiofool repository where people discuss the effect of fairies on the sound of their loudspeaker cables.



If you want to do something interesting, instead of trying to prove something which we all already accept (but don't think is important), why not try to find a mechanism by which it might be important! E.g. the human ear isn't a linear time-frequency analyser, so is it possible that a low pass filter's effect in the frequency domain can be inaudible, yet it's effect in the time domain is audible?

It's a question many have pondered. Though the human ear is clearly very non-linear, I can't bring myself to believe that any of the mechanisms in there allow it to behave like that.

The only aspects where the human ear's "time resolution" is better than you would expect from the frequency response are exactly the same aspects where the "time resolution" of PCM "is infinite". If you can show that the human ear, while it cannot hear frequencies above, say, 25kHz, can detect the movement of those waveform peaks caused by low pass filtering at 25kHz, you would be on to something.

Cheers,
David.
Title: What is "time resolution"?
Post by: ChiGung on 22 November, 2006, 11:48:34 AM
@2B and others,

Having examined the effects of bandlimitation on time domain details ......
I am in a position to thank you now for your continued efforts to argue the situation,
And to relinquish some truth to the claims made that time resolution of pcm
can be practicaly negligable.
And to acknowledge the failure of previous arguements I made which contended otherwise.

.....And by association, to perhaps acknowledge some merits in experience garnered with formal education

After I checked and tweaked the selection clause of accute reversals of apparent level (peaks/valleys) in my investigative program. I did find that nodes temporal position between differently lowpassed samples was very unaffected unless significant energy was present in the band removed by the lowpass.

A great 'immunity' to the removal of unenergetic frequency bands is surely a sublime and powerful aspect of bandlimited pcm interpretation.
I had not expected or described correctly, or acknowledged sensibly, that cutoff frequencies can normaly contain so little energy as to have negligable affect on timing details.

In fact i had expected and suggested that very low levels of rounding / quantisation / dither /noise should have more impact than i have been able to observe.

Without being able to find another explaination for the central spike in my correlation plots, i have had to acknowledge these conclusions, that an innate 
ability of pcm is the capability of maintaining accuracy of time details far finer than employed sample rates for adequately bandlimited source.
And also, for sources not completely adequately prebandlimited for the target sample rate, considerable resilience of temporal accuracy is also displayed.

I can understand now, why 'time resolution' of pcm is a discouraged/redefineable concept and that its ultimate limit can be that of the error limits of the systems used to process it.

Later I will post a simple sequence of correlation charts which illustrate the matter.

@2Bdecided
- the quotes break, when there are too many used in the reply (wether they are correctly closed or not)
Quote
This is a side issue, but if you don't accept that you can analyse in one domain, and then perfectly transform the results into the other domain, then you're denying well known and proven maths, and the FFT function itself!

I have understood this situation, but went straight to observing the time domain, for time domain details because I am not practiced in the methods which you might use to get the time domain details otherways.

Quote
Post 109 (http://www.hydrogenaudio.org/forums/index.php?s=&showtopic=49043&view=findpost&p=450207) was the long explanation (though I wrote "sample" when I meant "cycle")
Post 145 (http://www.hydrogenaudio.org/forums/index.php?s=&showtopic=49043&view=findpost&p=450893) was the correcy summary
I can read that more clearly now, but with the level of mutual exasperation at the time I got tripped up by expressions such as this:
Quote
Magic! Thus we "prove" (though it's more of a hand waving explanation!) your +/- 1/2 sample "time resolution", but we see it's really about frequency resolution.

In that case, it could be said that combinations of bandwidth of signal and bandlimitation of rate can produce timing uncertainties. I accept the veracity of the point that different bandwidths of the same source may not contain the same events anymore to correlate, but not yet the exclusivity of that point, maybe in time.... 

Quote
No one has ever doubted that, in "your" definition of time resolution (which is basically about what happens to waveform peaks when a low pass fitler is applied) it is, at worst, +/- 1/2 a wavelength at the cut-off frequency.

I had not confirmed that figure, only expected it from observing 'ealry principals' but if accurate there is something natural/relevant about that figure(?) perhaps that when storing 'least ideal' signals that will be the maximum expectable accuracy of readable time details?

Quote
....The similar argument with "time resolution" is that, with correct filtering (anti-alias and anti-image), inter-sample peaks do survive. Without correct filtering, they don't (and you don't know what or where they are).

Somewhere, i also imagined small higher frequencies which modify the forms created by collections of larger lower frequencies. But it turned out such details seem to be miniscule unless there is a great deal of noise in the higher band.

Quote
Interestingly, if you do not dither, and do not filter, then the amplitude error is only +/- 1/2 a least significant bit, and the position of individual waveform peaks which survive will only move by up to 1/2 a sample.

I can now more readily expect your word for such things'

Its a pity, that post is lost in quotemess, i cant respond to all of it now, maybe you can cut out some quotes to make it display properly for others browsing the topic.

Quote
This isn't some audiofool repository where people discuss the effect of fairies on the sound of their loudspeaker cables.

Accepted, but when criticisms employ riddicule, it can read that way.

I hope those of you who put substantial effort into clarifying matters, might forgive me for misreadings and polemic i exhibited.

Appreciating most of your outputs 

-R&Dchung
Title: What is "time resolution"?
Post by: ExUser on 22 November, 2006, 01:10:30 PM
Heh, I've been there (http://www.hydrogenaudio.org/forums/index.php?showtopic=34384), though maybe to a lesser degree. Good to see you came around eventually.
Title: What is "time resolution"?
Post by: ChiGung on 22 November, 2006, 01:49:57 PM
Thanks Canar, i was unsure whether to display your post - but see that you have have actualy been quite straightforward and civil.

-truce,

ill just run off these plots and then my levels of humility and stress should finaly normalise 

best'
cg
Title: What is "time resolution"?
Post by: ChiGung on 22 November, 2006, 03:46:10 PM
using a cut from the 96kHz 'bismark' recording sample, first a correlation against itself as control:

Code: [Select]
---------- Run java ----------
Reading in biss.wav

  Opening biss.wav
  SampleRate:96000
  Stereo input
  Samples 983043
  Trackime at 96000Hz :10.240

reading 10.240 seconds (of 1 channel)(Change chnkread for more)
Locating Nodes...

Total nodes in: biss.wav:8791 Total nodes in: biss.wav:8791
Missednodes=223, discreps=8568, Searchednodes=8791

8568:                                        **                                    
8032:                                        **                                    
7497:                                        **                                    
6961:                                        **                                    
6426:                                        **                                    
5890:                                        **                                    
5355:                                        **                                    
4819:                                        **                                    
4284:                                        **                                    
3748:                                        **                                    
3213:                                        **                                    
2677:                                        **                                    
2142:                                        **                                    
1606:                                        **                                    
1071:                                        **                                    
1535:                                        **                                    
----------------------------------------------------------------------------------------
Sums:    0     0     0     0     0     0    8568   0     0     0     0     0     0  
Devs: <  58    48    38    28    17    7     2     12    23    33    43    53    64  >

Distribution chart, range=128n (256n=1 sample)

Normal Termination
Output completed (1 sec consumed).

(The plot is currently tallying discrepancies of up to 1/2 a 96kHz sample, either way there)

And at the same scale, the origional 96k compared to:
soz.exe biss.wav biss48.wav filter 0-24000 
("sinc windowed lowpass w/len=128" simulating downsample to 48kHz:)

Code: [Select]
Total nodes in: biss48.wav:8506
Total nodes in: biss.wav:8791

Missednodes=741, discreps=7765, Searchednodes=8506

3950:                                        **                                    
3703:                                        **                                    
3456:                                        **                                    
3209:                                        **                                    
2962:                                        **                                    
2715:                                        **                                    
2468:                                        **                                    
2221:                                        **                                    
1975:                                        **                                    
1728:                                        **                                    
1481:                                        **                                    
1234:                                        ** **                                
_987:                                        ** **                                
_740:                                     ** ** **                                
_493:                                     ** ** **                                
_246:                                  ** ** ** ** **                              
----------------------------------------------------------------------------------------
Sums:    2     7     10    21   110   307   3950  429   123    39    14    5     3  
Devs: <  58    48    38    28    17    7     2     12    23    33    43    53    64  >

Distribution chart, range=128n (256n=1 sample)


And at the same scale, the origional 96k compared to:
soz.exe biss.wav biss32.wav filter 0-16000

Code: [Select]
Total nodes in: biss32.wav:7089
Total nodes in: biss.wav:8791

Missednodes=1769, discreps=5320, Searchednodes=7089


  534:                                        **                                    
  500:                                        **                                    
  467:                                     ** ** **                                
  433:                                     ** ** ** **                              
  400:                                     ** ** ** **                              
  367:                                  ** ** ** ** ** **                          
  333:                               ** ** ** ** ** ** ** **                        
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  166:                         ** ** ** ** ** ** ** ** ** ** **                    
  133:                      ** ** ** ** ** ** ** ** ** ** ** ** **                  
  100:                ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** **              
   66:             ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** **      
   33:    ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** **
----------------------------------------------------------------------------------------
Sums:    40    57   112   151   288   387   534   443   335   160    92    76    65  
Devs: <  58    48    38    28    17    7     2     12    23    33    43    53    64  >

Distribution chart, range=128n (256n=1 sample)


and finaly, at half previous scale, the origional 96k compared to:
soz.exe biss.wav biss24.wav filter 0-12000

Code: [Select]
Total nodes in: biss24.wav:5374
Total nodes in: biss.wav:8791

Missednodes=2136, discreps=3238, Searchednodes=5374


  280:                                        **                                    
  262:                                     ** **                                    
  245:                                     ** ** **                                
  227:                                     ** ** **                                
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   87:                ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** **              
   70:             ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** **              
   52:          ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** **        
   35:    ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** **
   17:    ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** **
----------------------------------------------------------------------------------------
Sums:    38    57   101   115   158   211   280   223   170   109    67    49    43  
Devs: < 117    97    76    56    35    15    5     25    46    66    87   107   128  >

Distribution chart, range=256n (256n=1 sample)


While making these i rewrote the correlation tallying loop, and a central
spike in all plots was reduced, because the previous tallying loop was buggy
like this: counting, vals from -3 to -2, -2 to -1, -1 to 1, 1 to 2, 1 to 3 etc..
(it was making the middle tally twice as big as it should have been),
This would have had something to do with my previous concessions.
But they probably should have been made even without the appearance of the spike,
and of course the simple soltution ive used to locate nodes has not been checked either.

So ill leave it here for now. 

-trying (in many ways),
cg
Title: What is "time resolution"?
Post by: AstralStorm on 22 November, 2006, 04:12:09 PM
using a cut from the 96kHz 'bismark' recording sample, first a correlation against itself as control:

<snip>

While making these i rewrote the correlation tallying loop, and a central
spike in all plots was reduced, because the previous tallying loop was buggy
like this: counting, vals from -3 to -2, -2 to -1, -1 to 1, 1 to 2, 1 to 3 etc..
(it was making the middle tally twice as big as it should have been),
This would have had something to do with my previous concessions.


Not at all. You're bandlimiting the signal below Nyquisit's theorem rule, therefore time domain change must happen.
Try that with a 1000-sample non-square wave instead and compare the effect.

Your starting signal requires exactly 96 kHz frequency resolution; 1/96000 s time resolution (and is half that frequency) to be encoded properly.
There are no such real-world audio signals short of USG (where you should use something in MHz range maybe?) or noise.

Just sample at a higher rate than required and you're okay.
Title: What is "time resolution"?
Post by: ChiGung on 22 November, 2006, 05:38:35 PM
While making these i rewrote the correlation tallying loop, and a central
spike in all plots was reduced, because the previous tallying loop was buggy
like this: counting, vals from -3 to -2, -2 to -1, -1 to 1, 1 to 2, 1 to 3 etc..
(it was making the middle tally twice as big as it should have been),
This would have had something to do with my previous concessions.

Not at all.

To be clear, it was the appearance of an exaggerated central bar in the plots which made me reconsider previous arguements, but as i said i think that was  probably a good thing.
Title: What is "time resolution"?
Post by: 2Bdecided on 23 November, 2006, 06:51:32 AM
Hey CG,

You'd got it in post 159 - quit while you're ahead.

Anyway, you managed to say what everyone was saying - there has to be something up there which you're removing in order for the peaks to move. If there's little up there, it has little effect, so removing it doesn't do much. Even your "correct" plots show this.

What you're doing is a kind of perverse frequency analysis - the proportion of peaks which "move" is "kind of, on average" somewhat proportional to the amount of content you've removed. So dropping a recording with lots of HF energy down to 32kHz sampling will move more peaks than dropping a recording with little HF energy down to 32kHz sampling will.

Have fun. Glad you came back to say what you'd found.

As Canar says, we've all been there. This was my best moment...

http://www.hydrogenaudio.org/forums/index....mp;#entry183857 (http://www.hydrogenaudio.org/forums/index.php?showtopic=18633&st=0&p=183857&#entry183857)
(you also need to read Pio2001's reply immediately below!)


My own "Nyquist was wrong" moments have been argued through with my PhD Professor, and on my own with lots of pieces of paper covered with scribbled diagrams and numbers! That's why I can be so confident that Nyquist was right!  The full implications are more interesting than most people take the time to realise.

Cheers,
David.
Title: What is "time resolution"?
Post by: ChiGung on 23 November, 2006, 10:39:11 AM
Anyway, you managed to say what everyone was saying - there has to be something up there which you're removing in order for the peaks to move. If there's little up there, it has little effect, so removing it doesn't do much. Even your "correct" plots show this.

To be clear (so not to be misrepresented) I repeatedly confirmed throughout this thread when presented with this that i understood that (signals with little energy above the cutoff would not have timings changed much within them)
The appearance of an inexplicable spike in my plots forced me to accept that there maybe something else about the system I handnt perceived -which is always a good thing.
So the concession was about that posibility (which stands, always) and over understandable use of terms.

Quote
What you're doing is a kind of perverse frequency analysis

What i did was attempt to move the debate about pcm 'time resolution' to examine the effects of bandlimitation (simulating sampling rates) on discrete timeable details. I dont think I can ever accept such an examination as 'perverse' If I could have used an adequate method to calculate times, then the plots generated would inform us about timing uncertainties to expect for different source types at different rates. With the less than adequate/untested method i used, it is just an illustration of 'what could be seen'

By 'details' there, i mean conditions in the waveform which may be physicaly/electricaly/origionaly formed by a wider band than that which is selected to record.

I can accept your assumption that the desireable section of reality to store in pcm is only the bandlimited section we might hear, so for your purposes the resolution of the record can be said to be infinite, but my focus is not the same, in my personaly developed conception of the matter (for no doubt different purposes), the discarded band is only completely dismissable when it is completely empty. Because i am not focused on audio capabilities but on informational capabilities.

Quote
- the proportion of peaks which "move" is "kind of, on average" somewhat proportional to the amount of content you've removed.

This is valid knowledge. Uncertain tendencies are quantifiable and useful.

Ive always understood the term 'resolution' to mean the finest detail with which a record can infer the reality with which its purpose is to store. -It may be a peculiar or plain incorrect use of the term for some subjects, but for me its a natural summary of most ways the term is employed.

Quote
My own "Nyquist was wrong" moments have been argued through with my PhD Professor, and on my own with lots of pieces of paper covered with scribbled diagrams and numbers! That's why I can be so confident that Nyquist was right!  The full implications are more interesting than most people take the time to realise.

I had a nyquist is wrong slip here, a year or so I think - that wasnt my error here. It was perhaps foremost, to not listen well enough and separate my own concepts from the solidified technical ones put to me. And to try and debate with a whole group of outspoken initiates of a feild of study, uninitiated notions concerning the same material as their feild.- An ultimately masochistic activity. Some errors in expression, others in manner and temper.

I do hope some day to be in a position to study the academic findings and methods around this material, and my understanding will be broadened by it.
Only now im not in that position, and i have unusual original methods to explore now which consume most of my available attentioned.
Thankyou for your representation and giving me some familiarity with your approach, before the times when I can learn the particulars of it.

all the best'
cg
Title: What is "time resolution"?
Post by: Woodinville on 24 November, 2006, 02:53:40 AM
After I checked and tweaked the selection clause of accute reversals of apparent level (peaks/valleys) in my investigative program. I did find that nodes temporal position between differently lowpassed samples was very unaffected unless significant energy was present in the band removed by the lowpass.



Hence my advice to try the summed Gaussian pulses, which you first spurned, then denied, then ignored.

Yes, it really is that simple, and, yes, you can make transients out of summed sine waves, and yes, the value of examining things in various domains is that what is hard in one is easy in the other.