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Biophysics, Limitations of Shannon and Issues with ABX Testing, Split from Topic ID: 57406 (TOS #5)
theorist1
post Jun 14 2013, 04:32
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As a scientist (biophysics) and an audiophile, I have my feet in both worlds, and have thus enjoyed this discussion. Here are some thoughts:

I. Open Access.

Several have written it’s unfortunate that this paper, which is of general public interest, is not available to those without an AES subscription (that includes myself). Agreed; and note that the landscape for scientific publication has been changing: researchers are increasingly realizing the value of “open access” papers – ones available freely, without a subscription. Some scientific journals have gone entirely open access, while others (for an additional fee) offer the option of open access publication of your paper. Let me suggest that, if AES doesn’t offer this option, it should, and that those publishing papers of broad interest should endeavor (if financially possible) to avail themselves of this.


II. ABX testing.

I assume from the discussion that this paper makes use of sequential ABX testing (by “sequential” I mean: present A, then B, then X, in sequence). I’d like to see basic research done into sequential ABX testing itself. In particular, sequential ABX testing (double-blinding will be assumed throughout this discussion) is highly regarded for assessing perceptual discrimination, because (with proper statistical analysis) it eliminates false positives – subjects can’t “pass” (i.e., achieve successful discrimination in) a sequential ABX test unless they truly can reliably distinguish A from B. But what about the converse? Achieving accurate discrimination in sequential ABX testing is hard, because it requires accurate memory of both A and B when judging X. Therefore I’d like to offer the hypothesis that subjects can “fail” sequential ABX testing even when they can successfully discriminate between A and B, and suggest a way of testing this. Essentially, one would use simultaneous ABX testing to eliminate the memory requirement, and then compare the results to those for sequential ABX testing. I can’t think of how you’d do simultaneous ABX testing with hearing, but it could certainly be done with vision (using color tiles). The experiment would be divided into three phases:

1) Find the smallest color difference that can be reliably distinguished during simultaneous ABX testing (present all three tiles – A, B, and X – simultaneously, so that the subjects can line them up next to each other for comparison).
2) Repeat the experiment, using that same color difference, with sequential ABX testing.
3) If the subjects fail phase 2 (thus confirming my hypothesis), find the smallest color difference that can be reliably distinguished using sequential ABX testing, and compare to the results of phase 1.

If it is found that subjects indeed fail to reliably distinguish colors when presented sequentially that they can reliably distinguish when presented simultaneously, this will suggest that sequential ABX testing may not be a good method for assessing our perceptual limits (i.e., for determining transparency) -- and not just for vision, but possibly for hearing as well.


III. High-resolution audio and the Shannon sampling theorem.

Here I’ll apologize in advance if my questions are na´ve – I’m no expert at signal processing. Anyways:

Those who are dismissive of high-res audio based on theory alone typically cite the Shannon sampling theorem (typically misattributed to Nyquist), noting correctly that we can’t hear over 20 kHz (if that), and that we only need >40 kHz sampling to accurately reproduce this. But 2 x max. frequency is not the theorem’s only requirement. It’s my understanding that it also assumes an infinite signal, perfect sampling, and perfect interpolation. I’ve never seen any of these assumptions discussed in this context, so I’d like to ask how much practical effect these requirements would have on Redbook (16 bit/44.1 kHz) vs. high-res conversion:

1) Infinite signal. I assume we can effectively satisfy this with signal length >> 1/frequency, and that this is thus a non-issue.

2) Perfect sampling. Clearly, sampling need not be perfect, but simply close enough to perfect to be transparent in amplitude and time. Timing errors lead to jitter (right?). So (and this is an engineering question): what’s the relationship between sampling rate and how easy it is to eliminate audible jitter errors?

3) Perfect interpolation. Another engineering question: Naively, unless implementing near-perfect (i.e., transparent) interpolation is trivial, I would think it would be easier to achieve transparent interpolation with a higher sampling rate, because the points are more closely spaced. Is transparent interpolation so easily achievable that the sampling rate has no practical effect?


IV. The effect of mastering.

Many have mentioned that the reason high-res disks do indeed sound better than CDs of the same performance is that they are mastered differently – as labors of love, and without the usual commercial pressures to alter the sound. Given this, I think it would be a pubic service if someone could produce a Blu-Ray disk corresponding to the songs tested in this study, containing both the high-res and Redbook versions of each, and make it available for sale. That way people could easily experiment for themselves.


V. General thoughts.

I think the reason for the continued controversy about digital audio performance is that we don’t completely understand the biophysics of human hearing (which is why it continues to be an active area of research). If we did, we would know, a priori, what constitutes a complete specification set sufficient to determine transparency, and thus could engineer transparent electronic gear (I say electronic because I am excluding transducers) without listening to it. To the best of my understanding, this is not yet the case, since the errors that our auditory system is capable of detecting can be extraordinarily subtle, and what would constitute a complete set of scalar specifications sufficient to ensure transparency thus remains an open question.

This post has been edited by greynol: Jun 14 2013, 14:02
Reason for edit: Added link to original discussion from which this one was split for being off-topic.
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Porcus
post Jun 15 2013, 18:38
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There is a sampling/interpolation/hearing issue that can only be resolved by studying the ear's response, namely to what extent the hair cells work so much as idealized strings that the sine functions are the appropriate basis. Such studies can, for all that I know, have been carried out explicitely; otherwise, a layman's gut feeling is that the effect is at most worth a slight miscalibration or margin of conservatism. I would be grossly surprised if this could possibly increase the 20 kHz figure by those ten percent required to break through the CD limit.

Anyway, the argument is that the canonical choice of sine functions is due to the wave equation, deduced by a 'spherical cow in vacuum' theoretical ideal string, which the hair cells are not. The periodic function that, around the 20 kHz mark, is "least painful given the hearing threshold" is likely not exactly the sine, but likely so close to that it is nothing to worry about for the purpose of the "20" figure.


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Woodinville
post Jun 16 2013, 07:34
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QUOTE (Porcus @ Jun 15 2013, 10:38) *
Anyway, the argument is that the canonical choice of sine functions is due to the wave equation, deduced by a 'spherical cow in vacuum' theoretical ideal string, which the hair cells are not. The periodic function that, around the 20 kHz mark, is "least painful given the hearing threshold" is likely not exactly the sine, but likely so close to that it is nothing to worry about for the purpose of the "20" figure.



I have no idea whatsoever you're talking about here. There is no "canonical" choice for a transform, and a Discrete Fourier Transform uses both sines and cosines, and this has nothing to do with an idea string at all.

The basis vectors for an FFT have to do with mathematics, not string vibrations.

The hair cells, which work somewhat differently, have nothing to do with "least painful given the hearing threshold", either, that I can think of.

So what are you asking?


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Porcus
post Jun 17 2013, 10:53
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QUOTE (Woodinville @ Jun 16 2013, 08:34) *
I have no idea whatsoever you're talking about here.


You seem to have the idea that I actually did write choice of 'transform' ...

A 19 kHz symmetric triangular and a 19 kHz sine are different. What does that difference mean in practice? Likely you would get one of two answers: (i) nothing, or (ii) if anything, the triangular is worse, as its useless higher order components are good for nothing and potentially bad for something.
Without choice of basis, it is absolutely no reason to claim that the latter has higher order components at all. It would not be so if we used triangular functions ( http://dx.doi.org/10.1016/S0898-1221(99)00075-9 - I am somewhat surprised that this had publishable news value as a research article as late as 1999 ...). We could do that, but there is a good reason why we don't. (Here's a lecturer who has or at last has a fond hope to have, students bright enough to spot that it isn't obvious: http://www.cv.nrao.edu/course/astr534/FourierTransforms.html .)

This post has been edited by Porcus: Jun 17 2013, 11:16


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Woodinville
post Jun 18 2013, 03:10
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QUOTE (Porcus @ Jun 17 2013, 02:53) *
A 19 kHz symmetric triangular and a 19 kHz sine are different.

D'oh. So?
QUOTE
What does that difference mean in practice? Likely you would get one of two answers: (i) nothing, or (ii) if anything, the triangular is worse, as its useless higher order components are good for nothing and potentially bad for something.

If I make a transform from triangle waves, which can by done by integrating a Hadamard transform, there will be no higher order components.

The ear, on the other hand, has a very strong resonant response, as in "coupled second order sections" with some delayed feedback. So these "higher order components" that one would see in a triangle wave as analyzed by a Fourier basis will simply not be captured by the ear unless they are within the bandwidth of the ear.

So, having said that, what's your point? I still see no point beyond a fallacious appeal to ignorance.


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Posts in this topic
- theorist1   Biophysics, Limitations of Shannon and Issues with ABX Testing   Jun 14 2013, 04:32
- - pdq   I don't know what you mean by "sequential...   Jun 14 2013, 05:17
|- - theorist1   QUOTE (pdq @ Jun 13 2013, 20:17) I don...   Jun 14 2013, 05:34
|- - greynol   QUOTE (theorist1 @ Jun 13 2013, 21:34) Th...   Jun 14 2013, 06:15
|- - 2Bdecided   QUOTE (greynol @ Jun 14 2013, 06:15) QUOT...   Jun 14 2013, 09:38
|- - Martel   QUOTE (2Bdecided @ Jun 14 2013, 10:38) Ex...   Aug 6 2013, 17:20
- - Kees de Visser   QUOTE (theorist1 @ Jun 14 2013, 05:32) (b...   Jun 14 2013, 10:33
- - greynol   I hate to do this, since drawing allusions to sigh...   Jun 14 2013, 13:55
- - drewfx   QUOTE (theorist1 @ Jun 13 2013, 23:32) Ac...   Jun 14 2013, 17:54
|- - theorist1   Thanks for all your comments! QUOTE (greynol ...   Jun 15 2013, 03:11
|- - theorist1   QUOTE ([JAZ] @ Jun 14 2013, 09:32...   Jun 15 2013, 03:12
||- - [JAZ]   QUOTE (theorist1 @ Jun 15 2013, 04:12) So...   Jun 15 2013, 16:43
||- - greynol   QUOTE (theorist1 @ Jun 15 2013, 04:12) So...   Jun 17 2013, 07:00
|- - krabapple   QUOTE (theorist1 @ Jun 14 2013, 22:11) ly...   Jun 20 2013, 11:17
- - [JAZ]   I will try to address the theory and reasoning of ...   Jun 14 2013, 18:32
|- - pdq   QUOTE ([JAZ] @ Jun 14 2013, 13:32...   Jun 14 2013, 18:44
||- - splice   QUOTE (pdq @ Jun 14 2013, 09:44) ... The ...   Jun 15 2013, 00:10
|- - phofman   QUOTE ([JAZ] @ Jun 14 2013, 19:32...   Jun 16 2013, 19:49
- - Woodinville   QUOTE (theorist1 @ Jun 13 2013, 20:32) If...   Jun 15 2013, 07:16
- - Porcus   There is a sampling/interpolation/hearing issue th...   Jun 15 2013, 18:38
|- - Woodinville   QUOTE (Porcus @ Jun 15 2013, 10:38) Anywa...   Jun 16 2013, 07:34
|- - Porcus   QUOTE (Woodinville @ Jun 16 2013, 08:34) ...   Jun 17 2013, 10:53
|- - Woodinville   QUOTE (Porcus @ Jun 17 2013, 02:53) A 19 ...   Jun 18 2013, 03:10
|- - Porcus   QUOTE (Woodinville @ Jun 18 2013, 04:10) ...   Jun 18 2013, 10:41
|- - knutinh   QUOTE (Porcus @ Jun 18 2013, 10:41) Now i...   Jun 18 2013, 13:01
||- - Porcus   QUOTE (knutinh @ Jun 18 2013, 14:01) It a...   Jun 18 2013, 23:26
||- - knutinh   QUOTE (Porcus @ Jun 18 2013, 23:26) QUOTE...   Jun 19 2013, 06:24
|- - Woodinville   QUOTE (Porcus @ Jun 18 2013, 02:41) Now i...   Jun 20 2013, 06:26
- - knutinh   Scientific curiosity aside: If it was found that s...   Jun 17 2013, 07:44
|- - Porcus   QUOTE (knutinh @ Jun 17 2013, 08:44) If [...   Jun 17 2013, 09:56
|- - knutinh   QUOTE (Porcus @ Jun 17 2013, 09:56) Long-...   Jun 18 2013, 10:19
- - antz   QUOTE (theorist1 @ Jun 14 2013, 04:32) If...   Aug 4 2013, 13:46
|- - greynol   QUOTE (theorist1 @ Jun 14 2013, 04:32) If...   Aug 4 2013, 18:31
|- - Woodinville   QUOTE (antz @ Aug 4 2013, 05:46) The fact...   Aug 4 2013, 21:42
|- - antz   QUOTE (Woodinville @ Aug 4 2013, 21:42) Q...   Aug 4 2013, 22:14
- - Light-Fire   QUOTE (theorist1 @ Jun 13 2013, 23:32) .....   Aug 4 2013, 17:43
- - mzil   QUOTE And what level-roving experiments show is th...   Aug 4 2013, 22:54
|- - Woodinville   QUOTE (mzil @ Aug 4 2013, 14:54) however ...   Aug 5 2013, 03:22
- - greynol   How can something that serves to make distinguishi...   Aug 5 2013, 04:33
|- - mzil   QUOTE (greynol @ Aug 4 2013, 23:33) How c...   Aug 6 2013, 17:15
|- - Kees de Visser   QUOTE (mzil @ Aug 6 2013, 18:15) Kees de ...   Aug 22 2013, 08:59
|- - Woodinville   QUOTE (Kees de Visser @ Aug 22 2013, 00:5...   Aug 24 2013, 13:11
|- - Arnold B. Krueger   QUOTE (Woodinville @ Aug 24 2013, 08:11) ...   Aug 25 2013, 01:21
- - 2Bdecided   Two mono samples, A and B. sequential: Listen to ...   Aug 5 2013, 10:46
- - Wayne Highwood   In light of the limits of serial audio testing rai...   Aug 5 2013, 19:14
|- - Arnold B. Krueger   QUOTE (Wayne Highwood @ Aug 5 2013, 14:14...   Aug 13 2013, 01:38
- - greynol   I see a distinction without a difference. Subject...   Aug 5 2013, 19:23
|- - Wayne Highwood   QUOTE (greynol @ Aug 5 2013, 12:23) I see...   Aug 5 2013, 19:59
- - 2Bdecided   So you are exploring the possibility that the reas...   Aug 5 2013, 20:59
|- - Wayne Highwood   QUOTE (2Bdecided @ Aug 5 2013, 13:59) So ...   Aug 5 2013, 22:05
|- - saratoga   QUOTE (Wayne Highwood @ Aug 5 2013, 17:05...   Aug 5 2013, 22:27
- - 2Bdecided   People who look for reasons to doubt DBTs generall...   Aug 6 2013, 10:15
|- - Wayne Highwood   QUOTE (2Bdecided @ Aug 6 2013, 03:15) Peo...   Aug 6 2013, 16:47
|- - [JAZ]   QUOTE (Wayne Highwood @ Aug 6 2013, 17:47...   Aug 6 2013, 17:45
|- - 2Bdecided   QUOTE (Wayne Highwood @ Aug 6 2013, 16:47...   Aug 6 2013, 18:16
|- - Wayne Highwood   I just hope you guys in the industry don't end...   Aug 6 2013, 21:13
|- - Wayne Highwood   QUOTE (2Bdecided @ Aug 6 2013, 11:16) * -...   Aug 15 2013, 00:31
|- - greynol   QUOTE (Wayne Highwood @ Aug 14 2013, 16:3...   Aug 15 2013, 00:45
|- - Woodinville   QUOTE (Wayne Highwood @ Aug 14 2013, 16:3...   Aug 15 2013, 01:01
||- - Wayne Highwood   QUOTE (Woodinville @ Aug 14 2013, 18:01) ...   Aug 15 2013, 14:39
||- - Woodinville   QUOTE (Wayne Highwood @ Aug 15 2013, 06:3...   Aug 17 2013, 04:57
|- - Arnold B. Krueger   QUOTE (Wayne Highwood @ Aug 14 2013, 19:3...   Aug 22 2013, 13:14
- - greynol   The point is that ABX is useful for more than the ...   Aug 15 2013, 15:08
|- - Wayne Highwood   QUOTE (greynol @ Aug 15 2013, 08:08) The ...   Aug 15 2013, 16:21
|- - saratoga   QUOTE (Wayne Highwood @ Aug 15 2013, 11:2...   Aug 15 2013, 19:26
- - greynol   I live on the West Coast so there's still time...   Aug 17 2013, 01:10


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