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Hydrogenaudio Forum => General Audio => Topic started by: zephirus on 2003-05-11 17:40:30

Title: 44 KHz (CD) not enough !? (Nyquist etc.)
Post by: zephirus on 2003-05-11 17:40:30
Remarks and conclusions added May 12 2003 - 1:55 PM, and edited May 14 2003 - 08:35 AM :

My dubious claims unfortunately had a very short life span due to the very successful enlightenment efforts of tigre, 2Bdecided, KikeG and mrosscook.

In short: I failed to come up with evidence that cd quality (I mean 44.1 KHz digital sampling) is somehow problematic. It basically was a story of using the wrong tools, jumping to the wrong conclusions, and not having enough of a clue about signal processing.

Nevertheless, I tried again to make less daunting claims that the 44.1 KHz digital sampling rate is not enough to represent all signals less than 22.05 KHz correctly.

And again my claims had a very short life span. This time due to further enlightenment efforts by DonP, 2Bdecided, KikeG, mrosscook and SikkeK.

The conclusion: Arguing against the technical specification of  cd quality (44.1 KHz/16 bit) should not be tried by someone that severely lacks in signal processing clue (like me).

If the cd sound quality is perceived as suboptimal, it may have more to do with poor recording, poor mastering, and suboptimal reproduction equipment (i.e. cd-player and sound system/headphones).

What one still could try are listening tests:

Such tests would need to be done with one and the same high end hardware for all signals and all tests (preferably with 192 KHz resolution, with 20-24 bit, and with a DAC that is perfectly shielded and outside of any system that is rich of EM signals, like a computer, and has a near perfect analog circuitry). And when testing the 192 KHz signal against the 44.1 KHz signal, the latter would need to be a digitally downsampled version (to 44.1 KHz), which was upsampled to 192 KHz again. Using the best available algorithms (Cool Edit may do a resonable job here).

And still, asking the test persons for audible artifacts would most likely not work at all. It might be more rewarding letting them rate how the music "felt" (e.g.: more or less "relaxing" for music that should be "relaxing" but is rich in high frequency content nonetheless). This could be done in a way that is scientifically sound and statistically relevant.

My original post:

____________

I have to admit: This 44.1 KHz topic more or less has been discussed to death already. It also seems likely that the following problem has been discussed on Hydrogenaudio several times as well (but I had no luck with the search function).

The 44.1 KHz sampling rate (CD quality) seems to create an infinite number of "mirrors" at its harmonics. These in turn create a complex set of distortion frequencies for every frequency in the analog source.

The strongest "mirror" is at at 22.05 KHz (44.1 KHz/2). But the problem can easily be demonstrated with the one at 11025 Hz (44.1 KHz/4) as well: if one creates a sine signal of 11025-1000 = 10025 Hz in a sound editor (e.g. Audacity, using a 44.1 KHz sampling rate) and plots the spectrum, then two additional frequencies are shown: one at 1000 Hz and one at 22050-1000 = 21050 Hz. More distortion signals can be seen if the FFT resolution is increased above 1024.

The general problem seems to be that a sampling frequency of 44.1 KHz does not guarantee that frequencies below 22.05 KHz are represented faithfully (as is mostly believed). Instead it probably more or less only guarantees that in the resulting complex signal the source frequency is significantly stronger than the numerous distortion signals.

Of course, the remaining question is if these distortions are audible (they resemble pretty much amplitude modulation). I cannot really test this with 44.1 KHz since I don´t have a 96 KHz soundcard. But the example with 11024 Hz surely looks rather disturbing (when looking at the waveform) and doesn´t sound very clean as well.

Did anyone do any respective (blind) listening tests?

zephirus

PS:
The following example is very audible: When using a sampling frequency of only 2000 Hz (instead of 44100 Hz) and creating a sine frequency of 750 Hz (well below the Nyquist limit of 1000 Hz) then the result sounds pretty ugly (it´s some kind of mixed signal of 750 Hz, 250 Hz and 1250 Hz).
Title: 44 KHz (CD) not enough !? (Nyquist etc.)
Post by: tigre on 2003-05-11 22:59:50
44.1KHz is enough to represent everything below 22.05Khz perfectly (unless you're talking about too high amplitude causes clipping - or quantization distortion/dither noise).

The additonal frequencies you see in spectral view are most likely caused by poor / "time-efficient" algorithms used by Audacity to create spectral view. To prove this you could try to
1. use another program (e.g. Cool Edit trial version)
2. upsamle using something decent (SSRC/foobar2000+diskwriter to a high sampling rate like 88200 or 96000 Hz and have a look at it with spectral view again. If the additional frequencies are visible somewhere else (or not at all) it's proven that they have not really been there before, otherwise they'd have been there after resampling too.

About your "audible" example: What do you use for playback? I could bet it's something that resamples (probably poorly) causing the "ugly" sound. Again: resample using something decent - and be sure you choose a volume for your test tones that can be handled by your soundcard('s driver). If you lower volume by e.g. 10dB and it sounds better/fine you'll know who's the guilty.
Title: 44 KHz (CD) not enough !? (Nyquist etc.)
Post by: mrosscook on 2003-05-12 04:32:47
The most recent thread to flog this issue is here (http://www.hydrogenaudio.org/forums/index.php?act=ST&f=1&t=8909&hl=bad+quality).  The posts by DigitalMan and KikeG speak to your aliasing issues, I think.
Title: 44 KHz (CD) not enough !? (Nyquist etc.)
Post by: 2Bdecided on 2003-05-12 12:08:17
Quote
I have to admit: This 44.1 KHz topic more or less has been discussed to death already. It also seems likely that the following problem has been discussed on Hydrogenaudio several times as well (but I had no luck with the search function).

Follow the link that's been posted.

Quote
The 44.1 KHz sampling rate (CD quality) seems to create an infinite number of "mirrors" at its harmonics.

Yes. The correct term is "image" - they're images of the orginal spectrum from 0-22.05kHz. The 22.05-44.1kHZ one is a reflection, the 44.1-66.15kHZ is a direct copy etc etc etc etc

Quote
These in turn create a complex set of distortion frequencies for every frequency in the analog source.


No, they don't. They're filtered out perfectly in a theoretically "ideal" DAC, and well enough in many real-world ones.

Quote
The strongest "mirror" is at at 22.05 KHz (44.1 KHz/2).


This is nonesense. Sorry!

Quote
But the problem can easily be demonstrated with the one at 11025 Hz (44.1 KHz/4) as well: if one creates a sine signal of 11025-1000 = 10025 Hz in a sound editor (e.g. Audacity, using a 44.1 KHz sampling rate) and plots the spectrum, then two additional frequencies are shown: one at 1000 Hz and one at 22050-1000 = 21050 Hz. More distortion signals can be seen if the FFT resolution is increased above 1024.


You're doing something wrong, or at least, your software isn't working properly.

Quote
The general problem seems to be that a sampling frequency of 44.1 KHz does not guarantee that frequencies below 22.05 KHz are represented faithfully (as is mostly believed).


Yes it does. Not everyone follows the full implications of this, but it is true.

Quote
PS:
The following example is very audible: When using a sampling frequency of only 2000 Hz (instead of 44100 Hz) and creating a sine frequency of 750 Hz (well below the Nyquist limit of 1000 Hz) then the result sounds pretty ugly (it´s some kind of mixed signal of 750 Hz, 250 Hz and 1250 Hz).


Your sound card probably can't reproduce a 2k sampled digital audio signal. It is probably making a complete mess of resampling it to some other value, and/or not using the correct filer to remove the high frequency (i.e. over 1kHz ) image frequencies.

If you get Cool Edit, you can generate a 1kHz tone sampled at, say, 44.1kHz. Resample it to 2kHz. Resample it back to 44.1kHz (so your sound card can play it). You should find that it survived it's little trip through 2kHz sampling pretty will. If the tone started and ended with a "click" then those clicks may sound different, but the tone shouldn't.

Have fun!

Cheers,
David.
Title: 44 KHz (CD) not enough !? (Nyquist etc.)
Post by: zephirus on 2003-05-12 13:07:28
Quote
The additonal frequencies you see in spectral view are most likely caused by poor / "time-efficient" algorithms used by Audacity to create spectral view.

You are right, of course. I don´t see these distortion frequencies in the Cool Edit spectrum analyser. I thank you for your suggestion to use Cool Edit!
Nevertheless, I played around with Audacity and Cool Edit some more and now believe that I understand all this somewhat better now (details in a later posting).

Quote
44.1KHz is enough to represent everything below 22.05Khz perfectly

I´m very confident that this is not the case. Just try this: Create a sine signal (using e.g. Cool Edit) at 11024 Hz (with a few seconds duration, using a sampling frequency of 44.1 KHz). Then simply look at the waveform (it´s obviously strongly amplitude modulated). This is a corner case, admittedly (extremely close to a strong harmonic of the sampling frequency).

Quote
About your "audible" example: What do you use for playback? I could bet it's something that resamples (probably poorly) causing the "ugly" sound.

Yes, that 2000/750 Hz example is fishy. Audacity simply doesn´t seem to do the necessary upsampling filtering. Cool Edit filters pretty much perfectly.

zephirus
Title: 44 KHz (CD) not enough !? (Nyquist etc.)
Post by: zephirus on 2003-05-12 13:14:09
Quote
The most recent thread to flog this issue is here (http://www.hydrogenaudio.org/forums/index.php?act=ST&f=1&t=8909&hl=bad+quality).  The posts by DigitalMan and KikeG speak to your aliasing issues, I think.

Thanks, these posts are very interesting.

But the following assertion of KikeG is simply wrong, as it seems (see my previous post about creating a sine signal with Cool Edit).

Quote
...any decent 44.1 KHz DAC is free of aliasing problems, frequency response problems, phase problems, ripple problems, etc, up to around 21 KHz or more.


zephirus
Title: 44 KHz (CD) not enough !? (Nyquist etc.)
Post by: KikeG on 2003-05-12 13:33:59
Quote
I´m very confident that this is not the case. Just try this: Create a sine signal (using e.g. Cool Edit) at 11024 Hz (with a few seconds duration, using a sampling frequency of 44.1 KHz). Then simply look at the waveform (it´s obviously strongly amplitude modulated). This is a corner case, admittedly (extremely close to a strong harmonic of the sampling frequency).

This apparent amplitude modulation is just a side effect of viewing the samples in time domain. If you play the tone, you'll hear no amplitude modulation. Surprise?? If you zoom a little bit into the wave, you will see how Cool Edit "interpolates" between samples and creates a continuous waveform that is not modulated. This interpolation is more or less the same one that a DAC performs: looking at the analog output of a 44.1 DAC won't show and amplitude modulation in this particular case. You can check it with an oscilloscope, you will see the same kind of continuous shape that Cool Edit interpolates.
Title: 44 KHz (CD) not enough !? (Nyquist etc.)
Post by: tigre on 2003-05-12 14:16:15
Quote
... Just try this: Create a sine signal (using e.g. Cool Edit) at 11024 Hz (with a few seconds duration, using a sampling frequency of 44.1 KHz). ...

I've done this already.

[EDIT] The following can't be the reason for "amplitude modulation" of 11024 Hz signal. The (hopefully) correct explanation is given in maths part (*).
___________________________
The following is true for a test tone near to Nyquist limit, e.g. a 22049Hz tone at 44100Hz sampling frequency:
[/EDIT]

The reason for the "amplitude modulation" visible in waveform view is the limited number of samples ("window") used for calculating the waveform. Try this: Create silence with Cool Edit and change one single sample in the middle to e.g. +30000. Now zoom in that you can see the waveform between the samples and zoom in vertically. You'll see that the changed sample causes a changed waveform in a range of 42 samples. In reallity this range is (should be) not 42, of course, but infinite. 42 is chosen, probably because it's a compromise between exactness of the result and computation power needed.
So if more samples e.g. 420 or 4200 arround a gap between two sample values are taken into account to compute the shape of the waveform in this gap, there won't be an "amplitude modulation" left.

Of cours you could choose a "test frequency" of 22049.99 Hz and you'll see "amplitude modulation" again, but I hope you get the point ...
______________
*
OK. Finally some maths: I've created the 11024 signal as you suggested and zoomed in at the max. and min. positions of so called "amplitude modulation" to get the sample values:

max.: 0 10361 0 -10361 0 10361 0 -10361 ...
min.: 7326 7326 -7326 -7326 7326 7326 -7326 ...

This corresponds to y=a*sin(alpha) with alpha values:
max:  0° 90° 180° 270° 360° ...; a = 10361/sin(90°) = 10361
min: 45° 135° 225° 315° 405° ...; a = 7326/sin(45°) = 7326*2^(1/2)= 10361

Result: at both positions the amplitude is identical, the reason for the visible "amplitude modulation" must be something cool Edit related.
Title: 44 KHz (CD) not enough !? (Nyquist etc.)
Post by: zephirus on 2003-05-12 14:23:23
Quote
Quote
I´m very confident that this is not the case. Just try this: Create a sine signal (using e.g. Cool Edit) at 11024 Hz (with a few seconds duration, using a sampling frequency of 44.1 KHz). Then simply look at the waveform (it´s obviously strongly amplitude modulated). This is a corner case, admittedly (extremely close to a strong harmonic of the sampling frequency).

This apparent amplitude modulation is just a side effect of viewing the samples in time domain. If you play the tone, you'll hear no amplitude modulation. Surprise?? If you zoom a little bit into the wave, you will see how Cool Edit "interpolates" between samples and creates a continuous waveform that is not modulated. This interpolation is more or less the same one that a DAC performs: looking at the analog output of a 44.1 DAC won't show and amplitude modulation in this particular case. You can check it with an oscilloscope, you will see the same kind of continuous shape that Cool Edit interpolates.

You are right, of course. So I better retract all my claims.

Seems like just another futile attempt in proving some inferiority of cd quality sampling. Oh dear.

I checked this in Cool Edit - thanks for your detailed description. So this again was more or less an artifact of the missing filtering/interpolation in Audacity (where it really looks like an amplitude modulation at any zoom factor). I should have verified this more thoroughly in Cool Edit. And generally should use more high end programs for such things anyways.

I also upsampled the signal to 192 KHz with Cool Edit. And, as suspected, the result was a clean 11024 Hz signal with no amplitude modulation.
Title: 44 KHz (CD) not enough !? (Nyquist etc.)
Post by: zephirus on 2003-05-12 17:12:21
Quote
OK. Finally some maths: I've created the 11024 signal as you suggested and zoomed in at the max. and min. positions of so called "amplitude modulation" to get the sample values:

max.: 0 10361 0 -10361 0 10361 0 -10361 ...
min.: 7326 7326 -7326 -7326 7326 7326 -7326 ...

This corresponds to y=a*sin(alpha) with alpha values:
max: 0° 90° 180° 270° 360° ...; a = 10361/sin(90°) = 10361
min: 45° 135° 225° 315° 405° ...; a = 7326/sin(45°) = 7326*2^(1/2)= 10361

Result: at both positions the amplitude is identical, the reason for the visible "amplitude modulation" must be something cool Edit related.

Thanks for your detailed explanations!

I believe I get this. As it seems one shouldn´t expect the digital sample values to be a visual representation of the analog source signal. And instead perhaps view the digital values simply as the right sequence of kicks that need to be delivered to the output filter. Which then indeed seems to recreate the original signal very well.

Quote
The following can't be the reason for "amplitude modulation" of 11024 Hz signal


Perhaps Cool Edit doesn´t bother with the interpolation/filtering business if one hasn´t zoomed in sufficiently. Then it might just average a rather small number of sample-values and calculate the wave amplitudes for display this way (for performance reasons maybe). Which would work well pretty much always - except in extreme cases like the 11024 Hz signal.

Anyways, all three artifacts I saw/heared were basically due to the missing filtering in Audacity (and my lack of knowledge that this filtering step is absolutely essential, even for just looking at the waveform). And in Cool Edit I obviously should have looked more thoroughly.

Quote
Of course you could choose a "test frequency" of 22049.99 Hz


Indeed I did... see next post.

Thanks again, and I hope you found this all not too much a waste of your time.

zephirus
Title: 44 KHz (CD) not enough !? (Nyquist etc.)
Post by: zephirus on 2003-05-12 18:22:46
Quote
Quote

The 44.1 KHz sampling rate (CD quality) seems to create an infinite number of "mirrors" at its harmonics.

Yes. The correct term is "image" - they're images of the orginal spectrum from 0-22.05kHz. The 22.05-44.1kHZ one is a reflection, the 44.1-66.15kHZ is a direct copy etc etc etc etc

Thanks for your details (which are new to me). But I believed to see "distortion mirrors" at frequencies below 44.1 KHz (at "sub-harmonics", perhaps).

Quote
Quote

These in turn create a complex set of distortion frequencies for every frequency in the analog source.

No, they don't. They're filtered out perfectly in a theoretically "ideal" DAC, and well enough in many real-world ones.

Quote
This is nonesense. Sorry!

I feel forced to agree.

Quote
You're doing something wrong, or at least, your software isn't working properly.

Yes - unfortunately you hit the nail on the head here.

Nevertheless:

Quote
If you get Cool Edit, you can generate a 1kHz tone sampled at, say, 44.1kHz. Resample it to 2kHz. Resample it back to 44.1kHz (so your sound card can play it). You should find that it survived it's little trip through 2kHz sampling pretty will.


Here, at last, you seem to be wrong. A 1000 Hz signal doesn´t survive the roundtrip. A 999 Hz signal survives partly, but is very much off. A 995 Hz signal is better. And a 980 Hz signal survives pretty well. Pre/post-filtering was enabled (which generally seems to be a good idea), and conversion quality was set to maximum (very computation intensive). The filters seemingly need some significant frequency headroom. But not really much.

Quote
Quote

The general problem seems to be that a sampling frequency of 44.1 KHz does not guarantee that frequencies below 22.05 KHz are represented faithfully (as is mostly believed).

Yes it does. Not everyone follows the full implications of this, but it is true.


22050 Hz seems to be the first frequency that cannot be reproduced (Cool Edit simply produces silence in this case, which basically seems to be correct). Frequencies below but near 22050 Hz do not seem to be reproduced correctly as well. So at least I have a very minor point. But anything below 20 KHz most likely can be reproduced very well. So this point is irrelevant. Just a little headroom needed for the output filter.

Anyways, thanks for you detailed reply!

zephirus
Title: 44 KHz (CD) not enough !? (Nyquist etc.)
Post by: zephirus on 2003-05-12 20:54:49
While my original dubious claims obviously had a very short life span, one minor issue remains:

The idea that digital sampling is able to reproduce any frequency up to half the sampling rate still seems to be wrong.

My rationale here is: A very steep output (lowpass cutoff) filter is absolutely necessary for reconstructing the original input signal. Without it there are aliasing distortions from the digital signal. And these aliasing distortions will create distortion frequencies well below 22.05 KHz (hopefully).

But no filter can realistically work without any frequency headroom.

Therefore: some frequency headroom is absolutely needed, and the claim that a sampling rate of X can correctly reproduce any frequency up to X/2 is technically not really true.

But the headroom needed seems to be rather small. Perhaps 2 KHz for a sampling rate of 44.1 KHz. Or 10% of the useful frequency range. So this issue seems to be irrelevant for frequencies up to 20 KHz (with a sampling rate of 44.1 KHz).

Therefore, I still do not have a point. But I´m still trying...

Next time, perhaps.

zephirus
Title: 44 KHz (CD) not enough !? (Nyquist etc.)
Post by: _Shorty on 2003-05-12 21:42:46
I thought that's what over-sampling DACs were for.
Title: 44 KHz (CD) not enough !? (Nyquist etc.)
Post by: zephirus on 2003-05-12 22:39:11
Quote
I thought that's what over-sampling DACs were for.

Hm... good point.

But it seems: Whatever you do with the digital signal before it becomes an analog output signal simply is some kind of filtering. Oversampling may be a part of it (or not).

Judging from the cpu intensity of Cool Edit´s upsampling (or oversampling) algorithm: Upsampling seems to be a very difficult task.

Upsampling/oversampling cannot recreate information that was lost at the time when the source signal was digitally sampled.

And for a sine signal of 22.05 KHz: When sampling it with 44.1 KHz the amplitude of the resulting digital signal is completely random (this can easily be demonstrated - for real this time).

For me, it seems inevitable that frequencies below 22.05 Khz suffer from the same problem (but to a lesser extent, of course). But this does not seem to be significant for frequencies below 20 KHz.

Therefore, this all does not seem to be really relevant anyways.

zephirus

PS: And I still believe that cd quality digital sampling creates subtle but complex and ugly distortions in the complete frequency spectrum. But this belief belongs to the realm of religious beliefs. Unfortunately.
Title: 44 KHz (CD) not enough !? (Nyquist etc.)
Post by: Doctor on 2003-05-12 22:54:24
An oversampling DAC still needs to lowpass the signal, it's just simpler to implement the brick wall filter in digital domain. The digital filter is almost guaranteed to be finite impulse response.

Suppose you are trying to reproduce a 22049 Hz sine when your DAC is running at 44100 Hz. Digitally, the signal will appear modulated as the phase of the sine very slowly lags behind the sampling. The modulation frequency will be 2 Hz.

Now, if your FIR filter stores 20 thousand samples, it will reproduce the sine perfectly (up to quantization noise). In other words, a perfect brick wall will operate perfectly. But the cost of such a filter, either in hardware or software, is prohibitive. So, both the DAC and the editor software will let the modulation through.

On the other hand, a 20 KHz sine will modulate at 4100 Hz requiring the filter to average about 12 samples. This is acceptable.

(I am a little unsure about these numbers. Factor of two, not two orders of magnitude kind of unsure.  )

In analogue domain the situation is exactly the same. Steep filtering, expensive hardware.

Zephirus is correct that very close to Nyquist limit real-world limitations necessitate distortion. However, the original spec for CD audio, and our knowledge of human hearing, require exact reproduction up to 20 KHz, tops. So a less steep filter that cuts well below 22 KHz is perfectly acceptable and there is nothing to bitch about.
Title: 44 KHz (CD) not enough !? (Nyquist etc.)
Post by: Doctor on 2003-05-12 22:57:47
The distortions you believe in are probably either quantization noise (ADC) or filter nonlinearity (DAC). They do exist in the entire frequency range anthough there are techniques (dithering, noise shaping and good filter design) that can make them practically inaudible.

Ed: sp
Title: 44 KHz (CD) not enough !? (Nyquist etc.)
Post by: KikeG on 2003-05-13 07:54:30
Quote
The idea that digital sampling is able to reproduce any frequency up to half the sampling rate still seems to be wrong.

A more correct formulation on Nyquist theorem would be that digital sampling is able to capture and reproduce perfectly any frequency below half the sampling rate. How below? Any below. In theory, with a sampling rate of 40000 Hz you could perfectly capture and reproduce up to 19999.99999... Hz. But this is from a theorical and mathematical point of view, in order for that to be possible you need a perfect filter that doesn't exist in reality, just in maths.

To cope with real world filter limitations, you need some headroom, and a sampling rate significantly over the double of the max. frequency is needed. For that reason (and others not related to this issue), 44100 Hz sampling rate was chosen for being able to reproduce up to around 20000 Hz , and not just 40000 Hz.
Title: 44 KHz (CD) not enough !? (Nyquist etc.)
Post by: ExUser on 2003-05-13 08:10:33
Quote
If you zoom a little bit into the wave, you will see how Cool Edit "interpolates" between samples and creates a continuous waveform that is not modulated.

How is an "interpolator" like this coded? Can it only be written using FIR filters, or is there some easy way to code it, like a linear interpolator?
Title: 44 KHz (CD) not enough !? (Nyquist etc.)
Post by: tigre on 2003-05-13 11:15:44
To approximate the waveform between two samples S[0](x[0]/y[0]), S[0](x[1]/y[1]) I'd use a function like

f: y = c0 + c1*x + c2*x^2 + c3*x^3 ... + cn*x^n ; n=odd number, the higher, the more exact will be the result.

Putting the x's and y's for the samples S[0.5-n/2] ... S[0.5+n/2] into it results in a linear simultaneus equation. Solve it and you have the c0 ... cn values, so using f will result in a nice curve between S[0] and S[1].

for every c value n-1 multiplications need to be done and n-1 additions; afterwards the same for every step you want to calculate between s[0] and S[1].

If you want to compute many steps between S[0] and S[1], judging the importance of c0 ... cn values and maybe disregarding some of them (for at least the steps near to S[0]) can save time (Because for x -> 0 : x^n -> 0 fast, so y -> c0 + c1*x).

I think this is easy to code, but I can't tell how fast it is compared to using FIR filters.

Sorry... In this field my English is really bad. If it's impossible to understand, tell me - I'll try again using a better dictionary.
Title: 44 KHz (CD) not enough !? (Nyquist etc.)
Post by: 2Bdecided on 2003-05-13 11:24:14
zephirus,
You were right about the 1kHz tone in the 2kHz system - I hadn't even read the numbers that I typed! As KikeG has said, nyquist says "below fs/2" - not at fs/2.
EDIT: btw, I agree that CD quality digital audio isn't enough, though the reasons may be more practical than theoretical. I'm in a small minority here

Canar
The interpolation is idealy performed with a sync function. There's a very good site here:
http://ccrma-www.stanford.edu/~jos/resampl...e/resample.html (http://ccrma-www.stanford.edu/~jos/resample/resample.html)
which goes into detail about the implementation issues.

Cheers,
David.
Title: 44 KHz (CD) not enough !? (Nyquist etc.)
Post by: tigre on 2003-05-13 11:42:51
Nice link you provided, 2Bdecided.

So it seems like I tried to  talk about Larange interpolation (http://www-ccrma.stanford.edu/~jos/waveguide/Lagrange_Interpolation.html).
Title: 44 KHz (CD) not enough !? (Nyquist etc.)
Post by: ExUser on 2003-05-14 07:35:37
Quote
Canar
The interpolation is idealy performed with a sync function. There's a very good site here:
http://ccrma-www.stanford.edu/~jos/resampl...e/resample.html (http://ccrma-www.stanford.edu/~jos/resample/resample.html)
which goes into detail about the implementation issues.

*whoosh* That's the sound of it all going right over my head. I'll try focussing more and re-reading until I actually get it all. It took me forever to understand what was going on with Wavelets when I first started studying them too, but I get 'em now. Hopefully this'll work like that.

I was hoping it'd be a nice simple implementation, but no.... It has to go and deal with infinities and things. Icky...  Bah. Shoulda figured. It is DSP stuff after all.

Anyhow, thanks for the link. I needed something mind-expanding, and all my usual hookups for such things are either disappearing or depleting.

The whole Lagrange interpolation bit reminds me of dealing with Taylor series.
Title: 44 KHz (CD) not enough !? (Nyquist etc.)
Post by: zephirus on 2003-05-14 12:23:07
Doctor, KikeG: Thanks for your explanations!

Quote
In theory, with a sampling rate of 40000 Hz you could perfectly capture and reproduce up to 19999.99999... Hz. But this is from a theorical and mathematical point of view, in order for that to be possible you need a perfect filter that doesn't exist in reality, just in maths.

I believe I found a rather simple possibility to practically demonstrate and theoretically argue the claim that signal distortions happen well below the Nyquist frequency. Even with an ideal and perfect filter.

A continuous signal of 21800 Hz (with 44.1 KHz sampling, -1.5 dB, 0.5s duration) looks very much amplitude modulated in Cool Edit. An ideal 192 KHz upsampling filter will create a correct (not modulated) signal regardless (the Cool Edit upsampling does a pretty good job here as well in highest quality mode).

But now (before upsampling) let´s silence 0.0000-0.0017 and 0.0023-0.0100. What remains is a small snippet between 0.0017 and 0.0023 (with silence around it).

Without the context around this short snippet, no filter on earth (or in the mathematical domain) should be able to know if that short snippet is meant as a low amplitude signal at around 21800 Hz or a full amplitude signal at exactly 21800 Hz (the upsampling filter will go for the wrong interpretation, and "smears" the signal as well).

The digital representation of such a short 21800 Hz snippet simply seems to be ambiguous due to the inevitable information loss that occurs when trying to represent the analog source as a digital sequence of numbers at a rate of 44.1 KHz.
(When digitizing anything analog - sound, video, whatever - it´s in principle inevitable that many different analog signals lead to the identical digital representation. When converting back to analog, it should be impossible to decide which of the possible source signals was the right one.)

I´m not sure however if it can be successfully argued (with signal theory) that the amplitude loss is irrelevant. But if not:

The major point is that such information loss (and therefore the inevitable distortion) occurs well below the Nyquist frequency.

doctor´s post seems to deliver further evidence:
Quote
...if your FIR filter stores 20 thousend samples, it will reproduce the sine perfectly...

But even a near perfect filter does not have 20 thousand samples of the signal if it is too short - like the above one.

I also tried this with 21500 Hz, with similar results.

So it seems: The Nyquist theorem only works for long, continuous signals, but not for short ones. Which are distorted well below the Nyquist frequency. Even with mathematically perfect filters.

I wouldn´t try to claim that any of this is audible. But now with possibly a slight dent in the Nyquist theorem, the next question would be if such digital ambiguities could be found with more complex source signals with the resulting distortions being well below 20000 Hz.

zephirus

PS: I suppose that Nyquist formulated his theorem for long continuous signals only. So there most likely is not really a dent in his theory.
Title: 44 KHz (CD) not enough !? (Nyquist etc.)
Post by: SikkeK on 2003-05-14 12:36:19
I think your snippet has alot of frequence components above 22.05 kHz......
Title: 44 KHz (CD) not enough !? (Nyquist etc.)
Post by: DonP on 2003-05-14 13:00:32
Quote
The digital representation of such a short 21800 Hz snippet simply seems to be ambiguous due to the inevitable information loss that occurs when trying to represent the analog source as a digital sequence of numbers at a rate of 44.1 KHz.
(When digitizing anything analog - sound, video, whatever - it´s in principle inevitable that many different analog signals lead to the identical digital representation. When converting back to analog, it should be impossible to decide which of the possible source signals was the right one.)

Hoo boy... That's why at school they start with trig and basic waves then work up through communications
systems hitting Nyquist along the way rather than just spitting out the 2x sampling thing leaving it at that.

I risk backing up not enough, but I'm not planning to write a whole book here.

A pure single frequency by its nature exists for all time.  If you want to limit the time of a signal, you
have to introduce other frequencies which sum up to what you want.  In other words, during the time
the signal is decaying it is not a pure sine.  The shorter this pulse of signal is in relation to its
period (1/frequency), the stronger the other frequency components will be compared to your base
frequency component.  The ultimate degenerate case is an impulse, or single instant of non-zero
amplitude, which contains ALL frequencies equally.

Anyhow, if you have just a very few non-zero samples, it will be ambigous how
to reconstruct the signal, but that ambiguity is due to components of the original signal higher  than the Nyquist frequency.
Title: 44 KHz (CD) not enough !? (Nyquist etc.)
Post by: morelli on 2003-05-14 13:06:17
it's all too complex for me to understand.
but i always wondered why you could get more clarity and detail
when using higher sampling rates for recording.
but that has to go along with a higher bitrate too ofcourse.

morelli
Title: 44 KHz (CD) not enough !? (Nyquist etc.)
Post by: zephirus on 2003-05-14 13:39:10
Quote
I think your snippet has alot of frequence components above 22.05 kHz......

This seems to be the problem I searched for but was unable to find...

zephirus
Title: 44 KHz (CD) not enough !? (Nyquist etc.)
Post by: 2Bdecided on 2003-05-14 13:40:03
Someone do a search. I'm too lazy. But I've written what amounted to an essay on the subject of time resoluion near the nyquist limit in some forum or another - probably more than once.

Basically, if a tone stops dead, it stops with a click. A click has (theoretically) all possible frequencies. But you're filtering out all the ones above 22.05kHz.

In otherwords, a 21kHz tone can't just "stop dead" in a band-limited system. In "stopping dead", it creates high frequencies. If you remove them, it doesn't "stop dead". Or, to put it another way, to avoid generating higher frequencies, you have to fade-out the 21kHz tone, rather than stop it dead.


If you start looking at this, it's all physics (or maths, but I never liked maths). Time and frequency are inter-twined (rather like the heisenberg uncertainty principle), the more accuracy (or greater restriction) is forced on one, the less accuracy (or less restriction) can be imposed on the other. To make sure that a signal is exactly any frequency, it has to exist for eternity. Confine a signal to a single moment, and it will contain all frequencies. With your experiment, you're trying to do both - have an exact frequency signal, and confine it exactly to a give time. For most sampling, this is inconsequential - confining a 1kHz tone to the band below 20kHz still gives sufficient time-resolution to allow it to start and stop almost instantaneously. But confining a 21kHz tone to the band below 22.05kHZ doesn't allow enough time resolution for it to start and stop almost instantaneously. In fact, both tones can start and stop within a few samples, but those few samples a several cycles at 21kHz, but just a fraction of a cycle at 1kHz. In both cases, in a "perfect" system, the extra cycles will be at 22.05kHz. That's just another way of looking at it: it's the ringing of the low pass filter.


You can also gain an interesting insight by generating 1 second of silence, then 1 second of a tone in Cool Edit. Examine the transition from silence to tone closely. See what the interpolation will be. It's a strange world.


After reading that long paragraph, I think I should have searched for the last time I wrote it! There are so many different ways of looking at the same thing. The important thing is that it's not a new constraint - it's just nyquist. It's one of those consequences of band-limiting that I hinted at much earlier. Since your ear is also band limited, it also has similar time-constraints. So, in theory, if everything is working properly, it shouldn't be a problem. Hmmm...

Cheers,
David.
Title: 44 KHz (CD) not enough !? (Nyquist etc.)
Post by: KikeG on 2003-05-14 14:04:18
From zephirus:
Quote
A continuous signal of 21800 Hz (with 44.1 KHz sampling, -1.5 dB, 0.5s duration) looks very much amplitude modulated in Cool Edit.

This is because the visual interpolation CE does is not perfect, at high frequencies it doesn't interpolate well enough.

Quote
An ideal 192 KHz upsampling filter will create a correct (not modulated) signal regardless (the Cool Edit upsampling does a pretty good job here as well in highest quality mode).


That would be a more proper interpolation, but takes some time to compute well.

Quote
But now (before upsampling) let´s silence 0.0000-0.0017 and 0.0023-0.0100. What remains is a small snippet between 0.0017 and 0.0023 (with silence around it).
Without the context around this short snippet, no filter on earth (or in the mathematical domain) should be able to know if that short snippet is meant as a low amplitude signal at around 21800 Hz or a full amplitude signal at exactly 21800 Hz (the upsampling filter will go for the wrong interpretation, and "smears" the signal as well).


This snippet has an only, non-ambiguous, interpretation, given that it doesn't contain any frequencies over 22050 Hz: the one that the accurate upsampling filter does. You say that it smears the signal: well, that is a consecuence of assuming that there are no components over 22050 Hz. If there were no smearing, the signal would have components over 22050 Hz, and it would be impossible to sample and reproduce it properly with a sampling frequency of just 44100 Hz, because it would violate Nyquist theorem.

Quote
So it seems: The Nyquist theorem only works for long, continuous signals, but not for short ones. Which are distorted well below the Nyquist frequency. Even with mathematically perfect filters.


No, it is not because of Nyquist theorem, it works always without exception. The problem is on the signal itself: any time-limited signal has infinite frequency components, and the reverse: any frequency-limited signal has infinite duration, from a mathematical point of view only infinitely periodic signals have finite frequency components.

Nyquist theorem says that in order to perfectly sample a signal, it has to be frequency-limited to below fs/2. That signal, in theory, will have infinite duration, it will "ring" forever (infinitely periodic) if it is totally frequency-limited.  In real world there are no perfect filters, and since the frequency limiting is not perfect, the time-ringing is limited too: that is the cause of temporal smearing. The sharper (and more ideal) the reconstruction filter, the more time smearing you will get.

This is a problem that happens no matter how high the sampling rate; it is just a question of degrees. How much smearing do you consider acceptable, taking into account human hearing? (smearing=frequency limiting). What is the acceptable duration, amplitude and frequency of the ringing due to the frequency-limiting, taking into account human hearing? (the ringing is of a frequency equal to the filter cutoff, and the duration and amplitude depend on the sharpness of the filter and the amplitude of the signal at the cutoff frequency).

I think that these issues, using a 44.1 KHz sampling rate and typical DAC filters, are not a problem considering human hearing limitations.

Edit: it seems that 2Bdecided was faster than me, but it's basically same explanation.
Edit: some minor modifications done in order to make it more understandable.
Title: 44 KHz (CD) not enough !? (Nyquist etc.)
Post by: DonP on 2003-05-14 14:26:56
For an example of this frequency vs time resolution in an easier to hear range,  find somebody with
a good subwoofer setup such that you can turn off (or disconnect) the main speakers and only
hear a lowpass filtered subwoofer cut off at, say, 80 Hz.

All the normally "sharply defined" bass notes like bass guitar or kick drums will sound smeared, like
mumbling elephants.  Adding the main speakers back in gives you those overtones that define the
edge of  the note.
Title: 44 KHz (CD) not enough !? (Nyquist etc.)
Post by: zephirus on 2003-05-14 14:40:44
Quote
A pure single frequency by its nature exists for all time.  If you want to limit the time of a signal, you
have to introduce other frequencies which sum up to what you want.  In other words, during the time
the signal is decaying it is not a pure sine.  The shorter this pulse of signal is in relation to its
period (1/frequency), the stronger the other frequency components will be compared to your base
frequency component.

If I understand your clarifications sufficiently well, then:

If the human ear was able to perceive all frequencies up to exactly 22050 Hz (and not anything above that at all, as if it had a perfect "brick wall" filter), then the ear could not perceive the beginning or end of a 22050 Hz signal (one would hear such a signal more or less always, regardless if it was real or not - since any frequencies below 22050 Hz wouldn´t be enough to stop such a signal, because frequencies higher than that would be needed as well).

Quote
Anyhow, if you have just a very few non-zero samples, it will be ambigous how
to reconstruct the signal, but that ambiguity is due to components of the original signal higher  than the Nyquist frequency.

I suspect I better believe you here...

Thanks,
zephirus
Title: 44 KHz (CD) not enough !? (Nyquist etc.)
Post by: mrosscook on 2003-05-14 15:07:32
Zephirus,

Harry Nyquist formulated his sampling theorem in, I think, 1928 -- 75 years ago.  If there were any true, practical limitations on its application to real-world signal processing, they would have been worked out and made clear decades ago.  This is the case with the requirement for an ideal filter, for example, mentioned above by 2BDecided, Doctor, and KikeG.

You can't really believe that you are going to poke holes in the theorem now by futzing around with signal samples in CoolEdit -- you are clearly a very bright and reasonable person, so just think about it.

I'm more interested in WHY you have this feeling that 44.1 kHz/16 bit is not good enough.  2B has mentioned before that he has a similar subjective feeling, and in the thread that I linked to above, bryant (another bright and reasonable guy) seems to agree also. And there are probably others, who are reluctant to speak because they don't want to get pounded for expressing an opinion that they can't back up.

When I hear such opinions from people who are clearly just audiosnobs, they are easy for me to dismiss; these are the people who insist on gold-plated speaker cables thick enough to jump-start a car, and who clean their vinyl only with brushes made of hair torn from the tail of a pregnant oryx.  It's clear what that's about.

But if you and 2B and bryant claim you hear some kind of distortion or limitation in the current CD standard, I don't want to just dismiss it out of hand.  So -- can you elaborate on what it is that you hear?  Under what conditions do you hear a problem?  What kind of music, what environment, what hardware, what software?  What kinds of distortion do you hear?  I'd be interested to know.
Title: 44 KHz (CD) not enough !? (Nyquist etc.)
Post by: DonP on 2003-05-14 15:21:32
Quote
\
If I understand your clarifications sufficiently well, then:

If the human ear was able to perceive all frequencies up to exactly 22050 Hz (and not anything above that at all, as if it had a perfect "brick wall" filter), then the ear could not perceive the beginning or end of a 22050 Hz signal (one would hear such a signal more or less always, regardless if it was real or not - since any frequencies below 22050 Hz wouldn´t be enough to stop such a signal, because frequencies higher than that would be needed as well).

Yes, that's pretty much the result, once you start hypothesizing about
ears containing perfect low pass filters and signals exactly at the
corner of the perfect filter.  Just remember that those conditions aren't realistic.

The Nyquist criterion just says that the sample frequency has to be > 2x the maximum signal
frequency (note: that is ">", not ">=".)  Not addressed there is that when you want to look critically at signals arbitrarily close to the limit, it becomes more and more important that the implementation  be more precise..
that is, small variations in the sampling time (aka jitter) and quantization errror become more visible.
So in a good design, you have some margin and don't try to exactly reproduce frequencies at
49.99% of the sample frequency.   

Given that human hearing becomes less precise at high frequencies,  a person hearing a signal near his own limit wouldn't hear  errors that you could easily see on a graph.
Title: 44 KHz (CD) not enough !? (Nyquist etc.)
Post by: budgie on 2003-05-14 16:07:06
Quote
I'm more interested in WHY you have this feeling that 44.1 kHz/16 bit is not good enough.  2B has mentioned before that he has a similar subjective feeling, and in the thread that I linked to above, bryant (another bright and reasonable guy) seems to agree also. And there are probably others, who are reluctant to speak because they don't want to get pounded for expressing an opinion that they can't back up.

But if you and 2B and bryant claim you hear some kind of distortion or limitation in the current CD standard, I don't want to just dismiss it out of hand.  So -- can you elaborate on what it is that you hear?  Under what conditions do you hear a problem?  What kind of music, what environment, what hardware, what software?  What kinds of distortion do you hear?  I'd be interested to know.

Main problem is poor (slovenly) CD mixing and mastering... That's really a problem. After all the years I've spent with music I firmly believe 16 bit/44,1 kHz is more than good for, say, 99.x% of all people.

20 bit /48 kHz would probably remove all the problems and complaints, but there were apparently other forces then which insisted on "lower" standard...
Title: 44 KHz (CD) not enough !? (Nyquist etc.)
Post by: zephirus on 2003-05-14 18:07:50
Quote
After reading that long paragraph, I think I should have searched for the last time I wrote it! There are so many different ways of looking at the same thing. The important thing is that it's not a new constraint - it's just nyquist. It's one of those consequences of band-limiting that I hinted at much earlier. Since your ear is also band limited, it also has similar time-constraints. So, in theory, if everything is working properly, it shouldn't be a problem.

Thanks for your very detailed and enlightening explanations!

I surely learned a lot during this discussion. But I hope I was not too much of a waste of your time (and the time of the others).

It´s an interesting observation of yours that physicists have similar problems regarding quantum physics.

Thanks,
zephirus
Title: 44 KHz (CD) not enough !? (Nyquist etc.)
Post by: ye110man on 2003-05-14 21:46:35
Quote
The Nyquist criterion just says that the sample frequency has to be > 2x the maximum signal
frequency (note: that is ">", not ">=".)   Not addressed there is that when you want to look critically at signals arbitrarily close to the limit, it becomes more and more important that the implementation  be more precise..
that is, small variations in the sampling time (aka jitter) and quantization errror become more visible.
So in a good design, you have some margin and don't try to exactly reproduce frequencies at
49.99% of the sample frequency.

i thought it was that any curve can be reconstructed with a sampling rate 2 times the frequency. you don't need more than that. of course this isn't factoring in jitter or quantization error but those aren't components of nyquist's theorem.
Title: 44 KHz (CD) not enough !? (Nyquist etc.)
Post by: DonP on 2003-05-14 22:22:03
Quote
i thought it was that any curve can be reconstructed with a sampling rate 2 times the frequency. you don't need more than that.

I could say something flippant like "Why did you think that?"

Here's a counter example:  If the signal frequency is exactly half the sampling frequency
then all the data points could be on the zero crossings.  It would appear to be no
signal at all.  In fact, no matter where the data points fall, they will be at the exact same
2 phase angles of the curve for every cycle, 180 degrees apart.  Since you can't tell from the points what those angles are, you can't reconstruct the amplitude and phase of the origninal sine wave.

If the sampling frequency is just a little higher than 2x your signal, then  each pair or data points will
shift to slightly different phase angles for each repetition, giving you new information; enough to
reconstruct the signal.

So you do need more than 2x, but just enough to qualify as ">"

Its like an asymptote... close but no touch.
Title: 44 KHz (CD) not enough !? (Nyquist etc.)
Post by: KikeG on 2003-05-15 00:03:59
Quote
20 bit /48 kHz would probably remove all the problems and complaints, but there were apparently other forces then which insisted on "lower" standard...

I don't know for sure what you want to say, but AFAIK when developing cd-audio specs, 14 bits was thought to be enough. 16 bits was chosen at last just because it was a more "round" number (two bytes).
Title: 44 KHz (CD) not enough !? (Nyquist etc.)
Post by: budgie on 2003-05-15 08:51:30
Quote
I don't know for sure what you want to say, but AFAIK when developing cd-audio specs, 14 bits was thought to be enough. 16 bits was chosen at last just because it was a more "round" number (two bytes).

DAT...
Title: 44 KHz (CD) not enough !? (Nyquist etc.)
Post by: dillee1 on 2003-05-17 10:44:08
Prove of Nyquist theory always use stationary signals. Sure problem does'nt occurs as stationary signals have no information about time.

According to the result of FT we knows that non-stationary signals are not band limited. Real life signals are not stationary. A direct concequencies if we band limit the signal is that the frequency components are no longer pin pointed in the time line, it smears.(uncertainty principle)

Does it mean that as we samples at 44.1KHz(bandlimit at 22.05KHz) cause us to lost resolution in time????
Title: 44 KHz (CD) not enough !? (Nyquist etc.)
Post by: DonP on 2003-05-17 13:11:17
Quote
Prove of Nyquist theory always use stationary signals. Sure problem does'nt occurs as stationary signals have no information about time.

Why do you say that?  I think you are confusing "proof" and "example".


Quote
Real life signals are not stationary. A direct concequencies if we band limit the signal is that the frequency components are no longer pin pointed in the time line, it smears.(uncertainty principle)

Does it mean that as we samples at 44.1KHz(bandlimit at 22.05KHz) cause us to lost resolution in time????


SInce you are citing Fourier transforms, you know that frequency components are never pinpointed in time
in that context.

The extent to which you could hear the loss in time resolution due to bandwidth limiting is directlly related
to your ability to hear in the eliminated frequency range.
Title: 44 KHz (CD) not enough !? (Nyquist etc.)
Post by: zephirus on 2003-05-17 17:37:00
Quote
This snippet has an only, non-ambiguous, interpretation, given that it doesn't contain any frequencies over 22050 Hz ...

It believe it does contain frequencies above 22050 Hz since I did not obtain it by properly downfiltering it (from e.g. 192 KHz). But instead by fiddling with Cool Edit in the 44.1 KHz domain. But I agree that there is, in fact, only one proper interpretation (for the frequencies below 22050 Hz).

Quote
: ... the one that the accurate upsampling filter does. You say that it smears the signal: well, that is a consecuence of assuming that there are no components over 22050 Hz. If there were no smearing, the signal would have components over 22050 Hz, and it would be impossible to sample and reproduce it properly with a sampling frequency of just 44100 Hz, because it would violate Nyquist theorem.

Yes. Nevertheless: I compared the Cool Edit upsampling algorithm with several of it´s filtering algorithms. I found: Doing the silence fiddling in the 192 KHz domain and then filtering out anything above 22050 Hz looks much better than doing that fiddling in the 44.1 KHz domain and then upsampling it.

Both should be equivalent - since effectively it´s both just frequency filtering. This simply might mean that the Cool Edit upsampling algorith works worse than it´s filtering algorithms. Or that upsampling may be much harder than just low-pass filtering all frequencies above 22050 Hz. But this is not of too much interest anyways.

Quote
Quote
So it seems: The Nyquist theorem only works for long, continuous signals, but not for short ones. Which are distorted well below the Nyquist frequency. Even with mathematically perfect filters.

No, it is not because of Nyquist theorem, it works always without exception. The problem is on the signal itself: any time-limited signal has infinite frequency components, and the reverse: any frequency-limited signal has infinite duration, from a mathematical point of view only infinitely periodic signals have finite frequency components.

Well, I believe that I see this now.

Quote
I think that these issues, using a 44.1 KHz sampling rate and typical DAC filters, are not a problem considering human hearing limitations.

It shouldn´t. I had a bad conflict with the (Nyquist) theory this all is based on anyways.

Thanks,
zephirus
Title: 44 KHz (CD) not enough !? (Nyquist etc.)
Post by: zephirus on 2003-05-19 15:05:53
Quote
Harry Nyquist formulated his sampling theorem in, I think, 1928 -- 75 years ago.  If there were any true, practical limitations on its application to real-world signal processing, they would have been worked out and made clear decades ago.  This is the case with the requirement for an ideal filter, for example, mentioned above by 2BDecided, Doctor, and KikeG.

Yes. My attempts at finding problems with (basically) the Nyquist theorem do seem rather clumsy in hindsight. Especially since my knowledge of the underlying theory is mostly nonexistent.

On the other hand: In principle it does seem to be a good idea to constantly challenge widely accepted scientific theories or belief systems. As it seems, many of such theories or beliefs can successfully be argued to most likely be wrong by knowledgeable people. Despite the fact that such theories or beliefs have persisted for many decades and are generally believed to be identical, or near to, absolute truth. Of course, the word "knowledgeable" is very important. Nonetheless: If there is no doubt, there is no progress.

My personal conclusion: My doubts in the CD format do remain, but they lost considerable energy. I learned a lot during the discussion, and I will listen to my CDs (and .ape or lossy or non-lossy .wv files) with more confidence now.

The major problem with this discussion primarily seems to be that I wasted the time of knowledgeable persons for the sake my own education. But for me, this discussion was very valuable.
At least, this discussion may be a worthwhile link if similar topics turn up in the future.

Quote
I'm more interested in WHY you have this feeling that 44.1 kHz/16 bit is not good enough.  2B has mentioned before that he has a similar subjective feeling, and in the thread that I linked to above, bryant (another bright and reasonable guy) seems to agree also. And there are probably others, who are reluctant to speak because they don't want to get pounded for expressing an opinion that they can't back up.

When I hear such opinions from people who are clearly just audiosnobs, they are easy for me to dismiss; these are the people who insist on gold-plated speaker cables thick enough to jump-start a car, and who clean their vinyl only with brushes made of hair torn from the tail of a pregnant oryx.  It's clear what that's about.

But if you and 2B and bryant claim you hear some kind of distortion or limitation in the current CD standard, I don't want to just dismiss it out of hand.  So -- can you elaborate on what it is that you hear?  Under what conditions do you hear a problem?  What kind of music, what environment, what hardware, what software?  What kinds of distortion do you hear?  I'd be interested to know.

At times, and with a number of recordings, I do hear distortions that are rather faint but very ugly nonetheless. And they surely (in my opinion) cannot be an intended part of the original signal.

Right now it seems to be a very good idea to attribute such distortions to poor recording, poor mastering, or poor reproduction equipment. And not to the CD standard.

Perhaps, in theory, a higher sampling frequency/resolution than 44.1 KHz/16 bit might indeed make sense and be helpful for practical reasons. The necessary filtering of the signal in the output equipment (cd player) might be easier, and therefore, usually of higher quality (perhaps). Also, more headroom may be a good idea since 44.1/16 is somewhat uncomfortably close to the limits of human hearing.

A major problem is that, just as most people, I cannot do a proper listening test. Since I lack the necessary high end hardware (96 or 192 KHz, 20-24 bit) and the necessary native test material at such resolution as well.

Thanks,
zephirus
Title: 44 KHz (CD) not enough !? (Nyquist etc.)
Post by: KikeG on 2003-05-19 15:48:01
If I could have access to some 24/96 music in wav format, I could set up one of those tests.

I would downsample the 24/96 wave to 16/44.1 using "realistic" filtering + resampling to 44.1 KHz in CEP (that should be equivalent to the filtering of a good ADC), and convert it to 16 bit with dither.

Then, I would play this wave with one of my cards, using its converters running at 44.1 KHz, and record the result with my other card at 48 KHz 16 bit. Ideally it should be recorded at 24/96, but I just have 1 good non-resampling card at 44.1 KHz that is used for playback, and happens to be the same one that also supports 24/96. My other card is non-resampling just at 48 KHz, but is limited to 16/48, although I think has pretty good quality. I think the the fact that the recording is done at 16/48 instead of 24/96 wouldn't have much influence in the test, specially if no differences are found at last. But this point should be analyzed with detail to see what problems it could have, and improved if found necessary. At first, I think that this 16/48 recording would capture all the "nastieties" (aliasing, smearing, etc) of the 16/44.1 DAC, but would introduce some of the 16/48 ADC, although at higher frequencies.

Then, I would upsample to 24/96 this 16/48 record, and people with good 24/96 cards could perform some blind listening tests comparing the original vs. the this other wave that has been downsampled, played, recorded and upsampled.


At the PCABX site there are some avalable clips to perform tests of this kind ( http://64.41.69.21/technical/sample_rates/index.htm (http://64.41.69.21/technical/sample_rates/index.htm) ). They are interesting and show that AFAIR there is no difference in practice, but the clips available are not very representative of real-word conditions. They are very short on duration (and typical fans of hig-res formats won't consider them very representative), and in fact no real-world DAC has been used in their generation, just software processing.
Title: 44 KHz (CD) not enough !? (Nyquist etc.)
Post by: budgie on 2003-05-19 15:58:25
Quote
A major problem is that, just as most people, I cannot do a proper listening test. Since I lack the necessary high end hardware (96 or 192 KHz, 20-24 bit) and the necessary native test material at such resolution as well.

Major problem is, you just jabber about the things you don't understand... If you lack the necessary high end hardware and the necessary native test material at such resolution, how do you know how does it sound? I have the opportunity, possibility and it is inevitable for me to deal everyday with this high end resolution workstations and I can swear it's not needed for listening purposes. It's needed for recording, adding effects, mixing and mastering, not for the real life. 16/44,1 is more than enough when made in an appropriate way... I've told it here at HA at least for hundred times.
Title: 44 KHz (CD) not enough !? (Nyquist etc.)
Post by: 2Bdecided on 2003-05-19 16:02:16
Quote
Quote
This snippet has an only, non-ambiguous, interpretation, given that it doesn't contain any frequencies over 22050 Hz ...

It believe it does contain frequencies above 22050 Hz since I did not obtain it by properly downfiltering it (from e.g. 192 KHz). But instead by fiddling with Cool Edit in the 44.1 KHz domain. But I agree that there is, in fact, only one proper interpretation (for the frequencies below 22050 Hz).

Doh! we were doing so well!  If it's sampled at 44.1kHz, it doesn't contain anything unique above 22.05kHz. Anything above this is a copy of what's below it. And anything below it that you intended to be above it, isn't! (I'm laughing, not at you, but with you, because it's just the kind of tangle I get myself in sometimes)

Quote
Quote
: ... the one that the accurate upsampling filter does. You say that it smears the signal: well, that is a consecuence of assuming that there are no components over 22050 Hz. If there were no smearing, the signal would have components over 22050 Hz, and it would be impossible to sample and reproduce it properly with a sampling frequency of just 44100 Hz, because it would violate Nyquist theorem.

Yes. Nevertheless: I compared the Cool Edit upsampling algorithm with several of it´s filtering algorithms. I found: Doing the silence fiddling in the 192 KHz domain and then filtering out anything above 22050 Hz looks much better than doing that fiddling in the 44.1 KHz domain and then upsampling it.


There shouldn't be any difference.

Quote
Both should be equivalent - since effectively it´s both just frequency filtering. This simply might mean that the Cool Edit upsampling algorith works worse than it´s filtering algorithms. Or that upsampling may be much harder than just low-pass filtering all frequencies above 22050 Hz. But this is not of too much interest anyways.


Maybe not. But you should be able to get a very similar result in CEP with the right filter. Really!

Cheers,
David.

P.S. CD "sound" (if there is one) is glassy, and less realistic than 24/96. This is what I heard with professional DCS convertors, comparing A>D>A at 44.1kHz and 96kHz (both 24-bits, so both are actually better than CD) with the original analogue signal.

I can't hear a difference using an audiophile 2496 and some Sennheiser HD580s, but I believe the effect is/was/will be much greater with speakers in a real room than via headphones (or even via speakers in an anechoic chamber - just a hunch - no evidence for this claim). The effect I heard was subtle, but then most things seem subtle the first time you notice them (e.g. coding artefacts). I can quite believe record producers who use this equipment everyday (and who hear live music every day) when they say that, to them, the difference is significant.

But almost all of the faults I hear with CDs at home are almost certainly the fault of bad mastering.

Cheers,
David.
Title: 44 KHz (CD) not enough !? (Nyquist etc.)
Post by: KikeG on 2003-05-19 16:39:43
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If it's sampled at 44.1kHz, it doesn't contain anything unique above 22.05kHz. Anything above this is a copy of what's below it. And anything below it that you intended to be above it, isn't! (I'm laughing, not at you, but with you, because it's just the kind of tangle I get myself in sometimes)

Well, from the point of operation of sampling theorem, the signal to be sampled is supposed to have no content at all over fs/2. In the same context, the reconstructed signal is supposed to have no content at all over fs/2. Is in this context where I say that the sampled points define a non-ambiguous analog signal given that it won't have anything over fs/2. If not, it depends exclusively on the reconstruction filter implementation, but here we are deviating from what Nyquist said.

Quote
P.S. CD "sound" (if there is one) is glassy, and less realistic than 24/96. This is what I heard with professional DCS convertors, comparing A>D>A at 44.1kHz and 96kHz (both 24-bits, so both are actually better than CD) with the original analogue signal.


I don't trust these kind of comparisons, that are not rigorously controlled. Could you give more details? Was it blind? Were the converters at your disposal? Were levels properly matched? Was the program material generated properly? Could the 44.1 KHz converters have been "customized" for the test or something similar? Who prepared the test?

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I can't hear a difference using an audiophile 2496 and some Sennheiser HD580s, but I believe the effect is/was/will be much greater with speakers in a real room than via headphones (or even via speakers in an anechoic chamber - just a hunch - no evidence for this claim). The effect I heard was subtle, but then most things seem subtle the first time you notice them (e.g. coding artefacts). I can quite believe record producers who use this equipment everyday (and who hear live music every day) when they say that, to them, the difference is significant.


I have read from a couple of respected and experienced professional recording engineers the opposite. One says that he can't hear anything different with 96 KHz as opposed to 44.1 KHz. The other says that the differences he could hear using 192 KHz in comparison with 44.1 KHz were minimal, almost insignificant, and not worth the use. Even here, the listening was not blind. However, according to this same person, on his tests, DSD did a great difference!!. He knows that this doesn't make much sense (24/192 is clearly superior to DSD from a technical point of view) , but that's what he heard. What guarantees in this case that the DSD (SACD) player was not doing "something" to the signal?

That's why I don't trust that kind of sighted, non-controlled, listening tests, because if not controlled, there are lots of things that can be making a difference apart from just the sample rates.

(Edit: added some more minor things.)
Title: 44 KHz (CD) not enough !? (Nyquist etc.)
Post by: Pio2001 on 2003-05-19 20:00:09
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I have read from a couple of respected and experienced professional recording engineers the opposite.

Not to mention Budgie's post above.

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Yes. Nevertheless: I compared the Cool Edit upsampling algorithm with several of it´s filtering algorithms. I found: Doing the silence fiddling in the 192 KHz domain and then filtering out anything above 22050 Hz looks much better than doing that fiddling in the 44.1 KHz domain and then upsampling it.


There shouldn't be any difference.

Resampling algorithms lead to more or less alias = more or less steep filtering.
Have a look at the § 3 of this page : http://perso.numericable.fr/~laguill2/cdr/cdr.htm (http://perso.numericable.fr/~laguill2/cdr/cdr.htm)
There are the spectrums of 3 different quality of resampling from 48 to 96 kHz in SoundForge.
Title: 44 KHz (CD) not enough !? (Nyquist etc.)
Post by: Pio2001 on 2003-05-19 20:16:26
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The major problem with this discussion primarily seems to be that I wasted the time of knowledgeable persons for the sake my own education. But for me, this discussion was very valuable.
At least, this discussion may be a worthwhile link if similar topics turn up in the future.

Forums are not only for developers, they are also for people who like to share their knowledge. Having to explain something that we think we know well often leads to question ourselves, and improve our knowledge of the topic.
Be assured that if this discussion was valuable for you, it was also valuable for other people who read but don't post.

BTW, this discussion was added to the FAQ 4 days ago, on top of the "High definition digital audio" section.
Title: 44 KHz (CD) not enough !? (Nyquist etc.)
Post by: budgie on 2003-05-20 11:12:17
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P.S. CD "sound" (if there is one) is glassy, and less realistic than 24/96. This is what I heard with professional DCS convertors, comparing A>D>A at 44.1kHz and 96kHz (both 24-bits, so both are actually better than CD) with the original analogue signal.

I can't hear a difference using an audiophile 2496 and some Sennheiser HD580s, but I believe the effect is/was/will be much greater with speakers in a real room than via headphones (or even via speakers in an anechoic chamber - just a hunch - no evidence for this claim). The effect I heard was subtle, but then most things seem subtle the first time you notice them (e.g. coding artefacts). I can quite believe record producers who use this equipment everyday (and who hear live music every day) when they say that, to them, the difference is significant.

But almost all of the faults I hear with CDs at home are almost certainly the fault of bad mastering.

You can't hear the difference, because it's so subtle that's not worth mentioning... It really doesn't affect anything important as for the resulting sound. And that's what's really important - under normal, usual listening conditions you don't hear any difference.

And you're right, the faults you can hear from CD under normal listening conditions are definitely the fault of bad mastering...
Title: 44 KHz (CD) not enough !? (Nyquist etc.)
Post by: 2Bdecided on 2003-05-20 17:34:02
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You can't hear the difference, because it's so subtle that's not worth mentioning... It really doesn't affect anything important as for the resulting sound. And that's what's really important - under normal, usual listening conditions you don't hear any difference.

Whilst it's virtually against the conditions of use here to suggest that CDs aren't transparent, if it were a problem in a psyhchoacoustic codec that was "so subtle that {it}'s not worth mentioning... under normal, usual listening conditions you don't hear any difference" there would be 10 people trying to track the "problem" down and fix it!
Title: 44 KHz (CD) not enough !? (Nyquist etc.)
Post by: 2Bdecided on 2003-05-20 17:35:12
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I don't trust these kind of comparisons, that are not rigorously controlled. Could you give more details?

I'm sure I've tried to write a definitive report of my experience before, but I can't find it, so here it is...

It's the 109th AES conference in LA. I'm presenting a paper, but while I'm there, my tutor has "volunteered" me to help with an audio demonstration. As it turns out, they don't need much help, but I go along anyway because it's very interesting.

The people involved are David Chesky (http://www.chesky.com/) and Kevin Halverson (http://www.museelectronics.com). Other "well known" people involved were dCS (http://www.dcsltd.co.uk/), who provided the converters, and Studer, who were kind enough to align the tape recorder before use.

David Chesky was there for reasons I'll explain in a moment. Kevin Halverson was there because most of it was his equipment, and he was operating it. They both had a very down-to-earth attitude to the audio industry: "How do you finish up with a small fortune after making a Jazz record? Start with a large fortune!" "Of course our company doesn't matter in the industry - heck - Sony's budget for paper clips is bigger than our turnover!" They both made quality recordings and equipment for the sake of it, though I was interested to hear the David Chesky would rather read a book when he gets home than listen to music. David was more of an artist, Kevin more of an engineer. They were kind enough to explain everything that was there, and let me play with all the equipment.

There were two demos, one relevant to this discussion, the other I'll explain too because it's probably more interesting!

Demo 1: 6-channel surround sound.

The main demo was 6-channel surround sound. Most of us have stereo. Some of us have 5.1. David was proposing that 5.1 isn't ideal for music. Since DVD-A and SACD actually have 6 full bandwidth channels, he wanted to use them. He didn't see the point of using one for the centre channel when his recordings already had a solid centre image. He didn't see the point of a dedicated .1 channel when music listeners should have full range speakers anyway, and their amplifiers should handle the bass management when they didn't. Plus, he had a much better use for these two channels.

He started with stereo (+/-30 degree spaced speakers), and used the normal surrounds (+/-110 degree spaced speakers, but this spacing could ideally be something else (I forget what) and in practice could be virtually anything that would fit into your room, so long as they were symmetrical behind you). To these four speakers, he added another two at +/-55 degrees front. The idea is that, in many real music listening situations, you get echoes from this direction. Good concert halls have their first main reflection at around this angle. So do many rooms. Since the human ear judges distance partly on the basis of comparing direct and reflected sound, it's good to make this cue more accurate. These extra speakers were raised off the floor by several feet, the idea being that in any realistic situation the audience would prevent you hearing anything lower from this angle.

You can argue with the reasoning behind this - whatever the justification, I think David chose it because it "just works". He'd decoded his B-format ambisonic masters into a 6-channel configuration and played with the result. For playback, he was using a PC with Cool Edit Pro running in multitrack mode. The 6 channels were output as 3 stereo pairs, to a special 6-channel sound card that Kevin had prepared for the demo. All files were 24-bit 96kHz. The PC could just keep up. You could switch channels on and off using the solo and mute controls in CEP, and I even dropped down into edit view a few times to try some spectral analysis on the various channels.

So, what did it sound like? These recordings were mostly things that David had already released on CD and got excellent reviews for. So, when listening to the stereo version, you were listening to a 24/96 version of what was available on CD. And it sounded pretty good. If you added the 2 rear surround channels, you got a nice bit of echo as well. This is like 5.1, but without the centre and sub. It's quadraphonic, if you like. It sounds nicer than stereo. Nice enough to go out and buy more amps and speakers? Depends. Then you switch on the two extra front speakers - wow! I mean - really - wow! The front sound stage went from maybe 6 feet to 20 feet across - and the depth! Sometimes CD reviewers go on about great depth in CD recordings - I know what they mean, but really, that's nothing! It's a few feet - this was like 20 feet! "You could shoot an arrow into that sound stage" was how one visitor described it.

Some of the recordings sounded "artificial" - larger than life. This was just due to the miking - David was still experimenting. Others sounded so realistic it was breathtaking. You had to be in the sweet spot for the most magic effect, but wow! Imagine sitting close to a cinema screen. Now imagine that it's in perfect 3D - so you know you're in a movie theatre because it's still there at the edge of your vision, but all in front of you is a different place. That's a visual analogy of what it sounded like.

I tried some interesting experiments. Firstly, if you turn off the main stereo pair, there's no real sense of sound stage or image - it's just sounds like random echo. Secondly, if you turn off just the back surrounds, leaving the front 4 speakers on, it still sounds amazing. OK, there's no echo from the back anymore, but the front sound stand is still as huge. If you only had four channels, it would be much better to have four at the front rather than two front and two back with these recording. Strange, but true. Try selling that to Joe public.

The speakers were $3000 a pair (3 pairs required), and the amps were much more expensive. So I have no idea what this would sound like on equipment that I could afford! But in the demo, it was just fantastic. Stereo was pathetic by comparison. I don't own a surround system myself, partly because 5.1 just can't compare to what I’ve heard from 6.0.


Demo2: different sampling rates.

Most people visiting the demo room wanted to hear demo 1. But a few were very interested in demo 2. We had a studer 2-track studio machine, a master tape from a 1960s classical recording (apparently an audiophile-beloved rendition of Scheherazade), dCS pro A>D and D>A converters, and the same amps and speakers from the 6-channel demo, just running the front stereo pair.

Simply, you could change the source selector on the pre-amp to compare the analogue source directly with the source sent via the A>D and D>A converters. On the A>D converter you could chose any rate you wanted, and the D>A would oblige. You couldn't switch sample rates while monitoring because there was a glitch while the D>A caught up - so any digital version was always interspersed with the direct analogue feed by switching the pre-map over while the A>D rate was changed. It was also possible to change the bit depth, but we left it at 24-bits. DSD was also possible, apparently, but would mean changing the digital interconnection, which we didn't attempt.

So, you could compare analogue, 32,44.1,48,96,192 digital. You could have 88.2 and 176.4 too, but we didn't bother.

People usually couldn't hear a difference. They'd ask us to switch more quickly than was possible, saying it was impossible to hear a difference, because by the time we'd switched, the mood of the music had changed. They wanted to hear the loud cymbal crashing bit most, convinced they stood most chance of discerning a difference during this. But most failed. And I'll tell you the truth - I sat in the sweet spot, listened both sighted and blind and couldn't hear any difference.

The next day, while the demo was being run for the Nth time, I was at the back of the room talking with someone. Suddenly, I heard a difference as the source switched. I was surprised, having failed to hear a difference the previous day listening in the sweet spot. I listened as it switched again, and heard it switch back – ah ha, it must have just gone analogue / digital / analogue. I kept listening – I couldn’t hear the difference next time it switched.

I went to the middle/back of the room, and listened through the next demo. Without being told, I could pick out 44.1 and 48kHz. The difference was more obvious back from the sweet spot than in the sweet spot itself. More importantly, the difference wasn’t what I (or the other people who failed to hear it) had been listening for. It didn’t make any difference to the frequency response at all, or to the clarity of the high frequencies.

What 44.1kHz and 48kHz did do was to make the sound slightly less realistic, like the difference between a good and bad CD player. If the lower sampling rate had any defined “quality” it was a glassy kind of sound – I’d heard that word associated with CD before and thought it was complete rubbish – but now I actually heard the difference, I understood exactly what people had meant.

The change from 44.1 or 48kHz to analogue to 96kHz slightly increased the depth of the sound stage. I’d been listening to the amazing demo 1 for 2 days, so it was hardly an impressive difference, but it was still there.

If you’re counting, that’s only two blind detections – once when I wasn’t even listening, and again when I went back to the middle of the room to check – I confirmed which had been which with Kevin afterwards – “The next to last one was 40something, wasn’t it?”


You can say many things about this. You could say it was just luck, but I don’t think it was – I wasn’t even listening for the difference because (having listened the previous day) I didn’t think there was one to hear! You can say that I was hearing sonic deficiencies in the equipment. Well, maybe. That may be what the whole 44.1/96k debate is based on. All I can say is that, if there are sonic deficiencies in this equipment (I think the dCS boxes are around 5k each, and are used in many recording studios) then there isn’t much hope for the rest of us!

What you could say, with some justification, is that the “character” of 44.1 was more obvious outside the sweet spot, so maybe it’s not such a big issue. That’s probably true – except that maybe I was just listening for the wrong thing when I was “in the sweet spot”. Maybe I had to stop listening to the Hi-Fi, and start listening to the music and the performance to hear what was happening.

What is significant is that the 44.1kHz version wasn’t just different from the 96k and analogue version, it was [I[worse[/I]. As the analogue was the master, any difference would be bad news, but for it to be subjectively worse makes matters even, well, worse!

I was upset to think how much recorded music only exists as a 44.1kHz or 48kHz sampled digital master tape. I discussed the subjective imperfections (the improved depth and realism of the 96k version) with Kevin, and he agreed. He was surprised that I’d noticed it that day, but couldn’t even hear anything wrong with 32kHz the previous day! I asked him what he heard with 16-bit (we’d been using 24-bit all along) and DSD. He said 16-bit was even worse – it made the whole sound “grungy”, and that DSD sounded nice, but added it’s own signature. “You can tell when you’re playing DSD through this system – the rooms heats up ” he said – I looked at the huge amps, and could believe it.

One thing I should note: I didn’t think the analogue master was particularly good quality. It was a gorgeous recording, but it had obvious flaws – e.g. background noise, and some audible edits. Also, I didn’t hear any difference between analogue, 96k and 192k. I can’t explain why 44.1kHz and 48kHz sounded worse, but they did. No one responsible for the demo had any reason to rig the results, and I played with enough of the equipment to know that everything was above board and fair, even though some of the cables we used might not have met with audiophile approval.


Demo 3

In another room, they had a 1960s recording studio set-up, and they had several master tapes from the 1950s and 1960s. Some actually were the masters (Jackie Wilson live somewhere), others were direct dubs from them, including Elvis, from a 3-track master – not many people have heard an Elvis recording in the original 3-track stereo!

There were plenty of other demos around. The DSD 5.1 demo was terrible, but that was due to equipment and volume. Most other demos sounded very harsh and artificial compared to the three I’ve mentioned. Not because they were using CDs as sources, but because modern studio and mastering practice gives rise to dubious quality recordings, as we often discus here.

It seemed quite perverse that the nicest sounds at the AES were a 6-channel demonstration of recordings and equipment that you can’t even buy, and a tape from the early 1960s which still hasn’t been released in it’s original 3-track format.


Hope this clarifies my thoughts and opinions.

Cheers,
David.
Title: 44 KHz (CD) not enough !? (Nyquist etc.)
Post by: zephirus on 2003-05-20 17:44:21
Quote
Quote

Quote

This snippet has an only, non-ambiguous, interpretation, given that it doesn't contain any frequencies over 22050 Hz ...

It believe it does contain frequencies above 22050 Hz since I did not obtain it by properly downfiltering it (from e.g. 192 KHz). But instead by fiddling with Cool Edit in the 44.1 KHz domain.

Doh! we were doing so well!  If it's sampled at 44.1kHz, it doesn't contain anything unique above 22.05kHz. Anything above this is a copy of what's below it. And anything below it that you intended to be above it, isn't!

Yes, exactly! I may have an explanation for this: Above 22.05 KHz there are no unique frequencies (as you pointed out earlier, these are mirrored and copied from below 22.05 KHz), but of course they are frequencies nonetheless. This way one can indeed represent frequencies above 22.05 KHz with a sampling frequency of 44.1 KHz. But only for the price of adding the respective (mirrored/copied) distortion frequencies below 22.05 KHz as well. And only if no filtering in the recording step is done (brickwall at 20 KHz).

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Quote

I compared the Cool Edit upsampling algorithm with several of it´s filtering algorithms. I found: Doing the silence fiddling in the 192 KHz domain and then filtering out anything above 22050 Hz looks much better than doing that fiddling in the 44.1 KHz domain and then upsampling it.

There shouldn't be any difference. (...) But you should be able to get a very similar result in CEP with the right filter. Really!

Perhaps the "implicit" frequencies above 22.05 Khz (see above) help the Cool Edit filters here. But this is not relevant anyways.

Quote
P.S. CD "sound" (if there is one) is glassy, and less realistic than 24/96. This is what I heard with professional DCS convertors, comparing A>D>A at 44.1kHz and 96kHz (both 24-bits, so both are actually better than CD) with the original analogue signal. (...) I can quite believe record producers who use this equipment everyday (and who hear live music every day) when they say that, to them, the difference is significant.

One could argue that the problem here lies in the (perhaps analog part) of the A/D or D/A circuitry. And that the different sound may have nothing to do with the digital representation in principle.
What I do remember is that some people complained that stradivaris do not reproduce too well. But unfortunately this all is "anecdotic" evidence, and therefore not really scientific evidence.

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But almost all of the faults I hear with CDs at home are almost certainly the fault of bad mastering.

I better agree here

zephirus
Title: 44 KHz (CD) not enough !? (Nyquist etc.)
Post by: zephirus on 2003-05-20 21:48:35
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If I could have access to some 24/96 music in wav format, I could set up one of those tests.

I would downsample the 24/96 wave to 16/44.1 using "realistic" filtering + resampling to 44.1 KHz in CEP (that should be equivalent to the filtering of a good ADC), and convert it to 16 bit with dither.

Then, I would play this wave with one of my cards, using its converters running at 44.1 KHz, and record the result with my other card at 48 KHz 16 bit. Ideally it should be recorded at 24/96, but I just have 1 good non-resampling card at 44.1 KHz that is used for playback, and happens to be the same one that also supports 24/96. My other card is non-resampling just at 48 KHz, but is limited to 16/48, although I think has pretty good quality. I think the the fact that the recording is done at 16/48 instead of 24/96 wouldn't have much influence in the test, specially if no differences are found at last. But this point should be analyzed with detail to see what problems it could have, and improved if found necessary. At first, I think that this 16/48 recording would capture all the "nastieties" (aliasing, smearing, etc) of the 16/44.1 DAC, but would introduce some of the 16/48 ADC, although at higher frequencies.

Then, I would upsample to 24/96 this 16/48 record, and people with good 24/96 cards could perform some blind listening tests comparing the original vs. the this other wave that has been downsampled, played, recorded and upsampled.

At the PCABX site there are some avalable clips to perform tests of this kind ( http://64.41.69.21/technical/sample_rates/index.htm (http://64.41.69.21/technical/sample_rates/index.htm) ). They are interesting and show that AFAIR there is no difference in practice, but the clips available are not very representative of real-word conditions. They are very short on duration (and typical fans of hig-res formats won't consider them very representative), and in fact no real-world DAC has been used in their generation, just software processing.

The best procedure for such test seems to be to use one and the same output equipment (soundcard) with one and the same output sampling frequency (96 or 192 KHz, 20-24 bit). And to do anything else only in the digital domain.

Otherwise there will always be analog components that may interfere and that may distort the result of such listening test. The output sampling rate must be the same for all tests (96 or 192 KHz). And the test signal/soundtrack would need to have been been sampled with true high quality equipment at 96 or 192 KHz (20-24 bit).

The goal should be to prove that 44.1/16 is not enough for all signals, and that there is at least one signal (soundtrack) where the 44.1/16 resolution fails.

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At the PCABX site there are some avalable clips to perform tests of this kind (...) and in fact no real-world DAC has been used in their generation, just software processing.

This probably is not good enough.

zephirus
Title: 44 KHz (CD) not enough !? (Nyquist etc.)
Post by: mrosscook on 2003-05-21 00:04:34
@2Bdecided -- You mentioned in your post that you discussed Demo2 with Halverson, and that he agreed with the impressions you had of a glassy sound with 44.1 and 48 kHz, and of more realism and depth with higher sampling rates.

Did he offer any possible explanations for the effect, gear-based or otherwise?  It was his equipment, after all, and he must have given it some thought; maybe even played with different gear to see if the effect was consistently reproducible?
Title: 44 KHz (CD) not enough !? (Nyquist etc.)
Post by: budgie on 2003-05-21 08:33:56
2Bdecided:

Nice post, but it proves nothing, sad to say... This is something all audiophiles (including me  ) suffer. It's about the feelings and direct comparisons. Under normal listening conditions, on very average equipment (between 1500-2500 Euro for CD player, amp, speakers and cables together) and when you have nothing to compare with, you must be definitely deeply satisfied with good made 16/44,1 CD.

But I think, too, it's important to chase the highest quality possible, but a lot depends on equipment you use... and the question is, what importance has this chase in the real life - and if it has any importance for Average Joe from the street. I am afraid not. People are very, but very satisfied with their clipped CDs and boomboxes  So it is just the matter of snobs (including me...).

And you're right in one thing - I am deeply convinced the best audio engineers were in job between 1954 and 1965 (approx.). They played with mikes, they could perfectly record the space, their recordings have depth... One just can't believe what they could do with the relatively poor equipment. The recordings from that era are just unbelievable, marvellous, monstrous, incredible... I have a lot of them (many on vinyls, but they sound good also from good remastered CD) and they make me always joy when I listen to them!
Title: 44 KHz (CD) not enough !? (Nyquist etc.)
Post by: KikeG on 2003-05-21 10:18:39
David (2Bdecided):

I find your report interesting, I hadn't read about it before. But, as you may imagine,  I see some problems with it.

First, the program material is not what I would consider "critical". I doubt that a 1960 analog recording will have much content over 20 KHz, if any. And this counts too for the differences you also perceived with the 48 KHz sampling rate, that allow up to nearly 24 KHz to be captured. Still, I could be wrong.

Then, what you talk is interesting, but is not more than anecdotal evidence. Who knows if you could have passed a double-blind, statistically sound listening test, even at the exact conditions you heard the differences.

Even if you passed it, it should be analyzed where the objective differences lie. We should analize if the differences are due to the particular setup you listened to, or just due to sampling rates. First, we could analize if there was some problem at the AD/DA chain. If not, we should analyze (measure) if the differences could be due to some "problems" with the converters at the show (I'm being bad here), or due to DCS converter implementation, or due to common converter implementation. For this, we could also try the high quality downsample/upsample process and compare.
Title: 44 KHz (CD) not enough !? (Nyquist etc.)
Post by: 2Bdecided on 2003-05-21 10:24:18
budgie,

I agree that this has no relevance in the "real world" of average Joes and boomboxes. But then, anything better than a reasonable 128kbps mp3 is irrelevant to 99% of people too.

If the audible differences are only present on equipment costing more than most people earn in a year, then maybe we can forget it. However, there's a 95%+ mark up on audio equipment compared to the cost of the raw components. This means some talented audio amatures could get close to this quality, given a lot of time, and maybe a month's wages to construct the equipment. So let's not talk about $20k audio systems as though they're unattainable. There are people who could get close enough with $1k, a soldering iron, and lots of patience. If this hobby is your passion, I think that may be worth it. As someone who might try it, I'd (selfishly) like some nice recordings to play on it, even if you lot can't hear the benefit!   

If there's any truth in the theory that, price for price, a DAC can sound nicer decoding 96k than 44.1k, even though an infinitely expensive DAC can do both perfectly, then 96k seems a good idea.


However, I'm worried that it might work in quite a different way. What if it's like, say, mp3 artefacts. To start with, for some people, they're hard to hear. Many people can't hear them. But some people do learn to hear them. You start with the most extreme examples, and, once you've learnt the "sound" of mp3, it's much easier to identify - even from quite difficult examples. Once your ear/brain learns the pattern, you can find it much more easily. Look at how the some of people involved with codec testing and tweaking are some of the most sensitive - Garf, Dibrom etc. It's probably practice.

So, I'm suggesting that, when it's more common place to experience CD vs something else (better?), more people will get a chance to notice the difference. The more you get to compare, the more you learn how to recognise it - and once you've learnt well, then the problems might annoy you. However, until something better becomes common, you have about as much chance of realising that CD isn't good enough as you would of realising that 160kbps mp3 wasn't good enough in a world where there was NOTHING better. You have live music, but if the recording doesn't sound like live music - well - that's just your stereo.


I'm not saying I actually think either of these things are true. I'm suggesting them as possibilities and speculation - time will tell, and I think I agree with your assessment. Whatever - stereo > multi-channel is a much greater leap than 44.1k>96k. If we can do both, great. If the multi-channel system is a version of ambisonics rather than 5.1 based, so much the better!


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And you're right in one thing - I am deeply convinced the best audio engineers were in job between 1954 and 1965 (approx.). They played with mikes, they could perfectly record the space, their recordings have depth... One just can't believe what they could do with the relatively poor equipment. The recordings from that era are just unbelievable, marvellous, monstrous, incredible... I have a lot of them (many on vinyls, but they sound good also from good remastered CD) and they make me always joy when I listen to them!


Totally totally agree! Some of the early stereo recordings are so good, it makes you think "how did they do that?!" and why can't we do as well today!

You've reminded me: at the same AES, there was a workshop session where various producers talked about work that they'd done, and played examples. One had brought in the theme tune from Austin Powers - the original version (it's been remixed on subsequent films, and the track itself is around 40 years old), which had been recorded on a 3 track recorder. Brilliant! You could see people in the audience enjoying it. "How clever of you to anticipate the moves of Austin powers 40 years ago!" joked the interviewer. Another producer brought some Bolton song from a Disney movie - he'd chosen to bring it because it was the first production he'd worked on where he needed more than 100 tracks. It sucked! Not just because it was Michael Bolton singing Disney - but the recording was just so artificial and flat and BORING! No one was in the least bit interested. (Maybe i'm exagerating, but the poor comparison with the 1960s 3 track recording wsa quite embarasing!)

Now, you could say that it was the songs themselves that made a difference - true, they certainly did. But there was a magic in the actual recording from the 1960s that was completely absent from the others. I'm sure it was the primative technology, and the comparative simplicity of the mixing process that made the recording distinctive, good, and enjoyable.


Cheers,
David.
Title: 44 KHz (CD) not enough !? (Nyquist etc.)
Post by: KikeG on 2003-05-21 10:25:53
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The best procedure for such test seems to be to use one and the same output equipment (soundcard) with one and the same output sampling frequency (96 or 192 KHz, 20-24 bit). And to do anything else only in the digital domain.

That's how PCABX test clips have been generated.

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Otherwise there will always be analog components that may interfere and that may distort the result of such listening test.


My suggestion would include actual DAC implementation on the test, but I guess that 24/96 recording would be very advisable.
Title: 44 KHz (CD) not enough !? (Nyquist etc.)
Post by: 2Bdecided on 2003-05-21 10:34:03
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@2Bdecided -- You mentioned in your post that you discussed Demo2 with Halverson, and that he agreed with the impressions you had of a glassy sound with 44.1 and 48 kHz, and of more realism and depth with higher sampling rates.

Did he offer any possible explanations for the effect, gear-based or otherwise?  It was his equipment, after all, and he must have given it some thought; maybe even played with different gear to see if the effect was consistently reproducible?

He seemed to accept it as a fact of life at 44.1kHz. He'd obviously used other convertors, but that didn't seem the issue.

As for why - I can't remember who said it, but most of the ideas that were mentioned are now discussed on the dCS website, or in papers written by my old tutor (Malcolm Hawksford - search for his AES conference papers if you can). Energy dispersion. Non linearities in the equipment and even in the air. The Japanese (?) paper showing the change of blood flow in the brain when ultra-sonic sounds were present was shown first at that AES (without a translation!), and none of us could follow it! There was a general feeling that, well, maybe it's something to do with something we don't know about human hearing (it is so non-linear), but it's much more likely that it's some engineering issue which is explanable with real science if only you track down all factors.

When you start to think about modelling everything in the signal chain carefully, it's quite conceivable that with any real-world equipment (no matter how expensive) there could be a just perceptible difference between 44.1kHz sampled material and 96kHz sampled material. What it's not possible to explain is why the latter sounds better.

Cheers,
David.
Title: 44 KHz (CD) not enough !? (Nyquist etc.)
Post by: 2Bdecided on 2003-05-21 11:02:34
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David (2Bdecided):

I find your report interesting, I hadn't read about it before. But, as you may imagine,  I see some problems with it.

Yep!

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First, the program material is not what I would consider "critical". I doubt that a 1960 analog recording will have much content over 20 KHz, if any. And this counts too for the differences you also perceived with the 48 KHz sampling rate, that allow up to nearly 24 KHz to be captured. Still, I could be wrong.


It wasn't critical. Well, depends what you're testing, but anyway - I agree. However, don't under estimate the frequency response of a good 2-track studio tape deck from the late 1960s.

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Then, what you talk is interesting, but is not more than anecdotal evidence. Who knows if you could have passed a double-blind, statistically sound listening test, even at the exact conditions you heard the differences.


I totally agree - it's just anecdotal. By the way that I didn't hear it when I was concentrating, but did hear it when I wasn't, it would have to be a well designed test. Certainly worth doing.

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Even if you passed it, it should be analyzed where the objective differences lie. We should analize if the differences are due to the particular setup you listened to, or just due to sampling rates. First, we could analize if there was some problem at the AD/DA chain. If not, we should analyze (measure) if the differences could be due to some "problems" with the converters at the show (I'm being bad here), or due to DCS converter implementation, or due to common converter implementation. For this, we could also try the high quality downsample/upsample process and compare.


Whilst that is all interesting and vital for scientific research, it's irrelevant to knowing whether 96k is better or not. Let's assume I could pass a blind test. Let's assume some of the other people who claim to hear a difference (they're not all using dCS convertors!) also pass a blind test. "Passing the test" means detecting 44.1k vs analogue, but failing to detect 96k vs analogue. This actually clears up most of your points.

Whilst, as a scientist, I want to know why... as a listener, I just want to listen to the better system.

As a scientist, "the high quality downsample/upsample process" is the most interesting one to try.

Cheers,
David.
Title: 44 KHz (CD) not enough !? (Nyquist etc.)
Post by: KikeG on 2003-05-21 11:13:37
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As for why - I can't remember who said it, but most of the ideas that were mentioned are now discussed on the dCS website, or in papers written by my old tutor (Malcolm Hawksford - search for his AES conference papers if you can). Energy dispersion. Non linearities in the equipment and even in the air. The Japanese (?) paper showing the change of blood flow in the brain when ultra-sonic sounds were present was shown first at that AES (without a translation!), and none of us could follow it! There was a general feeling that, well, maybe it's something to do with something we don't know about human hearing (it is so non-linear), but it's much more likely that it's some engineering issue which is explanable with real science if only you track down all factors.

The Oohashi japanese paper is the only thing I know of that offers some serious evicence of ultrasonic high frequencies being perceived in some way. Still, there are also some issues with it:

For one, the test signal had extremely rich ultrasonic content, and the whole system (including mic + speakers) used was flat up to 50 KHz, IIRC. All this is quite uncommon both at real-world recording studios and at real-world listening setups.

Also, I think the paper lacks some details over the experiment, such as some detailed measurements of the signals at the listening location, intermodulation figures of the test chain, nº of trials, etc, that would add more solidity to the results.

Then, this paper was peer-reviewed, approved and published at a neuropsychiatry journal, but a very similar one from the same authors was presented several years ago at the JAES, and AFAIK never passed the peer-review stage. Even when the paper has been published at a respected medical journal, I wait for anyone that can duplicate the results independently, nobody has done so so far AFAIK.

Now, I'll try to take a look at the DCS website and the papers available at there. I think that there is a possibility that nonlinearities in equipment/air/ear could account for a true perceivable difference. Then, and taking into account all possibilities, the issue would be which perception is more accurate to the real-world experience: the one caused from the signal lowpassed around 20 KHz, or the one that is NOT lowpassed? There would be some further discussion here.
Title: 44 KHz (CD) not enough !? (Nyquist etc.)
Post by: KikeG on 2003-05-21 11:20:45
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Whilst that is all interesting and vital for scientific research, it's irrelevant to knowing whether 96k is better or not. Let's assume I could pass a blind test. Let's assume some of the other people who claim to hear a difference (they're not all using dCS convertors!) also pass a blind test. "Passing the test" means detecting 44.1k vs analogue, but failing to detect 96k vs analogue. This actually clears up most of your points.

Yes, this is what I was implicitly trying to say too: one should know if the audible differences were due to DCS converters at the show, due to "standard" DCS converters, or common to all or most converters available. In this case, the use of 96 KHz would be an easy solution for a common problem. There would remain the issue of if using better 44.1 KHz converters the difference would remain, and in case that not, how good would the converters need to be.
Title: 44 KHz (CD) not enough !? (Nyquist etc.)
Post by: 2Bdecided on 2003-05-21 11:30:38
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Then, and taking into account all possibilities, the issue would be which perception is more accurate to the real-world experience: the one caused from the signal lowpassed around 20 KHz, or the one that is lowpassed?

That's the really strange thing - with all these "non linear" explanations, it should be better to remove the ultrasonic stuff and give the equipment an easier time; whereas the opposite appears to be true in practice.


FWIW the effect of huge amounts of ultrasonic noise on equipment are well known. It's often described as an "oily" sound. My guess is that the high frequencies are linearising the equipment in a similar manner to dither linearising a DAC. e.g. consider a graph of an audio amplifier's response - voltage in vs voltage out. Obviously the output voltage should always be a constant multiplied by the input voltage. It should be a straight y=kx graph, up to the point where the thing distorts at a high voltage, where for any increase in the input, the output stays stuck at some value.

Now, consider a non ideal amplifier, where the input/output characteristic isn't quite a straight line. Maybe there's a small kink in the graph around y=x=0. (i.e. the middle, the origin). In a normal system, very quiet signals are always going to hit this kink, because it happens around very small voltages. However, add a huge amount of ultrasonic noise, and any quiet audible signal can be pushed onto any part of the input/output curve, and to different parts moment by moment. Before, the kink added a predictable error to the input (we call this distortion) - now, it's having an almost random effect. Adding something random is basically adding noise. Because the process is radonmised by ultrasonic noise, the additional noise added by the "kink" will also be mainly ultrasonic. It's like magic - with enough ultrasonic noise, you can make the system perfect... If the system can handle the ultra sonic noise that is!

This is only my theory as to why ultrasonic noise makes audio equpiment sound nice and "oily". Whatever, much of the "nice" sound of SACD is, supposedly, quite predictable from this nice oily sound which you can get by adding huge amounts of random ultrasonic energy to any source.

Cheers,
David.
Title: 44 KHz (CD) not enough !? (Nyquist etc.)
Post by: mrosscook on 2003-05-21 15:15:46
2Bdecided,
Do you recall whether the setup of Demo2 involved any dithering steps, or was the digitization always done by simple truncation?  I realize that everything was done in 24-bit, but even so...
Title: 44 KHz (CD) not enough !? (Nyquist etc.)
Post by: DickD on 2003-05-21 19:45:50
With 24-bit there's enough thermal noise in the electronics that surely it's effectively dithered heavily in the ADC whether you want it to be or not! And remember this was coming from a studio quality analogue source medium then being digitized.
Title: 44 KHz (CD) not enough !? (Nyquist etc.)
Post by: DonP on 2003-05-21 20:36:54
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Now, consider a non ideal amplifier, where the input/output characteristic isn't quite a straight line. Maybe there's a small kink in the graph around y=x=0. (i.e. the middle, the origin). In a normal system, very quiet signals are always going to hit this kink, because it happens around very small voltages. However, add a huge amount of ultrasonic noise, and any quiet audible signal can be pushed onto any part of the input/output curve, and to different parts moment by moment.

There is a naturally a kink around x=y=0.  Most amps have a DC biased so this doesn't happen
at a zero input signal, but at some point on the curve where it is loud enough to cover up the kink.
A "class A" amp is defined as biased so you never hit that zero crossing.

Your idea of the ultrasonic bias is  pretty much what exactly what the bias on a tape recorder does,
though the effect they are quashing with the bias is I think hysteresis.
Title: 44 KHz (CD) not enough !? (Nyquist etc.)
Post by: Pio2001 on 2003-05-21 22:07:56
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Also, I think the paper lacks some details over the experiment, such as some detailed measurements of the signals at the listening location...

There are spectrums measured from the listening location : http://jn.physiology.org/cgi/content/full/83/6/3548/F1 (http://jn.physiology.org/cgi/content/full/83/6/3548/F1)
Title: 44 KHz (CD) not enough !? (Nyquist etc.)
Post by: budgie on 2003-05-22 09:09:05
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Totally totally agree! Some of the early stereo recordings are so good, it makes you think "how did they do that?!" and why can't we do as well today!

Now, you could say that it was the songs themselves that made a difference - true, they certainly did. But there was a magic in the actual recording from the 1960s that was completely absent from the others. I'm sure it was the primative technology, and the comparative simplicity of the mixing process that made the recording distinctive, good, and enjoyable.

I think, that partial explanation could be: because we have a lot of better technology, we lack the interest how to get really the best possible sound... we rely too much on machines and effects and lose our own creative potential, because it sounds great almost without any effort... 
And remember, then there was almost no post-production. The songs were recorded in one take, that's the reason why you can see on editions that are released nowadays various take-numbers. And the albums were made mostly in one or two days!
Title: 44 KHz (CD) not enough !? (Nyquist etc.)
Post by: towolf on 2003-05-24 00:43:15
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There are spectrums measured from the listening location : http://jn.physiology.org/cgi/content/full/83/6/3548/F1 (http://jn.physiology.org/cgi/content/full/83/6/3548/F1)

Finally some physiological measures. It's always good if you can backup psychophysically measured interaction effects with objective measures of the wetware implementation in neuroscience.

Nice gear they got.
Title: 44 KHz (CD) not enough !? (Nyquist etc.)
Post by: KikeG on 2003-05-24 12:54:50
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There are spectrums measured from the listening location : http://jn.physiology.org/cgi/content/full/83/6/3548/F1 (http://jn.physiology.org/cgi/content/full/83/6/3548/F1)

I know, but those are not what I'd call very detailed measurements. Also, if you compare carefully the FRS and the HCS spectrums (I did it cutting them from a paper print and superimposing them over a window at home), you'll see that they are not identical, there are minor but obvious differences at some parts of the spectrum.

For that reason, a more complete set of measurements and objective analysis of the process would have been necessary, in order to discard possible real audible diferences just at the audible band.