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[Bob Cain]

While I believe that Dan is correct in asserting that the bandwidth needed to encompass our ear's sensitivity is most likely less than 96 kHz and that there is a high probability that it need not be greater than 48 kHz, I don't think it can yet be stated with any certainty that the currently held view by most that 20 kHz, or thereabouts, is enough can be justified.

To speak of what the ear/brain can distinguish or sense in terms of Hz and to try and deduce its capabilities by probing it with sinusoids is to assume that the ear decomposes sound into them.  The only special thing about sinusoids are that they are the eigenfunctions of linear, time invariant systems.  Eigenfunctions are just functions with a fancy name such that feeding one through a system produces an output that is just a delayed and scaled version of the function it is stimulated with.  Only sinusoids can be guaranteed to have that property for any arbitrary linear, time invariant system.

The ear/brain is neither linear nor time invariant and in fact is _very_ far from it.  The fact that it isn't linear means that a pure sinusoid can cause at least electrical detection of more than one "frequency" when given a single tone and that when presented with sums of sinusoids at different frequencies it will hear sum and difference tones.  With more complex sound, rather arbitrary products occur.  I'm not up to date on the exact implications of being time variant (the ear/brain changes its sensitivity in response to what it is presented) are but they are similar.

Using sinusoids for probing the ear/brain has more subtle flaws that require a bit more maths to understand but the bottom line is that there is no reason to believe that the ear/brain decomposes sound into eigenvalues of linear, time invariant systems for further processing.  The decomposition it inherited via evolution is more likely to be based on features of a sound pressure wave that benefit survival than on abstract mathematics.

What this means is that simply because we cannot hear sin waves above a certain frequency there is no reason to believe that we don't extract features from sound whose Fourier decomposition would tell us have "frequencies" above the highest tone we can hear.  Those higher frequency components can be crucial in the detection of those features without our ability to hear those frequencies when presented as tones.

It is simply not true that complex sound is composed of sinusoids.  It is what it is and it is no more than that.  The fact that there is a domain of transformation, the Fourier domain, which nicely yields the eigenvalues of linear, time invariant systems is nothing but a mathematical artifice and meaningful only if the ear/brain transforms into the same domain in the same way.  It doesn't.  This is not to say that there isn't a sensitivity correlation with that basis, we all know there is, but there is not the equivalence that would be required for sinusoidal hearing tests to be definitive about what we can hear.

I am not claiming that there is a signifigant impact on perception when sound contains Fourier components above, say, 20 kHz but that at this point there is no psycho-physiological basis for ruling it out and some evidence that it should be and is the case.  Much more research is needed to determine what bandwidth suffices to encompass all that we can hear.

What I suggest is a recording and reproduction system with a bandwidth wider than mechanical properties of the ear alone would allow detection of.  That width shouldn't be too terribly difficult to determine on the high side but, since there is evidence of hair cells that are stimulated at 50 kHz, it's pretty high.  Then recorded source material, musical and environmental, known to contain very high bandwidth information should be presented to about 100 15-17 year old girls with with a high accuracy brick wall filter interposed in the repro chain and utilizing ABX testing to determine where that filter needs be set for those girls to be able to discern a difference with the filter switched in or out with statistical signifigance.  It's not all that difficult a protocol to set up and I wonder why it hasn't been done.


Bob Cain

[bobkatz]

Bob Cain wrote on Mon, 05 July 2004 02:35

What this means is that simply because we cannot hear sin waves above a certain frequency there is no reason to believe that we don't extract features from sound whose Fourier decomposition would tell us have "frequencies" above the highest tone we can hear.  Those higher frequency components can be crucial in the detection of those features without our ability to hear those frequencies when presented as tones.

With all due respect, as I have seen BC spout mathematics over at the Pro Audio List, I still feel that sometimes he can't see the forest for the trees. I distinctly recall that Bob Cain presented this "theory" on the Pro Audio Maillist, and it took hundreds of emails and explanations to get it through his head that he is using specious reasoning. And I thought he had understood and realized the basic contradictions in his statements.

Instead, BC chose to repost his crackpot "theory", which can be refuted by simply understanding the most basic principles of Fourier analysis.  Either Fourier was wrong, or Bob Cain is...

I suggest that instead of trying to fruitlessly explain to Bob Cain one more time why his use of "Fourier Decomposition" in the above quote yields a contradiction to his theory, that we instead have a fun argument over which "crackpot" category his easily-discreditable theory falls into:

Please visit

http://math.ucr.edu/home/baez/crackpot.html

Which crackpot is it? I vote for:

"10 points for each new term you invent and use without properly defining it. "

"10 points for arguing that while a current well-established theory predicts phenomena correctly, it doesn't explain "why" they occur, or fails to provide a "mechanism". "

and

"50 points for claiming you have a revolutionary theory but giving no concrete testable predictions. "

That about does it!

BK (partly in jest, but shaking his head in complete wonder)

[Loco]

Funny you mentioned that. Check the index adapted for audio here:

http://recforums.prosoundweb.com/index.php/t/982/1005/?SQ=aa 8cae40989386125d540cc5823d3a5b

[Chuck]

Bob Cain

What this means is that simply because we cannot hear sin waves above a certain frequency there is no reason to believe that we don't extract features from sound whose Fourier decomposition would tell us have "frequencies" above the highest tone we can hear.  Those higher frequency components can be crucial in the detection of those features without our ability to hear those frequencies when presented as tones.

I consider the above an important contribution in two ways.

First, for higher-frequency things in music we would not like to miss.

Second, for higher-frequency distortions that are introduced by not being able to convert accurately in the transition band.

Not being able to hear a single high tone, does not mean that humans are unaffected by the presence of complex high-frequency information.

Charles

[bobkatz]

Chuck wrote on Mon, 05 July 2004

I consider the above an important contribution in two ways. First, for higher-frequency things in music we would not like to miss. Second, for higher-frequency distortions that are introduced by not being able to convert accurately in the transition band. Not being able to hear a single high tone, does not mean that humans are unaffected by the presence of complex high-frequency information. Charles

That's fine, Charles, but that is NOT what Bob Cain wrote. He's implying some kind of a mystery that he can't explain, can't justify; all he does is cite some mysterious phenomenon with no experimental proof or demonstration, and which has no basis in currently accepted theory.

My personal judgment is that when you hear differences between two different sample rates, look into (approximately) the 20-20 kHz region (the "audible" band) for the reasons!

There are several legitimate possible explanations why differences may be audible among the higher sample rates other than that we have suddenly developed supersonic hearing   . And one of them is the possibility of intermodulation between the higher frequencies, though I consider that to be one of the weaker arguments based on my own and others' experimental evidence. For example, you don't have to have information above 20 kHz in a recording in order to hear differences between the sample rates!

Some possible explanations:

1) phase shift of the filters
2) distortion of the filters
3) ripple (in-band) of the filters
4) aliasing distortion (in band!!!) caused by the filters

and so on....

BK

[Bob Cain]

bobkatz wrote on Mon, 05 July 2004 08:10

Bob Cain wrote on Mon, 05 July 2004 02:35 What this means is that simply because we cannot hear sin waves above a certain frequency there is no reason to believe that we don't extract features from sound whose Fourier decomposition would tell us have "frequencies" above the highest tone we can hear.  Those higher frequency components can be crucial in the detection of those features without our ability to hear those frequencies when presented as tones. With all due respect,

With all due respect, I fail to find a trace of it in your response.

Quote:

as I have seen BC spout mathematics over at the Pro Audio List, I still feel that sometimes he can't see the forest for the trees. I distinctly recall that Bob Cain presented this "theory" on the Pro Audio Maillist, and it took hundreds of emails and explanations to get it through his head that he is using specious reasoning. And I thought he had understood and realized the basic contradictions in his statements.

Your memory is distorted.  What occured was that Dan asked me to desist because my point and the discussion that ensued was not addressing his original point about the need for 192 kHz sampling and instead following a divergence as to the adequacy of 44.1 kHz.  I agreed and respected his request.  This discussion has taken the same divergence and since it had not been deemed inappropriate for others, I sought to continue it here.  In no way was I disuaded by that discussion from my technical point of view.  

Sorry you feel it is specious.  Perhaps you should deepen your education in linear and non-linear systems and functional analysis rather than dismissing something you obviously know nothing about as specious.

Quote:

Instead, BC chose to repost his crackpot "theory", which can be refuted by simply understanding the most basic principles of Fourier analysis.  Either Fourier was wrong, or Bob Cain is...

Please explain how I contradicted Fourier?

Quote:

I suggest that instead of trying to fruitlessly explain to Bob Cain one more time why his use of "Fourier Decomposition" in the above quote yields a contradiction to his theory, that we instead have a fun argument over which "crackpot" category his easily-discreditable theory falls into:

I think one more time might be appropriate.  I would very much like to further address any perceived contradiction.  I broke that discussion off without addressing it on Dan's request and would welcome the opportunity correct any misperception.

What is the nature of the contradiction you see?

Quote:

Please visit http://math.ucr.edu/home/baez/crackpot.html

Interesting.  John is a close friend of mine (somewhat distanced by geography and time) and if you ask him I don't think he will put me in that class.  In fact with about a heartbeat to think about it I am certain he would corroborate everything I say.  As a mathematical physicist it would be obvious to him.

Quote:

Which crackpot is it? I vote for:

Could you offer us something a little more substantial than an ad hominem attack?  I substantiated my POV with numerous references that if understood would clarify the issue.

Quote:

"10 points for each new term you invent and use without properly defining it. "

Such as?

Quote:

"10 points for arguing that while a current well-established theory predicts phenomena correctly, it doesn't explain "why" they occur, or fails to provide a "mechanism". "

I don't understand this.

Quote:

and "50 points for claiming you have a revolutionary theory but giving no concrete testable predictions. "

I proposed a clear experiment at the end of the post you are responding to for testing this theory.  The theory is by no means new or revoltionary nor is it mine.  The theory of general signal decomposition is very well established as a generalization of Fourier's work.  It exploded in the late '80s with the work of Ingrid Daubechies.  A very large number of texts exist in the field and it is a productive area of research and Ph.D. thesis activity.  

If my suggestion that the ear/brain employs a mechanism more likely to be explained within this more general theory than exclusively by use of the Fourier (complex exponential) basis is original I'd be highly pleased, but I rather doubt I was the first to make the connection.


Bob Cain

[Johnny B]

Gee, I dunno, but I've never thought is was a crackpot idea to call for "more testing," in fact, I kinda think that's what good science always does. Test, re-test, learn or discover news things, throw out old theories and whatnot. In other words, it's a constant process, one that is never above any form of challenge and we keep moving forward in this way.

Now, Bob Cain has something he'd like to test, so I have a suggestion: Since Bob is in the Santa Cruz area, he might want to see if he could arrange for such a test to be set up and performed in conjunction with the University of California at Santa Cruz. I hear they have a pretty good engineering program there, so maybe they'd be interested in this.

I also have a goofy question of my own:

Would a 256Khz/32-bit chip make any sense at all?

Now why would I ask this?

Because the highest measured frequency I know of (so far) coming from a musical instrument is around 102Khz, give or take some Khz. Sure the downpoint is low, but it *is* there. So that would mean, even using Nyquist, at least a 204Khz sample rate.  

Why 32-bit? Because you'd have a chance to fix some of errors that occur now and possibly speed up the thru-put to a computer.

And we have 64-bit OS's and CPUs in our future. I think Apple has this now. So that's a factor to consider, making it target computer system friendly.

So, 256Khz/32-bit IC's---

Good idea? Bad idea? Or what?

Comments, thoughts?





   

[Zoesch]

Bob, are you referring to wavelet signal decomposition? (That's the only connection I can make out of your post)

As much as I lean towards wavelet theory it's going to confuse the hell out of everyone in this thread.

[steve parker]

"Bob, are you referring to wavelet signal decomposition? (That's the only connection I can make out of your post)

As much as I lean towards wavelet theory it's going to confuse the hell out of everyone in this thread."

Stefan,
are you saying you lean towards wavelet transform for audio purposes?
it's something i've thought about a bit.
i can't get my head around any possible implementation?

should this be a new (very short!!!) thread?

thanks.

steve parker.

[Zoesch]

Steve,

Very few people have gone the way of wavelet theory for audio, mainly because whether or not current implementations of digital audio are perfect or not they are easy to grasp and implement, and they have room for improvement (cf. what Graven is proposing on his latest paper)

I sort of lean towards spending a bit of time on researching wavelet theory for audio, the little work I've done with it has had to do with wavelet compression for telecommunications (And again, that was for imaging systems) and that was about 5 years ago.

I'm with you on this needing to be its own thread, the subject is fuzzy enough as it is to intersped it within this thread.

[Chuck]

bobkatz

There are several legitimate possible explanations why differences may be audible among the higher sample rates other than that we have suddenly developed supersonic hearing   . And one of them is the possibility of intermodulation between the higher frequencies, though I consider that to be one of the weaker arguments based on my own and others' experimental evidence. For example, you don't have to have information above 20 kHz in a recording in order to hear differences between the sample rates! Some possible explanations: 1) phase shift of the filters 2) distortion of the filters 3) ripple (in-band) of the filters 4) aliasing distortion (in band!!!) caused by the filters

Hi Bob,

I think I totally agree, its in the filters.

There is this monster called "alias distortion caused by undersampling".

In order to avoid that monster, we invite a second monster called "filter the hell out of it, so we will not see the alias monster".

In the end we have a mix of those two creatures.
The filter monster and the alias monster. Let's call it "filtias"

In a practical sense, I would like invite a third monster, to discard the first two monsters.

It's called "just sample the hell out of the signal".

I mean this in a unfiltered high-speed high-precision multibit way ...

Charles

[Zoesch]

Chuck wrote on Tue, 06 July 2004 23:03

In a practical sense, I would like invite a third monster, to discard the first two monsters. It's called "just sample the hell out of the signal". I mean this in a unfiltered high-speed high-precision multibit way ... Charles

Actually, consider inviting another kind of creature called "shape the way the filter behaves" before "sampling the hell out of the signal"

Moore law guarantees a certain degree of processing increase in time, but it has a limit, and sapling the hell out of the signal requires a hell of a lot of processing power to edit and process the signal.

[Chuck]

Zoesch

Moore law guarantees a certain degree of processing increase in time, but it has a limit, and sapling the hell out of the signal requires a hell of a lot of processing power to edit and process the signal.

Hi Zoesch,,

that's cool

I found this diagram:
http://www.intel.com/research/silicon/mooreslaw.htm

If we could do 44.1kHz in 1982, we would have been comfortable with 15MHz sample-rate in 2000.

I hope I will be able build a 18-bit - 1Msps machine this year. Should be pretty much like a tape.

Charles

[bobkatz]

Well, I apologize for being cantankerous. I got that way because I felt that Dick Pierce and Jim Johnston and others pretty much shot out your argument on the Pro Audio List and to my memory you were argued out of it. I certainly don't want to see us go down that road again (over 250 posts, probably, on the subject) over here.

[Bob Cain]

Zoesch wrote on Tue, 06 July 2004 04:13

Bob, are you referring to wavelet signal decomposition? (That's the only connection I can make out of your post) As much as I lean towards wavelet theory it's going to confuse the hell out of everyone in this thread.

Wavelets are an example of signal decomposition that uses basis functions which are not the complex exponentials used by Fourier but they are more mathematically constrained in their own way than is likely to be utilized by the ear/brain.  They have the properties of orthogonality and completeness which are very precisely and rigidly defined.  Those properties are not at all likely to have been selected by evolution.

Another way to view signal decomposition is as feature extraction and I just believe that nature would have selected for features that are both easier to implement and more relevant to the task at hand than are complex exponentials.

The salient point here is that being at least partially neurological in nature we are dealing with thresholding following detection and that it is entirely possible that a signal could have a feature which is matched sufficiently to trigger a threshold when it contains Fourier components that are not, by themselves, capable of triggering a threshold.  This is a hypothetical basis for requiring a higher bandwidth of reproduction than sinusoidal testing would indicate.

With regard to seeming to contradict or discard Fourier theory, this does no such thing.  We have been so steeped in it that many have come to believe that there is a physical principle that says that signals are actually composed of lots of sin waves.  This is not the case.  Fourier just showed that there is mathematical equivalence.  Fourier decomposition is not physics, it is mathematics.

Back to wavelets for a second, it is possible to prove also that a signal can be mathematically composed of lots of little signals called wavelets, the same signal that can be shown to be composed of lots of sins.  That it can be shown to be composable from either shows that this is not a physical property but a mathematical one.

My purpose is simply to point out that we cannot assume that the ear is not sensitive to aspects of a signal that contain Fourier components above 20 kHz or so just because we cannot get a response to sin waves above that frequency.  We cannot presume that it _is_ either and the only way to find out what bandwidth is required to encompass the ear's capability is by adequate experiment.  There have been some attempts at this and the results are equivocal so better experiments need to be done.

I am not trying to snow anyone with mathematical handwaving but merely to present enough of the general idea to justify the possiblity.  I am ready to accept that no one want's to consider this if that is the case.


Bob