24bit vs 16bit, the myth exploded!
Dec 13, 2019 at 4:10 PM

#### bigshot

Well, it's a good time to start comparing bit depth to sports cars and wine then!

Dec 13, 2019 at 7:14 PM

#### old tech

Therefore, there IS "such a thing as infinite resolution" in digital audio, in fact, the whole principle of digital audio is based on infinite resolution (Shannon/Nyquist)!
Now I am confused. As you point out, resolution is effectively dynamic range - which in turn is directly related to SNR. So isn't resolution in digital audio a fixed value directly related to bit depth (which can be perceptually increased with dither noise shaping)?

In other words, if a digital file had infinite resolution would it not by definition also have an infinite dynamic range and an infinite SNR?

Dec 13, 2019 at 7:46 PM

#### TheSonicTruth

Now I am confused. As you point out, resolution is effectively dynamic range
- which in turn is directly related to SNR. So isn't resolution in digital audio a
fixed value directly related to bit depth (which can be perceptually increased
with dither noise shaping)?

In other words, if a digital file had infinite resolution would it not by definition also
have an infinite dynamic range and an infinite SNR?

Confused?

Two words: Ethan. Winer.

Cuts to the chase, explains everything in simple terms, and won't try to tell you the sky is green and grass is blue, like a couple of guys on here do...!

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Dec 13, 2019 at 7:52 PM

#### bigshot

Within the range of the frequency response and the noise floor, dictated by sampling rate and bit depth, according to Nyquist sound is recreated *perfectly*. There isn't "more resolution" to be had. It's perfect. All you can achieve by increasing the sampling rate and bit depth is a wider range of frequencies and a deeper noise floor which are also recreated *perfectly*.

So therefore, if the intended recipient of the sound is a human, 16/44.1 reproduces the sound perfectly. You can increase the sampling rate and bit rate, but it doesn't add any resolution to the sound. All it adds is information that exists outside of the range of hearing. In order to effectively add resolution, you have to be able to perceive it.

The word "sound" assumes that it is possible to hear. Beyond the range of hearing it's just generalized "data".

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Dec 13, 2019 at 7:52 PM

#### Davesrose

Instead of "infinite resolution", the Nyquist-Shannon sampling theorem refers to finite resolution. Gregorio also tried to tell me that audio sampling is like vector graphics, which it's not. With vector graphics, you only have a point in XY (or Z) space when there's a change in angle. With audio sampling, it's based on time intervals.

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Dec 14, 2019 at 1:47 AM

#### old tech

Within the range of the frequency response and the noise floor, dictated by sampling rate and bit depth, according to Nyquist sound is recreated *perfectly*. There isn't "more resolution" to be had. It's perfect. All you can achieve by increasing the sampling rate and bit depth is a wider range of frequencies and a deeper noise floor which are also recreated *perfectly*.

So therefore, if the intended recipient of the sound is a human, 16/44.1 reproduces the sound perfectly. You can increase the sampling rate and bit rate, but it doesn't add any resolution to the sound. All it adds is information that exists outside of the range of hearing. In order to effectively add resolution, you have to be able to perceive it.

The word "sound" assumes that it is possible to hear. Beyond the range of hearing it's just generalized "data".
Yes but it is not infinite resolution... I agree that any more resolution than 16/44 is not going to be perceptible to humans and also beyond the range of most recorded music, I just cannot get my head around resolution being infinite as that would measure as an infinite SNR/dynamic range and would imply and infinite bit depth and perfect implementation. I appreciate that this is academic as infinite resolution does not exist even in the natural world, I'm just trying to fill gaps in my (laymanish) understanding of digital audio.

Funnily enough, there are quite a few analog types (particularly vinylphiles) that believe records have infinite resolution, yet they cannot provide a convincing reason why then does its SNR and dynamic range is substantially less than CD. Not helped of course by misinformation sites like howstuffworks claiming the same nonsense.

Dec 14, 2019 at 2:01 AM

#### bigshot

How do you get more infinite than perfect? This may be a theological question!

the point is that within the range, it can’t have any more resolution because it’s perfect.

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Dec 14, 2019 at 2:55 AM

#### old tech

How do you get more infinite than perfect? This may be a theological question!

the point is that within the range, it can’t have any more resolution because it’s perfect.
I think you are missing the point. It is not a theological question either. Forget about the bounds of human perception, the question is how is it possible to have infinite resolution without an infinite SNR and dynamic range?

Dec 14, 2019 at 10:55 AM

#### gregorio

[1] What started the latest round of picture analogies is my response to post number 1 on this very thread: where Gregorio claimed it's easy to see bit depth with images. My preface for that was it might be common for older people who had experience with color spaces that were below 256 colors.
[2] With my engagement with Gregorio, I can tell he hasn't considered image capture and current photo and video formats...
[3] so while the topic isn't specifically sound related, ...

1. You're effectively arguing against yourself here, or rather, effectively arguing that you didn't really pay attention to the OP before you decided to dispute it. Sure, it's considerably more difficult today to see the difference between different bit depth/resolution images but the OP was written nearly 12 years ago, when consumer digital photography, video formats and online digital image formats were significantly lower resolution than today! However, it is still possible today to tell the difference in some typical consumer viewing situations, while with 16bit vs 24bit digital audio, there were no typical consumer listening situations where the difference could be differentiated, either when 24bit was first introduced to consumers or at any time since!

2. Again, what you "can tell" - is erroneous. I'm certainly no expert but I certainly HAVE considered current video formats in particular, as my job requires a certain level of familiarity.

3. Exactly and that's the problem! You seem to believe that digital imaging is more "sound related" than is actually the case and are therefore using analogies which are as misleading as they are analogous.
[1] Instead of "infinite resolution", the Nyquist-Shannon sampling theorem refers to finite resolution.
[2] Gregorio also tried to tell me that audio sampling is like vector graphics, which it's not.
[2a] With vector graphics, you only have a point in XY (or Z) space when there's a change in angle. With audio sampling, it's based on time intervals.

1. This statement is false, the sampling theorem refers to both finite and infinite resolution. The concept of infinite resolution was described in Shannon's seminal 1948 paper "A Mathematical Theory of Communication" (upon which the Nyquist/Shannon sampling theorem is predicated), which states: "If a function of time is limited to the band from 0 to W cycles per second it is completely determined by giving it's ordinates at a series of discrete points spaced 1/2W seconds apart" and in his article of the same year ("Communication in the presence of noise") Shannon provides: "A mathematical proof showing that this is not only approximately, but exactly, true ..." - What do you think "completely determined" means, if not infinite resolution?

2. Again, your statement is false! What I actually tried to tell you is that while there are some similarities, the analogy between vector graphics and audio sampling ultimately fails (is invalid)!! Following on ...
2a. That's not entirely true, which is why there is SOME validity to my analogy. The statement quoted above (from "A mathematical theory of communication") was not innovative, it was effectively stated by Harry Nyquist some 20 years earlier, what was innovative was Shannon's mathematical proof of the statement and various other aspects of implementing digital audio, one of the most important of which was approaching the issue and formulating a solution in terms of Euclidean geometry (quote: "Geometrical representation of the signals"). IE. The representation of a signal as a point in an N-dimensional Euclidean space. In fact, Shannon's summary of his article states "A method is developed for representing any communication system geometrically. Messages and the corresponding signals are points in two "function spaces," and the modulation process is a mapping of one space into the other.".

Yes but it is not infinite resolution... I agree that any more resolution than 16/44 is not going to be perceptible to humans and also beyond the range of most recorded music, I just cannot get my head around resolution being infinite as that would measure as an infinite SNR/dynamic range and would imply and infinite bit depth and perfect implementation. I appreciate that this is academic as infinite resolution does not exist even in the natural world, I'm just trying to fill gaps in my (laymanish) understanding of digital audio.

That "gap" is tricky to fill because it requires more than a "laymanish" understanding of digital audio. We experience acoustic sound and can relate that experience to analogue audio precisely because it's analogous. However, digital audio is not analogous to acoustic sound (or analogue audio) and therefore requires a conceptualisation (thinking about it) that is different. This requires going beyond "layman", and is somewhat difficult because it's not especially intuitive. It is possible to explain in terms that are "beyond layman" but still "laymanish", but bare in mind that such an explanation is rather like an analogy that is only somewhat accurate:

With acoustic sound we have sound waves, a signal that includes a noise floor. In the case of a music performance, that noise floor is created by the breathing and movement of both the musicians and the audience, extraneous sound entering the venue and one or two other variables. Analogue audio is also a signal that includes a noise floor, given a theoretically ideal/perfect analogue device that noise floor is defined by thermal noise (the collision of electrons within electrical circuits). A way to conceptualise digital audio is: A system that, unlike acoustic or analogue signals, does NOT include any noise floor at all (IE. Has infinite SNR). What it does include, that acoustic sound and analogue audio do not, is quantisation error, a type of signal distortion that provides a limit to "resolution". However, this quantisation error can be completely eliminated by a process intrinsic to all digital audio, dither. So now we have a perfect signal, with no distortion and unlimited resolution. Unfortunately though, as far as what we're going to hear after the DA conversion is concerned, the result of this dither process is white noise. So we seem to be back where we started, a dynamic range/resolution that is NOT infinite, that is limited by an included noise floor (dither noise). However, that's not really the case because dither noise is not an intrinsically "included noise floor", it's effectively separate. This might appear to be a purely semantic statement, as we can't remove this dither noise (without also loosing the elimination of quantisation error) but it's not just semantics, it's fundamental to how digital audio works. In other words, what we effectively have with digital audio is a signal with infinite resolution but you can't hear all of it because it's obscured by dither noise. It's important to conceptualise digital audio as two entirely separate but overlaid signals, an infinite resolution signal and a dither noise signal, because although we can't get rid of dither noise, we can process it entirely independently (of the infinite resolution signal). The demonstration (and practical implementation) of this fact is noise shaped dither. 16bit digital audio has an theoretical max resolution/dynamic range limit of ~96db (6.02db x 16bits) but using a typical noise shaped dither algorithm, to process/move the dither noise independently, we can extend this dynamic range/resolution to ~120dB (in the critical hearing band). Question: How is this possible, that extra 24dB of dynamic range (4 bits of resolution) can't exist in 16bit digital audio, where has it come from? The answer is: It was always there, the resolution is effectively infinite at virtually any bit depth but you'll have to eliminate the quantisation error and move the dither noise which obscures it. Incidentally, the most aggressive noise shaped algorithms I've used, allow a dynamic range/resolution of ~150dB with 16bit. In practice of course this can't actually be realised (unless you deliberately screw-up the gain staging big time, specifically to create a signal to test for it), because at -120dB below peak (and even at ~96dB), the noise floor of the analogue signal chain is higher and the noise floor of the original acoustic signal is higher still.

Not sure if this helps?

G

Dec 14, 2019 at 11:53 AM

#### Davesrose

1. You're effectively arguing against yourself here, or rather, effectively arguing that you didn't really pay attention to the OP before you decided to dispute it. Sure, it's considerably more difficult today to see the difference between different bit depth/resolution images but the OP was written nearly 12 years ago, when consumer digital photography, video formats and online digital image formats were significantly lower resolution than today! However, it is still possible today to tell the difference in some typical consumer viewing situations, while with 16bit vs 24bit digital audio, there were no typical consumer listening situations where the difference could be differentiated, either when 24bit was first introduced to consumers or at any time since!

2. Again, what you "can tell" - is erroneous. I'm certainly no expert but I certainly HAVE considered current video formats in particular, as my job requires a certain level of familiarity.

3. Exactly and that's the problem! You seem to believe that digital imaging is more "sound related" than is actually the case and are therefore using analogies which are as misleading as they are analogous.

1. This statement is false, the sampling theorem refers to both finite and infinite resolution. The concept of infinite resolution was described in Shannon's seminal 1948 paper "A Mathematical Theory of Communication" (upon which the Nyquist/Shannon sampling theorem is predicated), which states: "If a function of time is limited to the band from 0 to W cycles per second it is completely determined by giving it's ordinates at a series of discrete points spaced 1/2W seconds apart" and in his article of the same year ("Communication in the presence of noise") Shannon provides: "A mathematical proof showing that this is not only approximately, but exactly, true ..." - What do you think "completely determined" means, if not infinite resolution?

2. Again, your statement is false! What I actually tried to tell you is that while there are some similarities, the analogy between vector graphics and audio sampling ultimately fails (is invalid)!! Following on ...
2a. That's not entirely true, which is why there is SOME validity to my analogy. The statement quoted above (from "A mathematical theory of communication") was not innovative, it was effectively stated by Harry Nyquist some 20 years earlier, what was innovative was Shannon's mathematical proof of the statement and various other aspects of implementing digital audio, one of the most important of which was approaching the issue and formulating a solution in terms of Euclidean geometry (quote: "Geometrical representation of the signals"). IE. The representation of a signal as a point in an N-dimensional Euclidean space. In fact, Shannon's summary of his article states "A method is developed for representing any communication system geometrically. Messages and the corresponding signals are points in two "function spaces," and the modulation process is a mapping of one space into the other.".

That "gap" is tricky to fill because it requires more than a "laymanish" understanding of digital audio. We experience acoustic sound and can relate that experience to analogue audio precisely because it's analogous. However, digital audio is not analogous to acoustic sound (or analogue audio) and therefore requires a conceptualisation (thinking about it) that is different. This requires going beyond "layman", and is somewhat difficult because it's not especially intuitive. It is possible to explain in terms that are "beyond layman" but still "laymanish", but bare in mind that such an explanation is rather like an analogy that is only somewhat accurate:

With acoustic sound we have sound waves, a signal that includes a noise floor. In the case of a music performance, that noise floor is created by the breathing and movement of both the musicians and the audience, extraneous sound entering the venue and one or two other variables. Analogue audio is also a signal that includes a noise floor, given a theoretically ideal/perfect analogue device that noise floor is defined by thermal noise (the collision of electrons within electrical circuits). A way to conceptualise digital audio is: A system that, unlike acoustic or analogue signals, does NOT include any noise floor at all (IE. Has infinite SNR). What it does include, that acoustic sound and analogue audio do not, is quantisation error, a type of signal distortion that provides a limit to "resolution". However, this quantisation error can be completely eliminated by a process intrinsic to all digital audio, dither. So now we have a perfect signal, with no distortion and unlimited resolution. Unfortunately though, as far as what we're going to hear after the DA conversion is concerned, the result of this dither process is white noise. So we seem to be back where we started, a dynamic range/resolution that is NOT infinite, that is limited by an included noise floor (dither noise). However, that's not really the case because dither noise is not an intrinsically "included noise floor", it's effectively separate. This might appear to be a purely semantic statement, as we can't remove this dither noise (without also loosing the elimination of quantisation error) but it's not just semantics, it's fundamental to how digital audio works. In other words, what we effectively have with digital audio is a signal with infinite resolution but you can't hear all of it because it's obscured by dither noise. It's important to conceptualise digital audio as two entirely separate but overlaid signals, an infinite resolution signal and a dither noise signal, because although we can't get rid of dither noise, we can process it entirely independently (of the infinite resolution signal). The demonstration (and practical implementation) of this fact is noise shaped dither. 16bit digital audio has an theoretical max resolution/dynamic range limit of ~96db (6.02db x 16bits) but using a typical noise shaped dither algorithm, to process/move the dither noise independently, we can extend this dynamic range/resolution to ~120dB (in the critical hearing band). Question: How is this possible, that extra 24dB of dynamic range (4 bits of resolution) can't exist in 16bit digital audio, where has it come from? The answer is: It was always there, the resolution is effectively infinite at virtually any bit depth but you'll have to eliminate the quantisation error and move the dither noise which obscures it. Incidentally, the most aggressive noise shaped algorithms I've used, allow a dynamic range/resolution of ~150dB with 16bit. In practice of course this can't actually be realised (unless you deliberately screw-up the gain staging big time, specifically to create a signal to test for it), because at -120dB below peak (and even at ~96dB), the noise floor of the analogue signal chain is higher and the noise floor of the original acoustic signal is higher still.

Not sure if this helps?

G

How can one claim to need to know a passing knowledge of photography for their line of work, and then demonstrate lack of knowledge of what dynamic range is (in relation to photography), or what standards there are for video formats? Especially 12 years ago, when 16 million colors where so common place, and cinema standards were moving to higher resolution and DR.

As for resolution of sound, why are you ignoring your quote, which clearly states it's a series of points spaced at a time apart (where that means a finite increment)? There may be different approaches for interpolation and improving sound....but sampling refers to to specified intervals.

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Dec 14, 2019 at 12:00 PM

#### SoundAndMotion

@gregorio , do you know the limits of your knowledge? Do you know that some of what you write above is absolutely true and some is absolutely nonsense? That is why I mentioned Dunning Kruger a little while back. I can't get into it too much at this moment, but I'll get back to you.
Quick summary: 1. Your quote from Shannon does not imply the ridiculous concept of infinite resolution in digital audio.
2. Noise shaping in digital audio requires oversampling, that is, you must have more samples than Shannon describes.
3. Euclidean space and function space are not the same thing. Do you know what a function space is?

I'll help you out to understand this (or explain to others who are misled by what you say) when I get a chance, soon.

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Dec 14, 2019 at 12:24 PM

#### SoundAndMotion

@bigshot , is there a link for the BigShot Dictionary, because your definitions of "perfect" and "sound" don't match any I know of.
An original signal to which you have added noise due to a finite resolution cannot be recreated perfectly. You have added noise!!! No longer "perfect"!
"Sound" is not limited to what you can hear, e.g. ultrasound is sound and you can't hear it.

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Dec 14, 2019 at 1:10 PM

#### bigshot

I normally don’t get into dumb arguments over definitions, but the term “ultra” in Latin means “beyond”. Whatever the definition you want to use, ultrasonic stuff isn’t what you listen to when you play your stereo. It’s as useless as teats on a bull hog. You’re better off without it. And if it’s there and it isn’t causing you trouble, you can safely ignore it. It sure isn’t worth arguing about.

I think you are missing the point. It is not a theological question either. Forget about the bounds of human perception, the question is how is it possible to have infinite resolution without an infinite SNR and dynamic range?

There is infinite inwards... Within the parameters of frequency response and noise floor dictated by Nyquist it is infinite resolution. You can't "blow it up and see the halftone dots". In this sense, it is like vector graphics. It doesn't matter what scale you look at it, within the boundaries of Nyquist, it is perfect.

Infinite outwards is a different story... if I say that salt shaker is perfect, it doesn't mean the pepper shaker is perfect, or the table it's sitting on, or the room, or the house, or the city... Infinite outwards is when theology comes in... "Can God create a rock so big even He can't pick it up?" Infinite outwards is a rabbit hole that audiophiles love to chase down... How perfect is perfect? How much is enough?

Snatch the pebble from my hand, Grasshopper.

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Dec 14, 2019 at 5:07 PM

#### TheSonicTruth

Infinite outwards is a different story... if I say that salt shaker is perfect, it
doesn't mean the pepper shaker is perfect, or the table it's sitting on, or the room,
or the house, or the city... Infinite outwards is when theology comes in... "Can God
create a rock so big even He can't pick it up?" Infinite outwards is a rabbit
hole that audiophiles love to chase down... How perfect is perfect? How much
is enough?

Y'know, I've begun to wonder exactly what 'bigshot' looks like .....

Now I have a clearer idea: !

Dec 14, 2019 at 6:05 PM

#### bigshot

I look like a little dog in a top hat and tails!