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Hydrogenaudio Forum => Scientific Discussion => Topic started by: thesurfingalien on 2011-06-08 01:16:42

Title: Dynamic range question
Post by: thesurfingalien on 2011-06-08 01:16:42
Hi All,

I am having problems understanding the concept of dynamic range, and more specific how the dynamic range of human hearing relates to the dynamic range as specified for audio equipment.

What I have read on the Net is that the dynamic range of human hearing is, on average, 135 dB (the pain limit / threshold?). 

I also understand that the dynamic range of a CD (16 bit) is limited to 96 dB, and for HD (24 bit) recordings 144 dB.  This dynamic range is calculated by the bit-depth.

For playback of music (I use 44.1/16 flac only) I use a E-MU 1820 that has a dynamic range of about 115 dB (or so).  I am not sure what my amp can do...

However, when I play music I hardly pass 80 dB (or so) listening volume, so the 96 dB CD data (if the recording makes full use of the range that is) gets "compressed", while the relative dynamic range remains.

After the long intro my question in essence is:

Does the human hearing have a similar "resolution" that is comparable to the resolution defined by the bit-depth in (digital) audio? Or am I just comparing apples and pears?

Regards,
Peter

Title: Dynamic range question
Post by: ExUser on 2011-06-08 01:44:32
However, when I play music I hardly pass 80 dB (or so) listening volume, so the 96 dB CD data (if the recording makes full use of the range that is) gets "compressed", while the relative dynamic range remains.
I think this is where the problem in your reasoning lies. Your 96dB of CD dynamic range is kind of wasted. You hear the "top" 80dB while the lower 16dB is lost beneath the noise floor. Realistically, playing at 80dB, there's maybe 30-40dB of noise in your room, so you get maybe 40dB of dynamic range in your environment.
Title: Dynamic range question
Post by: pdq on 2011-06-08 01:51:16
...and with proper dither the dynamic range of 16 bits is considerably more than 96 dB.
Title: Dynamic range question
Post by: Woodinville on 2011-06-08 02:28:42
In most any modern room, the lower limit of masking noise is well above 0dB.  The greatest output level you get from most speakers is under 115dB.  For most circumstances, 16 bits is good enough. 20 bits is more than enough to accomodate atmospheric-noise levels to speaker-overload levels.  24 bits is usually wishful thinking.
Title: Dynamic range question
Post by: knutinh on 2011-06-08 09:20:58
Given that background noise can have all kinds of distributions, frequency range, etc. How should one measure background noise to arrive at some level reading that can be compared with the dynamic range of recording medium and the maximum SPL of your loudspeakers to be assured that the noise level of the room dominates the noise level of the recording medium at all times, all frequencies etc?

If room noise was some white noise source rated at 20 dB A-weighted, and the noise level of the recording medium (at some sensible playback level) was similar to a white-noise source rated at 20dB A-weighted, I think that it is fair to believe that _some_ perceptual gain might be expected by lowering the noise level of the medium by 3 or 10 dB?

-k
Title: Dynamic range question
Post by: Woodinville on 2011-06-08 09:30:46
Given that background noise can have all kinds of distributions, frequency range, etc. How should one measure background noise to arrive at some level reading that can be compared with the dynamic range of recording medium and the maximum SPL of your loudspeakers to be assured that the noise level of the room dominates the noise level of the recording medium at all times, all frequencies etc?

If room noise was some white noise source rated at 20 dB A-weighted, and the noise level of the recording medium (at some sensible playback level) was similar to a white-noise source rated at 20dB A-weighted, I think that it is fair to believe that _some_ perceptual gain might be expected by lowering the noise level of the medium by 3 or 10 dB?

-k


You need to know the noise spectrum, there is no simple answer.  If you're talking noise on noise masking, 3dB is about the limit.
Title: Dynamic range question
Post by: knutinh on 2011-06-08 10:15:55
You need to know the noise spectrum, there is no simple answer.  If you're talking noise on noise masking, 3dB is about the limit.

That was kind of my rhetorical point: simplistic claims about acoustic noise floor masking medium noise floor may well be practically correct, but they must be making some assumptions that are seldomly communicated clearly.

-k
Title: Dynamic range question
Post by: DonP on 2011-06-08 10:50:05
For listening to high dynamic range material (say, 80 dB)  turn off any nearby PC's, turn off the heat, unplug that fridge in the kitchen.  I've had no luck requesting that the passenger jet 20 miles away cut it's engines for a few minutes.

So what steps would you need to take over that in a home environment  to hear another 20 dB and talk about needing more than 16 bits?
Title: Dynamic range question
Post by: knutinh on 2011-06-08 11:19:15
For listening to high dynamic range material (say, 80 dB)  turn off any nearby PC's, turn off the heat, unplug that fridge in the kitchen.  I've had no luck requesting that the passenger jet 20 miles away cut it's engines for a few minutes.

So what steps would you need to take over that in a home environment  to hear another 20 dB and talk about needing more than 16 bits?

I am not claiming that 16 bits is not enough, and I am certainly not claiming that I have heard its limitations. I still think that claims from a sceptic/scientific forum like this should be subject to some dissection before being broadcast as a bullet-proof advice.

Question is: is 20dB room-noise/recording-noise headroom enough to say with certainty that recording does not matter in any perceptual way? I think that perceptual mechanisms as well as pdf/frequency distribution are needed in that argument, knowing your way around log10(x1/x2) is not sufficient.
Title: Dynamic range question
Post by: thesurfingalien on 2011-06-08 12:29:59
@All:

Thanks so far for your replies, but it's not actually what I am looking for (or I just don't understand).

I am having trouble with the relation between bit-depth (the resolution) and the dB scale.  I know the formula for calculating this, but what is that based upon.

The second question is if there is any relation between this dB-scale, and the sound pressure dB-scale.

Thanks,
Peter



Title: Dynamic range question
Post by: knutinh on 2011-06-08 13:37:16
The second question is if there is any relation between this dB-scale, and the sound pressure dB-scale.

dB is just that - a scale. It says how large something is compared to some other thing using a non-linear scale that is appropriate for many applications.
Quote
I am having trouble with the relation between bit-depth (the resolution) and the dB scale. I know the formula for calculating this, but what is that based upon.

Not knowing what formula you are talking about, it is hard to comment.

The rule is that for e.g. 16 bits you have 2^16 = 65536 discrete levels available. Any continous signal that is directly discretized as 16 bits will have an error that is limited by a half stepsize in each direction. We are sometimes interested in the power of the full-scale signal compared to the power of the corresponding error. Given some assumptions this turns out to be approximately 6*#bits, or 96dB in the case of 16 bits.

-k
Title: Dynamic range question
Post by: drewfx on 2011-06-08 17:05:26
@All:

Thanks so far for your replies, but it's not actually what I am looking for (or I just don't understand).

I am having trouble with the relation between bit-depth (the resolution) and the dB scale.  I know the formula for calculating this, but what is that based upon.


I'm not sure which formula you are referring too, but assuming it's the "simplified" ~6dB per bit formula, the long explanation is it works like this:

A dB is just a logarithmic way of expressing a ratio of 2 values. For digital audio we use the ratio of the squares of the amplitudes, which equates to:

dB's = 20*log10(ratio of amplitudes)

So for a ratio of "2" (twice the amplitude), you get 20*log10(2) = ~6dB

And since each added bit doubles (a ratio of 2) the the maximum value you can store, that's where you get the ~6dB per bit. Or to put it another way, using the ratio of the largest number at a given bit depth to 1, for 16bits:

dB's = 20*log10(65536/1) =  +96.3dB

Sorry if you already knew this.
Title: Dynamic range question
Post by: [JAZ] on 2011-06-08 19:04:30
Like others have said, the key is knowing that talking in dBs is just talking about ratios (difference between two values).

Then, dBs are used to calculate different things, which can be compared. The two that matters to us are these ones:

dB SPL  (dB Sound pressure level), which is a reference scale from no pressure (no signal) upwards.
I.e. 0db SPL is the minimum signal possible.

db FS (dB Full scale), which is a reference scale from the maximum level of the media downwards.
I.e. 0dB FS is the maximum signal possible in the medium (or in some cases, like with floating point math, the value that represents the physical maximum, when it is to be converted to integer and/or analog).


As such, a non-dithered CD has the noise floor at -96dB FS, which means that has a SNR of 96dB. (How to calculate this and why is explained in the thread by drewfx.)

Like others have said, the minimum (reasonable) noise floor of a quiet room is 30dB SPL (An anechoic chamber might have lower levels, but that's not an usual room). (An office room is said to have a noise floor around 50dB SPL, with people talking and machines running). On big discotheques, the music can reach values around 100dB SPL. (or sometimes 110dB SPL). I can't comment on concerts, but concerts are reallly different from each other and big ones use to be on open spaces.

One can say that if you were to hear the noise floor of a CD in this quiet room, the strongest signal of this CD would be reproduced at 30+96 = 126dB SPL. (At least. Intersample peaks could be higher, but that's another subject, just like the comment about dither).


Title: Dynamic range question
Post by: saratoga on 2011-06-08 19:15:07
You need to know the noise spectrum, there is no simple answer.  If you're talking noise on noise masking, 3dB is about the limit.

That was kind of my rhetorical point: simplistic claims about acoustic noise floor masking medium noise floor may well be practically correct, but they must be making some


The assumption is generally that room noise is white.  I don't think one needs to communicate this, its fairly obvious. 

I don't think the assumption is all the relevant though.  Given the equal loudness contour, and that quantization noise is effectively white, the only part of the quantization noise at 16 bits really contributing to the noise floor would be about 2k-4khz, which incidentally is the only part of the room noise spectrum that really matters.  So unless your room is an anechoic chamber with a perpetually running tuning fork, the exact distribution of noise doesn't matter too much
Title: Dynamic range question
Post by: DVDdoug on 2011-06-08 19:37:54
Quote
The second question is if there is any relation between this dB-scale, and the sound pressure dB-scale.
Yes.  There is a one-to-one relationship.  (But, the exact conversion factor isn't usually known.) 

Let's assume you are playing a -6dBFS test-tone file on your computer, and the sound is coming out of your speakers at 80dBSPL.  If you boost the digital signal by 6dB (to 0dBFS), you'll get 6dB more from your speakers (86dBSPL).  ...Assuming your amplifier is not clipping, and that your speakers are linear, etc, etc, etc.

But since, we usually don't have a calibrated system,  we can't make conversions between the two.  Obviously, when you adjust the volume control, or move closer to the speaker, you change the acoustic SPL level without affecting the data in the file.    Movie theaters are calibrated, so if everything is set-up correctly and you are sitting in the "right" location, etc., you can know the approximate SPL level in advance.

Oh... SPL measurements get a little more complicated with things like "A weighting" and averaging.  (SPL is often measured in a way that corresponds with human perception of loudness.)


Title: Dynamic range question
Post by: Woodinville on 2011-06-08 19:38:01
The assumption is generally that room noise is white.  I don't think one needs to communicate this, its fairly obvious.


Room noise is almost never white. In fact, I don't think I've seen such a thing.
Title: Dynamic range question
Post by: Northpack on 2011-06-08 20:15:27
I guess room noise usually has the least amount of energy in the 2kHz range - we naturally build our accommodation in a way that we allow higher noise levels in those frequency domains we are less sensitive to (we're instinctively "noise-shaping" our environment). Think of all the noise emitting devices and how walls filter the sound from outside. Either we have low frequencys which pervade the walls or we have high frequency noise generated by all kinds of electric gear.
Title: Dynamic range question
Post by: knutinh on 2011-06-08 20:49:09
I guess room noise usually has the least amount of energy in the 2kHz range - we naturally build our accommodation in a way that we allow higher noise levels in those frequency domains we are less sensitive to (we're instinctively "noise-shaping" our environment). Think of all the noise emitting devices and how walls filter the sound from outside. Either we have low frequencys which pervade the walls or we have high frequency noise generated by all kinds of electric gear.

If your theory on acoustic room noise tending to follow perception, and dithering of digital quantization follows the same general curves, then measurements of both should be comparable?

I'd think that some major mechanisms are:
1. The tendency of thick, heavy housing materials to attenuate high frequencies more than the very low frequencies.
2. The 50/60Hz powerline frequency and any in-room equipment that generate noise at it or one or more multiples
3. Temporal fluctuations - passing cars may influence long-term averaged mesurements but in-between passing cars, the noise level could dip significantly

For "harmonic" noise sources (e.g. mechanical AC), what spacing is needed between harmonics before measuring them as if they were dense stochastic noise will lead to very wrong conclusions as to human perception in our context?

-k
Title: Dynamic range question
Post by: saratoga on 2011-06-08 20:58:02
The assumption is generally that room noise is white.  I don't think one needs to communicate this, its fairly obvious.


Room noise is almost never white. In fact, I don't think I've seen such a thing.


I didn't say it was white, just that by comparing it based on total energy to a white noise source, you are assuming its white

Given the modes that fit into a typical room, I doubt its all that white.  But as I argued before, I also doubt it matters much unless you've got some loud fan or something next to you in an otherwise quiet room.
Title: Dynamic range question
Post by: DonP on 2011-06-09 00:17:21


dB SPL  (dB Sound pressure level), which is a reference scale from no pressure (no signal) upwards.
I.e. 0db SPL is the minimum signal possible.


dB is a logarithmic ratio of power, 1/10 of a bel.  A bel is a 10:1 power ratio, so a dB is the tenth root of 10 power ratio.

no signal would be negative infinity dB.  Ratios, remember?

0dB spl is nominally the minimum volume a human can detect.  About as accurate as "the width of the king's thumb" if you don't know which king.  So they've standardized the reference at 20 micropascals. 

There are other 0dB references for other contexts like dBm (reference = 1 milliwatt) and the mentioned dB FS.
Title: Dynamic range question
Post by: greynol on 2011-06-09 00:32:00
Let's not forget dBu and dBV.
Title: Dynamic range question
Post by: Woodinville on 2011-06-09 02:02:49
The assumption is generally that room noise is white.  I don't think one needs to communicate this, its fairly obvious.


Room noise is almost never white. In fact, I don't think I've seen such a thing.


I didn't say it was white, just that by comparing it based on total energy to a white noise source, you are assuming its white

Given the modes that fit into a typical room, I doubt its all that white.  But as I argued before, I also doubt it matters much unless you've got some loud fan or something next to you in an otherwise quiet room.


Actually, the world nowadays is annoyingly noisy, when you get right down to it. (sigh)
Title: Dynamic range question
Post by: drewfx on 2011-06-09 02:17:20
And to further clarify the use of "dB" vs. "dB SPL"/"dB FS"/"dBu"/"dBV"/...

The thing to remember is "dB" alone is always used to compare 2 values - it's an expression of the ratio between the 2 values. "Signal A peaks at -7dB relative to signal B".

But "dB with a suffix" is used to compare a single value to a predefined reference value specified by the suffix. As previously noted, "dB FS" defines 0dB FS as "the maximum value that can be represented (Full Scale)". So if you use "dB FS", it means you are comparing your value to this predefined value. "Signal A is -22dB FS" means "Signal A is -22dB compared to the predefined value of 0dB FS".
Title: Dynamic range question
Post by: MichaelW on 2011-06-09 04:42:13
Actually, the world nowadays is annoyingly noisy, when you get right down to it. (sigh)


Yes, but when I spend time in the country I'm struck by how very noisy birds can be. Not to mention the time I was having a cup of coffee on the sidewalk in urban Adelaide, and the parrots in a nearby tree were drowning the traffic noise. Real quiet is hard to find (and rather freaky when you do).
Title: Dynamic range question
Post by: WernerO on 2011-06-09 10:12:23
when I spend time in the country I'm struck by how very noisy birds can be.


Last week we spent a lot of time in the garden (agricultural village, meaning detached houses on plots sized 500 - 1000 square meters each, lawns lined with trees, ...) and it struck me too what a racket the few remaining birds here make. So I went and measured ~60dB (C-weighted), with excursions to 70dB.

We need more cats.

Title: Dynamic range question
Post by: thesurfingalien on 2011-06-09 13:02:54
Actually, the world nowadays is annoyingly noisy, when you get right down to it. (sigh)


Yes, but when I spend time in the country I'm struck by how very noisy birds can be. Not to mention the time I was having a cup of coffee on the sidewalk in urban Adelaide, and the parrots in a nearby tree were drowning the traffic noise. Real quiet is hard to find (and rather freaky when you do).


In our place in Brasil we have Cicadas (Cigarras do Brasil), and they make a terrible noise!  I read that the males can produce some 100 dB, and if one starts, the rest (a lot!) follows.  Listening to music, even inside, is pretty much out of the question when they go at it...

I still need to make a recording of their song and see what kind of tones they produce.  That will have to wait until the winter is over.  Now we have some peace and quiet here :-)
Title: Dynamic range question
Post by: knutinh on 2011-06-10 10:31:56
I seem to remember that people who record ambient sounds for movies etc (animals, weather, water) have a hard time finding spots on the earth that are not affected by passing planes, kids with a boomblaster etc. Acoustic pollution.

-k
Title: Dynamic range question
Post by: Kees de Visser on 2011-06-10 22:18:00
Absolutely ! Last year I've spent quite some time recording 3D sound ambience and it is really frustrating that most of the recording is polluted. The best option is to record hours and hours and select the usable parts (if any!) back home in the studio.
Title: Dynamic range question
Post by: thesurfingalien on 2011-06-11 10:59:59
@All,

Although all info was useful and interesting, I am still struggling with the concept of relating bit-depth to a dB scale...

Perhaps if I (again) rephrase my question...

Given that (for CD) the 16 bit depth is limiting dynamic range to 96 dB, on which basis was decided that the 96 dB was (good) enough?  Why not, for example, 128 dB?  To me it looks like that will only require a change in the step-size on the dB scale...

Thanks again!
Peter



Title: Dynamic range question
Post by: lvqcl on 2011-06-11 11:11:20
To me it looks like that will only require a change in the step-size on the dB scale...


Sorry, but what do you mean? 'dB scale' cannot be changed by its definition.
Title: Dynamic range question
Post by: thesurfingalien on 2011-06-11 14:11:53
To me it looks like that will only require a change in the step-size on the dB scale...


Sorry, but what do you mean? 'dB scale' cannot be changed by its definition.


The scale itself can not be changed, but by step-size I mean steps of (for example) 0.1 dB or steps of 0.2 dB.

Title: Dynamic range question
Post by: lvqcl on 2011-06-11 14:19:12
The scale itself can not be changed, but by step-size I mean steps of (for example) 0.1 dB or steps of 0.2 dB.


If variables A and B differ by 0.1 dB, then A/B = 1.01157945...;  if A and B differ by 0.2 dB, then A/B = 1.02329299...
So... how the step-size can be changed?
Title: Dynamic range question
Post by: thesurfingalien on 2011-06-11 15:37:16
The scale itself can not be changed, but by step-size I mean steps of (for example) 0.1 dB or steps of 0.2 dB.


If variables A and B differ by 0.1 dB, then A/B = 1.01157945...;  if A and B differ by 0.2 dB, then A/B = 1.02329299...
So... how the step-size can be changed?


If the step-size is 0.1 dB, it takes 960 steps to get to 96 dB.  For 0.2 dB that's 480 steps. 
Title: Dynamic range question
Post by: drewfx on 2011-06-11 17:33:50
@All,

Although all info was useful and interesting, I am still struggling with the concept of relating bit-depth to a dB scale...

Perhaps if I (again) rephrase my question...

Given that (for CD) the 16 bit depth is limiting dynamic range to 96 dB, on which basis was decided that the 96 dB was (good) enough?  Why not, for example, 128 dB?  To me it looks like that will only require a change in the step-size on the dB scale...

Thanks again!
Peter


96 dB of dynamic range represents the ratio of the loudest sound to the quietest sound - it's the ratio of the largest number available using 16 bits to "1". Thus to get more dynamic range, you need a bigger ratio, which means you have to add more bits.

The "step size" is fixed by the fact that it's binary.
Title: Dynamic range question
Post by: dv1989 on 2011-06-11 17:37:04
1 bit represents 6 dB of amplitude (i.e. a doubling/halving initially, then tailing off hence the logarithmic shape of the dB curve). Ergo 16*6=96.
Title: Dynamic range question
Post by: lvqcl on 2011-06-11 18:34:09
If the step-size is 0.1 dB, it takes 960 steps to get to 96 dB.  For 0.2 dB that's 480 steps.


1 step is 1 bit, or ~6.02 dB. 16 steps -> 96 dB.
Title: Dynamic range question
Post by: DonP on 2011-06-11 19:21:58
If the step-size is 0.1 dB, it takes 960 steps to get to 96 dB.  For 0.2 dB that's 480 steps.


1 step is 1 bit, or ~6.02 dB. 16 steps -> 96 dB.


16 bits isn't 16 steps, it's 2**16 steps, a number in the range +/- 32767.  In terms of "line in" voltage, each step is about 1/30 mv.  If you declare that each step is twice as big, that just makes everything louder.  It doesn't change the ratio between the loudest and quietest signal you can represent.
Title: Dynamic range question
Post by: Notat on 2011-06-12 18:10:33
Given that (for CD) the 16 bit depth is limiting dynamic range to 96 dB, on which basis was decided that the 96 dB was (good) enough?  Why not, for example, 128 dB?  To me it looks like that will only require a change in the step-size on the dB scale...

During the development of the CD format, a 14-bit format (84 dB) was originally proposed. The 14-bit proposal was based on the capabilities of the ADCs and DACs available at the time and on calculations that you see in this thread of ideal dynamic range of real listening environments. The resolution was pushed to 16 bits at the insistence of Sony.
Title: Dynamic range question
Post by: Brand on 2011-06-12 22:11:17
I must admit I have the same questions as the OP regarding digital dB and "real world" dB (sound pressure) or perceived loudness.

I've been once told that going from 0 dB to -6 dB in the digital side (PC) halves the loudness. And testing this quickly seemed to confirm it.
Now, does this mean that the sound pressure dB goes from, let's say, 80 dB to 40 dB?

Also, does perhaps the relation between the digital dB and sound pressure change, depending on the volume?


1 bit represents 6 dB of amplitude (i.e. a doubling/halving initially, then tailing off hence the logarithmic shape of the dB curve). Ergo 16*6=96.

This kind of confirms my suspicion that it's only from 0 dB to -6 dB that the halving occurs, while later a 6 dB decrease doesn't affect the loudness as much (logarithmic curve and all). But again, I'm mostly talking from some limited empirical experience/messing around. I've yet to properly grasp the theory behind this.
Title: Dynamic range question
Post by: DonP on 2011-06-12 22:38:02
I must admit I have the same questions as the OP regarding digital dB and "real world" dB (sound pressure) or perceived loudness.

I've been once told that going from 0 dB to -6 dB in the digital side (PC) halves the loudness. And testing this quickly seemed to confirm it.
Now, does this mean that the sound pressure dB goes from, let's say, 80 dB to 40 dB?


Perceived loudness nominally doubles/halves with a 10 dB change, which is a 10x change in power.  Perception is by nature at least somewhat subjective, so that may not be exact for you.

If your speakers are in their linear range (aka not distorting) then halving the voltage (quartering the power) is a 6 dB cut in the electrical signal and also a 6 dB cut in the acoustic power. 

Quote
Also, does perhaps the relation between the digital dB and sound pressure change, depending on the volume?


No.

Quote
This kind of confirms my suspicion that it's only from 0 dB to -6 dB that the halving occurs, while later a 6 dB decrease doesn't affect the loudness as much (logarithmic curve and all). But again, I'm mostly talking from some limited empirical experience/messing around. I've yet to properly grasp the theory behind this.


No, decibels are a logarithmic scale in both domains.  Again, your perception of loudness is subjective so may not perfectly track the model of 10dB = halving of apparent loudness all across the range, but a dB is the same change in measured power whether acoustic or electrical.
Title: Dynamic range question
Post by: lvqcl on 2011-06-12 22:47:10
I've been once told that going from 0 dB to -6 dB in the digital side (PC) halves the loudness.

-3 dB: halves the power
-6 dB: halves the amplitude

Now, does this mean that the sound pressure dB goes from, let's say, 80 dB to 40 dB?

This means that the sound pressure goes from 80 dB to 74 dB.

This kind of confirms my suspicion that it's only from 0 dB to -6 dB that the halving occurs, while later a 6 dB decrease doesn't affect the loudness as much (logarithmic curve and all).

dB scale is logarithmic too.
Title: Dynamic range question
Post by: Brand on 2011-06-13 10:25:31
I've been once told that going from 0 dB to -6 dB in the digital side (PC) halves the loudness.

-3 dB: halves the power
-6 dB: halves the amplitude

Now, does this mean that the sound pressure dB goes from, let's say, 80 dB to 40 dB?

This means that the sound pressure goes from 80 dB to 74 dB.

I see. I thought amplitude was directly correlated with sound pressure.
Is there another [analog] scale that's more suited for measuring amplitude changes?
Title: Dynamic range question
Post by: lvqcl on 2011-06-13 10:51:29
Is there another [analog] scale that's more suited for measuring amplitude changes?

Sound pressure, measured in pascals.
Title: Dynamic range question
Post by: DonP on 2011-06-13 12:13:02
Quote

-3 dB: halves the power
-6 dB: halves the amplitude

I see. I thought amplitude was directly correlated with sound pressure.
Is there another [analog] scale that's more suited for measuring amplitude changes?


Power is directly related to sound pressure.

The amplitude represents the voltage.  Power = voltage * current, but  current goes up with voltage  (current = voltage/resistance)
so power is proportional to voltage squared.  That's why halving the amplitude (voltage) quarters the power and makes a 6 dB difference.

I'm still seeing gaps in the basic concept of dB in this thread.  When kids in middle school math class ask when they'll ever use logarithms,  maybe the answer should be so they can talk about stereos.
Title: Dynamic range question
Post by: Soap on 2011-06-13 13:02:03
I'm still seeing gaps in the basic concept of dB in this thread.

I believe one of the problems seen here is a confusion concerning the difference between amplitude and power.  Between the height of a wave (curve) and the area underneath said curve.
Title: Dynamic range question
Post by: DVDdoug on 2011-06-13 21:52:18
Quote
Given that (for CD) the 16 bit depth is limiting dynamic range to 96 dB, on which basis was decided that the 96 dB was (good) enough?
If you listen to a file that's been reduced by 90dB, I think you'll agree it's enough...

Quote
Why not, for example, 128 dB? To me it looks like that will only require a change in the step-size on the dB scale...
Since all the steps are the same size (with linear PCM) and we are talking about ratios, the size of the step doesn't matter!  If you run your DAC into an amplifier, the steps get bigger, and -6dB is still half. 

But, you are right! You can have a non-linear coding scheme where the steps are not equal.    i.e. Imagine a logarithmic system where each step is 0.01dB.  (I believe u-law and a-law encoding use a nonlinear system, but I haven't really studied these formats..)

Title: Dynamic range question
Post by: Northpack on 2011-06-14 08:15:32
I think this relation 1bit to 6.02dB is where some all-too-common misconceptions rely on. The most notorious: the digital-loathing audiophile who thinks than he can hear the "switching of the bits"... you know, those harsh digital steps in a PCM waveform who completely ruin the smooth analogue siginal.

So, if someone really wants to explain digital audio to the layman without proper mathematical knowledge, I think it would be best to start by debunking this very misconception, explaining why there isn't such a thing as an arbitrary step size in digital audio and how the dynamic range is limited by quantization noise.

Anyone interested in writing such an explanation? I think it could save hundreds of souls from ignorance... he or she would gain some Karma!
Title: Dynamic range question
Post by: knutinh on 2011-06-14 09:13:20
I think this relation 1bit to 6.02dB is where some all-too-common misconceptions rely on. The most notorious: the digital-loathing audiophile who thinks than he can hear the "switching of the bits"... you know, those harsh digital steps in a PCM waveform who completely ruin the smooth analogue siginal.

So, if someone really wants to explain digital audio to the layman without proper mathematical knowledge, I think it would be best to start by debunking this very misconception, explaining why there isn't such a thing as an arbitrary step size in digital audio and how the dynamic range is limited by quantization noise.

Anyone interested in writing such an explanation? I think it could save hundreds of souls from ignorance... he or she would gain some Karma!

Properly dithered digital behaves similar to analog systems where the noise floor is (best case) about 6*#bits below the maximum signal.

For CD (16 bits) this works out to be about 96dB, or 2^16 or 65536:1. For hirez formats using 24 bits, this would ideally mean 144 dB, but in practice man cannot make AD and DA-converters of such high precision.

When doing proper level-aligned blind testing, somewhere around 14-16 bits seems to*) be enough for all sound playback applications. More resolution mainly buys you peace of mind.

-k
*)Blind tests cannot prove that any resolution is "high enough" for all applications, but it repeatedly failing to prove it is often considered a convicing indication.
Title: Dynamic range question
Post by: Fedot L on 2011-06-14 10:43:31
...I thought amplitude was directly correlated with sound pressure.

Yes, it is.
===
Sound pressure, measured in pascals.

Sure.
===
Power is directly related to sound pressure.

Electric power of an amp is directly related to sound intensity (acoustic intensity), W/m2 (watts per square metre), and sound pressure is directly related to voltage.
http://en.wikipedia.org/wiki/Sound_intensity (http://en.wikipedia.org/wiki/Sound_intensity)
===
I'm still seeing gaps in the basic concept of dB in this thread.

Is there another [analog] scale that's more suited for measuring amplitude changes?

I hope, two conversion instruments links may help in particular cases:

1. dB vs V (or Pa).
Substitute V for voltage or Pa (pascal) for "sound pressure":
http://www.crownaudio.com/apps_htm/designtools/db-volts.htm (http://www.crownaudio.com/apps_htm/designtools/db-volts.htm)

2. dB vs W (or W/m2).
Substitute W for wattage or W/m2 for "sound intensity":
http://www.fab-corp.com/pages.php?pageid=1 (http://www.fab-corp.com/pages.php?pageid=1)
Title: Dynamic range question
Post by: Northpack on 2011-06-14 11:00:39
Properly dithered digital behaves similar to analog systems where the noise floor is (best case) about 6*#bits below the maximum signal.

Sure, that's the way it is, you and I know that because we know the math behind digital audio. But it is not an explanation to those who don't know the math and are misguided by audiofoolish reasoning. If you want to enlighten people you have to explain things in a way they can follow instead of making assertions, how true they may be. That's why Plato always wrote in the form of dialogues...
Title: Dynamic range question
Post by: dhromed on 2011-06-14 11:01:23
Anyone interested in writing such an explanation?


Since I'm a little hazy on the concepts as well, here's what I've pieced together from crucial posts in this thread that seemed to gloss over a few details that I think were assumed to be self-evident, but are not (at least to me).

Here goes.

#
96 dB of dynamic range represents the ratio of the loudest sound to the quietest sound


# It is a ratio, and not a linear distance, because dB is a logarithmic scale, which in turn is because that's how our ears/brains perceive volume.

# This ratio is a number, obviously.

# This number can be expressed or approximated as a fraction of n:1

# To get a certain n, you need a certain amount of bits to put that number in. Self-evident to anyone familiar with computers (such as myself), but probably not to a sizeable section of curious listeners.

#
During the development of the CD format, a 14-bit format (84 dB) was originally proposed. The 14-bit proposal was based on the capabilities of the ADCs and DACs available at the time and on calculations that you see in this thread of ideal dynamic range of real listening environments. The resolution was pushed to 16 bits at the insistence of Sony.


#
For CD (16 bits) this works out to be 65536:1 or 2^16 or about 96dB.


(reordered the above post to better sequence the train of concepts)

# Taken to an extreme: suppose you have 2-bit audio, the ratio would be tiny, and everything would drown in the noise.

And there you have it, I believe. If I made a mistake, please correct it. There's nothing worse than to learn you're actually fundamentally confused by objects that you use on a daily basis (i.e. foobar and my receiver).
Title: Dynamic range question
Post by: knutinh on 2011-06-14 11:12:30
Properly dithered digital behaves similar to analog systems where the noise floor is (best case) about 6*#bits below the maximum signal.

Sure, that's the way it is, you and I know that because we know the math behind digital audio. But it is not an explanation to those who don't know the math and are misguided by audiofoolish reasoning. If you want to enlighten people you have to explain things in a way they can follow instead of making assertions, how true they may be. That's why Plato always wrote in the form of dialogues...

For those who seek true insight, I would expect them to be able to search wikipedia or buy a book where the topic should be far greater explained than I am capable of. That involves doing actual calculations yourself.

For those who dont want true insight, simple assertions may be good enough. How to phrase those assertions, what level of detail/argumentation to include, what (if any) analogys to include, and how to be sure that the assertions are correct and relevant is an open question.

I think that given the knowledge that CD can (at best) do 96dB-ish SNR/DR or so, and that no analog media or acoustic listening-room/speaker-combo can do anything close to that, for pragmatic assertion-based discussions there is not much more to it. Of course, if you want to true insight, you could discuss the type of noise, the audibility of noise, how one noise source masks or dont mask another etc.

-k
Title: Dynamic range question
Post by: Arnold B. Krueger on 2011-06-16 13:05:30
I seem to remember that people who record ambient sounds for movies etc (animals, weather, water) have a hard time finding spots on the earth that are not affected by passing planes, kids with a boomblaster etc. Acoustic pollution.


Once you avoid the human-related noises, you are still left with natural noises which are often quite loud. I'm talking about water, wind, animal calls, thunder, and leaves driven by wind.

It can be quite quiet out in nature. Along the Minnesota-Ontario border and in northern Ontario you can get 20-40 miles from the nearest road or other man-made noise source. The exhaust sound of a small gasolene generator can carry for over a dozen miles.
Title: Dynamic range question
Post by: dc2bluelight on 2011-06-17 09:58:06
Very interesting discussion.  I'd like to add a couple of things.

The 96dB FS to Noise ratio of a 16 bit system is theoretical.  It's almost never exactly 96dB, though.  Dithering shaves off 3dB or so, then the so called "noise shaping" D/A converters put 8dB or so back in, if that's even real.  But FS is a maximum peak figure, we measure noise using an RMS meter with (hopefully) a weighting filter in front of it, either A or ITU-R468, either of which will tend to push the reading downward making 96dB look more like 103 or so. 

Rooms, on the other hand, generally have their noise figures expressed as NC (Noise Criterion) figures.  NC is a set of curves, and to qualify for a given NC curve, each octave band of measured noise must fall below that standardized curve. So, the actual measurement of room noise is done flat, but the result has to fit a curve that allows lots more energy at the low end.  It's not an A weighting curve, so it's not directly related to a SNR figure of a digital system.  And, though I can't site a reference, it's been shown recently that the "average" living room hovers around NC-25.  By the way, you can't actually measure below an NC-20 with a 1/4" measurement mic.  Too much self noise., you need a 1" mic with a quiet pre to do it.

Also, when we say we listen to our music at 80dB SPL, again, that's an average level, and might be measured with an average meter (probably) or an RMS meter.  Depending on how a CD is mastered, the average levels might be as much as 15dB - 20dB below FS, or as little as 8dB below FS (hope not, but they crunch 'em pretty hard these days).  It's not unreasonable to expect to listen at 80dB SPL (average,  unweighted) and still get a peak or two at 95 - 100dB SPL.  Depending on your SPL meter ballistics, you may or may not see that peak or read it properly, though. 

It would still seem that 16 bits is more than enough to handle a 95dB SPL peak in an NC-20 room. 

There is an advantage to recording at 24 bits.  For one, if you're recording live, you've got (theoretically!) 48dB more room to make a level error in.  If you're mixing, or processing, you've got more resolution in which to adjust gain, process, eq, etc.  But there's a really big rub: Almost without exception, 24 bit sound cards NEVER produce 144dB of dynamic range!  Just check the specs of almost any "affordable" sound device,oh heck, even the unaffordable ones.  In fact, I've found exactly one A/D that is commercially available that has a real 24 bit's worth of dynamic range: http://www.stagetec.com (http://www.stagetec.com)  They get 153dB A, and don't even bother with a mic preamp!  Everything else is WAY less. 

Which is the point.  Why would to stretch your system to handle 24 bits when even the so-called 24 bit material has a dynamic range of more like 18 - 20 bits?

So I'm saying 16 bits is enough for "release" material, perhaps a little shy for capture.  And I'm reminded that ratio of 0dB SPL to the Threshold of Pain is about 22+ bits.
Title: Dynamic range question
Post by: pdq on 2011-06-17 13:21:40
Very nice first post. Thanks. 
Title: Dynamic range question
Post by: Arnold B. Krueger on 2011-06-17 14:02:56
Very nice first post. Thanks. 


First serious omission - a real world discussion of noise levels in the place where the recording is made.  For example my live recording kit actually has close to 100 dB dynamic range under ideal conditions. I don't think I've ever made a live recording with better than about 67 dB dyanmc range.  The balance of the noise is usually due to HVAC and humans being in the room.

Second serious omission - discusison of what kind of dynamic range we can actually perceive.

As JJ has said from time to time, the ear has about 30 dB instantaneous dynamic range that slides up and down. The sliding is is subject to a number of timing and memory conditions.

I think most people have been around some loud sound that caused a temporary threshold shift that was readily perceptible. IOW, they went to a loud concert or were in a noisy industrial environment and noticed that they were having a hard time hearing soft sounds for hours or even days later. That reperesnts a memory effect that vastly reduces the effective dynamic range of the human ear.
Title: Dynamic range question
Post by: Arnold B. Krueger on 2011-06-17 14:20:54
In fact, I've found exactly one A/D that is commercially available that has a real 24 bit's worth of dynamic range: http://www.stagetec.com (http://www.stagetec.com)  They get 153dB A, and don't even bother with a mic preamp!  Everything else is WAY less.


The means that they use to obtain the 153 dB dynamic range has been around for a long time.

They basically run a bunch of converters in parallel. Each converter has an input attenuator with a different amount of attenuation.  They then pick an output from a converter that is neither clipping nor close to the bottom of its range, and scale it digitally based on that converter's input attenuation.

For example, let say we have two medium-priced converters with 110 dB dynamic range. We connect one to the source with no attenuation, and put a 30 dB attenuator in line with the other converter.  We then monitor the status of the two converters. In general we use the output of the unattenuated converter, but when it gets within 3 dB of clipping, we switch over the the converter with the 30 db attuator.  On the digital side we multiply the digital output of the attenuated converter by 30 dB in the digital domain.  When we switch over to the output of the unattenuated converter we simply use its digital output as is. 

The net result is a system with about 140 dB dynamic range made out of out of two $5 ADC chips, and a few other relaitvely inexpensive parts.  We do have to pay attention to the recovery time of the unattenuated converter, because it may take a few milliseconds to recover from clipping when the input signal gets too high and it clips.

The other approach to extending the dynamic range of conveters is to simply run them in parallel and obtain a 3 dB noise reduction every time we double the number of converters. I've never seen more than 8 convertors used this way.

Neither of these approaches reduce nonlinear distortion. They just address noise.
Title: Dynamic range question
Post by: dc2bluelight on 2011-06-17 16:40:05
Wow.  You guys are tough here.
Title: Dynamic range question
Post by: dc2bluelight on 2011-06-18 00:53:54
First serious omission - a real world discussion of noise levels in the place where the recording is made.  For example my live recording kit actually has close to 100 dB dynamic range under ideal conditions. I don't think I've ever made a live recording with better than about 67 dB dyanmc range.  The balance of the noise is usually due to HVAC and humans being in the room.

Let me apologize for my "serious omission".  What you say is certainly true of live recording, but recording studios are built to NC-15 and below, including HVAC, and NC-10 and NC-5 is not unachievable.  Keep in mind, you won't  be able to correlate an unweighted dynamic range measurement with a room noise measurement based on NC curves, though. If you take into account positioning a mic close to a source (inverse square law), you can indeed record a dynamic range in excess of 100dB, even in an NC-20 room.  No, it's not typical, but it's done quite often.
Second serious omission - discusison of what kind of dynamic range we can actually perceive.

As JJ has said from time to time, the ear has about 30 dB instantaneous dynamic range that slides up and down. The sliding is is subject to a number of timing and memory conditions.

I think most people have been around some loud sound that caused a temporary threshold shift that was readily perceptible. IOW, they went to a loud concert or were in a noisy industrial environment and noticed that they were having a hard time hearing soft sounds for hours or even days later. That reperesnts a memory effect that vastly reduces the effective dynamic range of the human ear.


Again, if I've made another "serious omission", I apologize.  As to the "discusison" (sic), however, the instantaneous dynamic range you refer to has a time element.  If the music in question has a volume envelope that makes level transitions slower than the sliding dynamic range window you describe, it is possible to perceive a dynamic range to the limits of an individual's hearing.

I thought I was agreeing with you re: 16 bit being more than adequate.  My point on it being a little light for capture is, as I'm sure you're very aware, live situations often present unexpected levels.  Would you rather "waste" a few bits, store some more data and capture the entire event without issue, or go ahead and clip the A/D every so often?  HDD storage is cheap, 24 bit A/D, even if they have a noise floor of a 20 bit A/D, are affordable to everyone.  Why not use them, then once you're finished in post, release in a well-mastered, controlled, real, unclipped, perfectly adequate 16 bit format?

I thought the Stagetec thing was a cool idea, and unique in the market.  If not, I guess I've had my head under a rock, which is completely possible.  But I don't see anyone else doing the multiple (cheap??) A/D trick in a product at any price.  And if it doesn't address nonlinear distortion (I assume you refer to the distortion products caused by linear quantization), ok, but we're discussing dynamic range here, right?

I'm not sure why in a discussion of dynamic range, the idea that 16 bits is "overkill" because of environmental noise in recording and reproduction is so pertinent.  You know, when you listen to music in a car at 65mph, the available dynamic range is less than 18dB, and in a truck, more like 10.  So when we know we're recording for the car, should we use a 3 or 4 bit converter because the other 12 bits are overkill?  We already have 16 bits in common use, for better or worse.  It's not going to change to anything else quickly for the main stream consumer.  And the direction it's going is more bits at a higher rate, as wasteful and ineffective as that is.  We can't reproduce 16 bits, true.  But why not record with more bit depth so we can work with some elbow room in post?  Seems the recording industry from music to location film sound thinks it's a good idea.

Ok, I hear ammunition being loaded... I'm ducking back into the fox hole and putting my helmet on...





Title: Dynamic range question
Post by: Woodinville on 2011-06-18 04:32:16
Just so it's clear, the 30dB number applies for instantaneous masking inside of one ERB/Critical Band.

Over all frequency, you can have an instantaneous dynamic range of at least 70dB.
Title: Dynamic range question
Post by: dc2bluelight on 2011-06-18 07:17:06
Yes, that clears it up.  Critical band masking would be a special case of dynamic range limiting in hearing. 

I did look look around for something about a temporary 30dB dynamic range limit in hearing, nothing found of course.  I thought it might be a reference to temporal masking, in which the masking effect exists for at least 50ms after the masker terminates, and can extend to 200ms (post-masking), with pre-masking also working up to 20ms before the masker.  But since the masking effect in time is a curve, the 30dB figure didn't make sense, which is why I mentioned the time factor.

Thanks for the clarification.
Title: Dynamic range question
Post by: knutinh on 2011-06-18 09:31:20
I'm not sure why in a discussion of dynamic range, the idea that 16 bits is "overkill" because of environmental noise in recording and reproduction is so pertinent.  You know, when you listen to music in a car at 65mph, the available dynamic range is less than 18dB, and in a truck, more like 10.  So when we know we're recording for the car, should we use a 3 or 4 bit converter because the other 12 bits are overkill?  We already have 16 bits in common use, for better or worse.  It's not going to change to anything else quickly for the main stream consumer.  And the direction it's going is more bits at a higher rate, as wasteful and ineffective as that is.  We can't reproduce 16 bits, true.  But why not record with more bit depth so we can work with some elbow room in post?  Seems the recording industry from music to location film sound thinks it's a good idea.

I think that this forum in many ways is an "anti-Stereophile-mag". Both camps claim to be interested in music and good sound, but other than that, whenever some audiophool claims to be able to hear staircaising in lowly 24-bit recordings, the gut-feeling of any hydrogenaudio-member is to strike him hard in the head with science (or rather her perception of what is science).

The debate should not be read as "using (e.g.) 7-bit recording in studio would be a smart choice that we recommend for all recordists", but perhaps rather "given the constraints that your particular end-to-end chain is presenting, 7 bits would be marginally enough, and anything in excess of that would only buy you margin for user-error, calculation error etc". The point is that if this marginal number is considerably smaller than regular available technology (16bits, 20bits, whatever), then one would be well adviced to spend money and research time on other parts of the business rather than drooling over 150dB SNR ADC/DACs.

I would think that when 100dB of recording SNR is really worth it, you typically would not need 40dB of headroom above that to allow for error in setting input gain? In cases where I have had problems setting input levels sort of right, it has invariable been live recordings  where sound quality was so-so anyways. The gear most priced by my studio friends is typically old analog gear and tube microphones that was not designed to have extremely wide dynamic range, but rather other qualities. This indicates to me that most studio people (even really good ones) really are not looking for 120dB SNR, even though they may say otherwise. Perhaps there are exceptions in the classical/acoustic camp.

-k
Title: Dynamic range question
Post by: Arnold B. Krueger on 2011-06-18 18:58:55
I thought the Stagetec thing was a cool idea, and unique in the market.  If not, I guess I've had my head under a rock, which is completely possible.  But I don't see anyone else doing the multiple (cheap??) A/D trick in a product at any price.


I think that most of the market addresses needs that are widely perceived. The argument that you should do it just because you can do it doesn't sell a lot of equipment. 

Right now  converters priced for installation in middle-of-the-road production equipment  have about 110 dB dynamic range. Converters in production equipment for the low end market are about 10 dB worse.  Even low end consumer gear has converters that spec out above 80-85 dB.

There are converters that do 120 dB and up that are priced right for equipment in the $500-1K range, but so far they are only showing up in high end audio products that aren't needs-based, anyway. I think that most practitioners know that it isn't a lot of work getting systems and productions working subjectively noise free with 110 dB or worse converters. Therefore there isn't a lot of market for anything better.


Quote
And if it doesn't address nonlinear distortion (I assume you refer to the distortion products caused by linear quantization), ok, but we're discussing dynamic range here, right?


By the many standards spurious responses due to nonlinear distoriton (By which I include the things that are commonly called IM and THD)  count the same towards dynamic range the same as the noise floor. 

IOW there is a school of thought that counts THD+N towards dynamic range, and a less-critical school of thought that only counts noise.

Quote
I'm not sure why in a discussion of dynamic range, the idea that 16 bits is "overkill" because of environmental noise in recording and reproduction is so pertinent.


At this point you head off into a discussion of playback contexts, but I think that the recording context is more important since it affects the playback no matter where you play back.

The general thrust of this all heads into the same place, which is clearly a place that you want to be, which is that 16 bits is really all we need for most applications.
Title: Dynamic range question
Post by: thesurfingalien on 2011-06-18 21:04:54
@All,

I am ashamed to tell that, although the discussion has been very informative, I hve not been able to distill an answer for my question from it.

Sticking to CD specs, the 16-bit signed integers (-32768 to 32767; 65536) in my mind represent the steps to map the analogue waveform to.  Since CD specs also state a 96.### dB dynamic range, it seems logical to me that the same 65536 steps also have a relation to the dB scale. 

I am sure that, if we would map a waveform into 4 bits and played that waveform back at 96 dB, everybody would hear it as a rather coarse sound, and if we would lover the sound to 15 dB (theoretically, not taking into account background noise ) that same coarseness would be significantly lower.  At some point however, if we increase the number of bits in which the waveform is coded in, the coarseness disappears, and the sound gets smooth enough. 

There must be research done by Philips / Sony that would prove the 16 bits coding / mapping and the 96 dB were good enough for CD playback. 


Peter
Title: Dynamic range question
Post by: knutinh on 2011-06-18 21:40:57
Sticking to CD specs, the 16-bit signed integers (-32768 to 32767; 65536) in my mind represent the steps to map the analogue waveform to.  Since CD specs also state a 96.### dB dynamic range, it seems logical to me that the same 65536 steps also have a relation to the dB scale.

The CD-specs probably does not state some dynamic range. It depends on a lot of things.

The relationship between 65536, 96 and the dB-scale is a direct one, and I believe that it has been presented in this thread:
2^16 = 65536
20*log10(2^16) ~= 96dB.

Briefly: Add one more bit of (true) resolution, and the AD or DA will have 6dB more of SNR, everything else equal.
Quote
There must be research done by Philips / Sony that would prove the 16 bits coding / mapping and the 96 dB were good enough for CD playback.

The fact that 16 bits was economically feasible and sounded better than existing media would have been enough.

-k
Title: Dynamic range question
Post by: lvqcl on 2011-06-18 21:45:25
Since CD specs also state a 96.### dB dynamic range, it seems logical to me that the same 65536 steps also have a relation to the dB scale.

Yes. 20 * lg (65536) ? 96.3295986.

everybody would hear it as a rather coarse sound

Not coarse, but noisy.
Title: Dynamic range question
Post by: Wombat on 2011-06-19 00:55:42
Just so it's clear, the 30dB number applies for instantaneous masking inside of one ERB/Critical Band.

Over all frequency, you can have an instantaneous dynamic range of at least 70dB.


Very interesting number here besides the nice discussion in this thread. That may correlate to times of a day i can hear the low noise of my Aquarium pump working into my living and listening room. At nights it gets more obvious and of cause i don´t need loud music then. On a typical day i never recognize it. When i listen music loud and switch off i don´t hear it at all!
So besides all that talk about the need of more bits for bigger dynamics that little phenomenon gets ignored totaly and may smaller the needed number again
To sad i can´t find a study about that...

Title: Dynamic range question
Post by: Notat on 2011-06-19 01:21:05
But why not record with more bit depth so we can work with some elbow room in post?  Seems the recording industry from music to location film sound thinks it's a good idea.

This is the thinking among mainstream audio engineers. No one uses 16-bit ADCs for professional recording. Arnold is being argumentative. He does that.

To my knowledge, the Stagetec converter is a novel idea. Like many such good ideas, one can only discount it as obvious once one has been introduced and understands it.
Title: Dynamic range question
Post by: Arnold B. Krueger on 2011-06-19 11:44:32
I am sure that, if we would map a waveform into 4 bits and played that waveform back at 96 dB, everybody would hear it as a rather coarse sound, and if we would lover the sound to 15 dB (theoretically,


There would be no coarse sound because dither must be applied for everything to be kosher.

Dither inherently randomizes the coarse steps into background noise. It is not a mask but an actual randomzing of the data. Since threre are only 4 steps, the background nnoise level would be very high, but it would be noise, not any sort of coarsness related to the step size or the sampling frequency,
Title: Dynamic range question
Post by: drewfx on 2011-06-19 18:56:02
I am sure that, if we would map a waveform into 4 bits and played that waveform back at 96 dB, everybody would hear it as a rather coarse sound, and if we would lover the sound to 15 dB (theoretically, not taking into account background noise ) that same coarseness would be significantly lower.  At some point however, if we increase the number of bits in which the waveform is coded in, the coarseness disappears, and the sound gets smooth enough. 

There must be research done by Philips / Sony that would prove the 16 bits coding / mapping and the 96 dB were good enough for CD playback. 


Peter


If you play back 4bit audio at 96dB SPL, that "96dB SPL" has little to do with the dynamic range. You are amplifying both the peaks and and the noise floor (i.e. quantization error).

The ratio of the loudest possible peak to the noise floor is always about 6dB per bit no matter how you set the playback volume (i.e. dB SPL). Adding bits lowers the level of the quantization error relative to the loudest possible signal.

So if you consider how loud (in terms of dB SPL) you might want the highest peaks in your audio to play back at, and compare it to how loud (in terms of dB SPL) the quietest sound you can hear above the ambient noise in the listening environment, that tells you how much dynamic range you need in your recorded media, which tells you how many bits you need.

If you amplify anything enough (regardless of its bit depth), you will always reach a point where you can hear the quantization. However, if the amount of amplification this requires results in the loud parts being so loud that they cause permanent hearing damage, most of us would say we've got more than enough dynamic range.
Title: Dynamic range question
Post by: Soap on 2011-06-19 20:01:55
I belive the problem thesurfingalien is having is in understanding why 4 bits = "noisy" and not "dramatic stair-stepping volume fluctuations", something I don't see clearly addressed yet.

While he is correct that 4 bits means every sample is at one of only 16 volume levels, I believe thesurfingalien thinks this means the volume of the track will coarsely jump up and down.

I think I understand why thesurfingalien is incorrect, but I'll give the experts a fair chance to answer it before I risk bastardizing the answer.
Title: Dynamic range question
Post by: Woodinville on 2011-06-20 02:43:49
Just so it's clear, the 30dB number applies for instantaneous masking inside of one ERB/Critical Band.

Over all frequency, you can have an instantaneous dynamic range of at least 70dB.


Very interesting number here besides the nice discussion in this thread. That may correlate to times of a day i can hear the low noise of my Aquarium pump working into my living and listening room. At nights it gets more obvious and of cause i don´t need loud music then. On a typical day i never recognize it. When i listen music loud and switch off i don´t hear it at all!
So besides all that talk about the need of more bits for bigger dynamics that little phenomenon gets ignored totaly and may smaller the needed number again
To sad i can´t find a study about that...



There are quite a few studies about TTS (Temporary Threshold Shift). Look for something under that phrase, perhaps.

By the way, I'm not sure how this relates to the aquarium pump, though. If it's low frequncy hum, it won't be masked by high frequencies.

But a bit of low frequency noise will bury it.

Airplanes flying overhead provide a startling amount of low frequency energy. During the post 9-11 flight ban, the silence in our part of New Jersey (USA) was amazing. Then the flights started again, rumble 24/7.
Title: Dynamic range question
Post by: DigitalMan on 2011-06-20 02:59:13
@Soap - agree we've not given thesurfingalien an answer they can digest (plus we got off topic which doesn't help.....)  I'll take a shot based on your observations...

@thesurfingalien - Remember that as we increase the number of bits of resolution, all we're really doing is reducing the size of the error in representing (measuring) the waveform at each sample.  In your 4-bit example, with only 16 distinct amplitude levels (2^4 = 16), you can picture that a few things will be true:

1) We don't have very many measurement levels, so we'll have to pick the level that is closest to the waveform during that sample and accept that there will be an error.  This error will lead to effectively adding noise when we play back the sample.
2) The error will be different for every sample - some times we'll get it exactly right with our lowly 4-bit system but usually we'll be off as much as 1/2 of level (or, halfway between levels; any more than that and we should pick the next level).  The amount of the error should be random across the range of zero to 1/2 of a measurement level for each sample in a well designed analog to digital conversion system (using dither, etc.), so the noise added during playback will also be random, leading to a white noise addition to the playback (white noise is the sound of pure randomness).
3) The ratio of how loud the white noise is due to the errors vs. the music signal (that ratio being equal to the dynamic range) will depend on how many measurement levels we have - basically the errors get smaller the more bits we have to accurately measure the waveform which leads to a lower level of noise vs. the signal and an improved dynamic range.

Also remember that in audio recording, the dynamic range of the recording is related to the ratio of the largest signal to the noise floor.  The playback dynamic range is a totally separate discussion.  The level recorded on a CD does not correspond to a volume level in playback due to variations in how loud you're playing it, the listening environment, etc.  So these ratios define the dynamic range of the recording system (in this case its the CD).  There is also the idea of whether the playback system can reproduce a 96dB or greater dynamic range using the same ideas - noise floor vs. loudest signal.  It is possible that even with a 24 bit recording system we would have a tough time finding a playback system that could reproduce the 24 bit dynamic range for the listener (that is ~144dB, after all).

Does that help or just muddy the water more?
Title: Dynamic range question
Post by: Soap on 2011-06-20 03:45:01
What I was going to say (please correct me where wrong) is that a waveform represented by 4 bits (16 distinct possible "volumes") doesn't stairstep because stair steps would be square waves and square waves = lots of high frequency components and said HF components get cut off in the post DAC filter ("smoothing" the waveform) but the reproduced waveform is still not the original one, and the difference between the 4 bit waveform and the original one (the error) is really when it comes down to it nothing but additional energy in different (unintended) frequencies, which is what noise is.

Again correct me where I'm wrong, but if there wasn't a filter post DAC the 4 bit waveform would be stairstepped (but of course any real-world speaker would act as a low-pass filter effectively "smoothing" said signal somewhat because to perfectly reproduce a square wave the speaker cone would need to instantly move from peak to trough and no object with a non-zero mass can do such).

/ end rant
Title: Dynamic range question
Post by: WernerO on 2011-06-20 11:33:55
I am sure that, if we would map a waveform into 4 bits and played that waveform back at 96 dB, everybody would hear it as a rather coarse sound, and if we would lover the sound to 15 dB (theoretically, not taking into account background noise ) that same coarseness would be significantly lower.


You can give it a try yourself.

These are music excerpts reduced to an equivalent of 4 bits (or slightly more, IIRC).


Undithered:

http://www.audiochrome.net/clips/Venice_4b_nodither.mp3 (http://www.audiochrome.net/clips/Venice_4b_nodither.mp3)

Dithered:

http://www.audiochrome.net/clips/Venice_4b_dither.mp3 (http://www.audiochrome.net/clips/Venice_4b_dither.mp3)

Noise-shaped:

http://www.audiochrome.net/clips/Venice_4b_noiseshapeE.mp3 (http://www.audiochrome.net/clips/Venice_4b_noiseshapeE.mp3)


And here are solo drums at 5 bit equivalent.

http://www.audiochrome.net/clips/drums_dither.html (http://www.audiochrome.net/clips/drums_dither.html)
Title: Dynamic range question
Post by: DonP on 2011-06-20 14:48:18
This will probably add confusion to those already having trouble with bits vs dB, but here goes.

It turns out you can get that 96 dB range even with 1 bit samples IF you choose the percentage chance of rounding up (to 1) vs rounding down (to zero) to correspond with the signal voltage.  You do need a lot higher sampling frequency but less component precision and it turns out this is how many/most  DAC's work internally.
Title: Dynamic range question
Post by: dhromed on 2011-06-20 20:34:13
You can give it a try yourself.

These are music excerpts reduced to an equivalent of 4 bits (or slightly more, IIRC).


I'm completely surprised at how good these clips sound.

Apart from the unlistenable noise, of course. I'd expected there to be nothing left.
Title: Dynamic range question
Post by: dhromed on 2011-06-20 20:41:16
It turns out you can get that 96 dB range even with 1 bit samples IF you choose the percentage chance of rounding up (to 1) vs rounding down (to zero) to correspond with the signal voltage.


Isn't that exactly what pulse-density modulation (http://en.wikipedia.org/wiki/Pulse-density_modulation) is?
Title: Dynamic range question
Post by: Woodinville on 2011-06-20 20:58:50
I am sure that, if we would map a waveform into 4 bits and played that waveform back at 96 dB, everybody would hear it as a rather coarse sound, and if we would lover the sound to 15 dB (theoretically, not taking into account background noise ) that same coarseness would be significantly lower.


You can give it a try yourself.

These are music excerpts reduced to an equivalent of 4 bits (or slightly more, IIRC).


Undithered:

http://www.audiochrome.net/clips/Venice_4b_nodither.mp3 (http://www.audiochrome.net/clips/Venice_4b_nodither.mp3)

Dithered:

http://www.audiochrome.net/clips/Venice_4b_dither.mp3 (http://www.audiochrome.net/clips/Venice_4b_dither.mp3)

Noise-shaped:

http://www.audiochrome.net/clips/Venice_4b_noiseshapeE.mp3 (http://www.audiochrome.net/clips/Venice_4b_noiseshapeE.mp3)


And here are solo drums at 5 bit equivalent.

http://www.audiochrome.net/clips/drums_dither.html (http://www.audiochrome.net/clips/drums_dither.html)


There is an entire CD of such signals, published by the AES, that came out of the technical committee I co-chair.

http://www.aes.org/blog/2010/6/digital-audio-educational-cd (http://www.aes.org/blog/2010/6/digital-audio-educational-cd)

As well as some other "interesting" sounds.
Title: Dynamic range question
Post by: Woodinville on 2011-06-20 21:04:08
This will probably add confusion to those already having trouble with bits vs dB, but here goes.

It turns out you can get that 96 dB range even with 1 bit samples IF you choose the percentage chance of rounding up (to 1) vs rounding down (to zero) to correspond with the signal voltage.  You do need a lot higher sampling frequency but less component precision and it turns out this is how many/most  DAC's work internally.


This is called "delta-sigma" or "sigma-delta" conversion, both of which are the same thing.  There's a slide deck on how this works at www.aes.org/sections/pnw/ppt/jj/adc.ppt

And PDM (pulse density modulation) or PPM (pulse position modulation) are other ways to accomplish this. Many 'class D' amplifiers use PWM (pulse WIDTH modulation) as well.

All of which use noise shaping to push the noise from the 1 bit quantizer up in frequency to where it doesn't hopefully matter. But SACD has a 6th order Chebychev filter at 50kHz due exactly to that noise causing heartburn for some analog equipment, as it turns out.
Title: Dynamic range question
Post by: Wombat on 2011-06-20 21:21:54
There are quite a few studies about TTS (Temporary Threshold Shift). Look for something under that phrase, perhaps.
By the way, I'm not sure how this relates to the aquarium pump, though. If it's low frequncy hum, it won't be masked by high frequencies.
But a bit of low frequency noise will bury it.
Airplanes flying overhead provide a startling amount of low frequency energy. During the post 9-11 flight ban, the silence in our part of New Jersey (USA) was amazing. Then the flights started again, rumble 24/7.

The pump has pretty low frequency hum that is caused by some resonance of the cabinet even when i damped the pump well.
I found several readings about this TTS and really wonder if i already listen to loud when i do my daily listening. Nowhere i found an explanation of how much exatly the treshold is shifted in a way i can relate it to music listening. So playing music with lets say 85dB loudness and how much the ear itself does mask then already. I can imagine that even at this loudness the ear alread can´t hear tones that are only 15db loud when switching off suddenly, or even less when discerning silent elements in the music mix.
I pulled these numbers out of my A** of cause but there must be something to this. If so, the debate about we have to higher higher the dynamic-range of distributed music became even more moot.
Title: Dynamic range question
Post by: Woodinville on 2011-06-20 22:02:28
So playing music with lets say 85dB loudness and how much the ear itself does mask then already.


Ok, some basics. Loudness is sensation level. It is not measured in dB SPL.  85dB (I presume you mean SPL) is intensity, not loudness.

85dB average is too loud.  Short peaks are ok to some level above that, but I hesitate to say how much above that.  In order to know "how much the ear masks" you have to know intesity vs. ERB frequency, after dealing with cochlear filttration. Then once you know the loudness, you can estimate the masking spectrum.
Title: Dynamic range question
Post by: Notat on 2011-06-20 22:58:25
I'm completely surprised at how good these clips sound...I'd expected there to be nothing left.

We've only removed 3/4ths of the information. We know it's possible to remove much more than that through perceptual coding and still have happy ears.
Title: Dynamic range question
Post by: DonP on 2011-06-21 02:18:41
This is called "delta-sigma" or "sigma-delta" conversion, both of which are the same thing.  There's a slide deck on how this works at www.aes.org/sections/pnw/ppt/jj/adc.ppt


My department designed a bunch of these in the late 80's for everything from electronic circuit breakers to ultrasound scanners.

Title: Dynamic range question
Post by: Woodinville on 2011-06-21 03:49:40
This is called "delta-sigma" or "sigma-delta" conversion, both of which are the same thing.  There's a slide deck on how this works at www.aes.org/sections/pnw/ppt/jj/adc.ppt


My department designed a bunch of these in the late 80's for everything from electronic circuit breakers to ultrasound scanners.


Hmm, you know Jim Candy, Joe Condon, or Steve Norseworthy? 
Title: Dynamic range question
Post by: DonP on 2011-06-21 12:01:55
Hmm, you know Jim Candy, Joe Condon, or Steve Norseworthy? 


Jim Candy sounds familiar, but I was in  sensors and signal processing  at GE Research.
Title: Dynamic range question
Post by: Woodinville on 2011-06-21 22:48:19
Hmm, you know Jim Candy, Joe Condon, or Steve Norseworthy? 


Jim Candy sounds familiar, but I was in  sensors and signal processing  at GE Research.



Ah. I knew the Bell Labs bunch.