http://www.physics.sc.edu/kunchur/Acoustics-papers.htm

http://www.physics.sc.edu/kunchur/papers/FAQs.pdf

I'm not sure wether they have actually tested the impact of high frequencies on human hearing or just the impact of a single-capactitor low pass filter.

Nice to see this topic here where it can be discussed calmly and rationally.

--Ethan

from the link:


Exactly how does some air vibration < 18kHz only last 5 microseconds?

Also,

.000005 = 200 KiloHertz

Does this mean we need > 400kHz sampling rates?

Well, I guess what we can conclude from Prof. Kunchur's research is that indeed, you might need 400 kHz to digitally represent a 7-kHz square wave transparently. I'm not listening to such square waves in my free time very often, though.

Would be curious to see what vinyl makes out of a "perfect" 7-kHz square wave.

Chris

Well, 400kHz aside, if he was anywhere vicinity of being right - what I'm not willing to swallow, yet - the long time objectivist argument would be broken:

• Humans can't hear anything above 20kHz.
• 44.1kHz sample rate is enough to cover all that completely according to Nyquist.
• -> The Redbook storage format is completely sufficient for transparency.

Well after reading through the first 3 PDF's and the FAQ, I surmise (from my novice knowledge of digital audio concepts) that his main point is centered on arrival times / phase differences. His blind testing groups could identify with good confidence down to about 5 microseconds. Apparently bandwidth restriction (44.1 kHz sampling for example) and loudspeaker placement (within a few millimeters) can each independently introduce timing variances > 5 microseconds that can be blind-test identified. Also there is a mention of two ultrasonic off-phase samples which cause (unwanted) lower sonic harmonics that can be identified as well.

I wonder what kind of design changes and production costs could accommodate typical electronic audio hardware sampling at > 192 kHz or even > 400 kHz? And what software encoding scheme would be required?

I'm still why the usually quite vocal "44.1kHz ought to be enough for anybody"-crowd doesn't take a stand on this...

I have prepared a set of audio files to verify Professor Kunchur's claims for the domain of digital standard vs. high rez audio, that is not subject Kunchur's lowpass circuitry. 7kHz square waves were directly generated into the corresponding output formats. It was quite difficult to get done, even Audition 3 could not generate 7kHz squares without notable artifacts. The results are interesting! You'll need a high end DAC, though.

Use files of equal bit rate for ABX testing! They are normalized to -10db and have short fade-in/-outs applied to prevent transient clicks while looping:

32 bit, 192 kHz:
Click to view attachment
32 bit, 192 kHz upsampled from 44.1kHz (Sox VHQ):
Click to view attachment

32 bit, 110 kHz, optimized for Benchmark DAC1s:
Click to view attachment
32 bit, 110 kHz (DAC1) upsampled from 44.1kHz (Sox VHQ):
Click to view attachment

32 bit, 44.1 kHz (for reference only):
Click to view attachment

Please re-download! I had accidentally uploaded the wrong set of files.

PS These are 32 bit integer files, which is Sox' default. Some applications (Audition and as reported even Foobar) have trouble playing them. Convert them to 32 bit float if you are affected. I also opted for integer because they are easier to verify with a hex editor.

rpp3po, the 192kHz versions are still different. The 44.1kHz sample matches the upsampled sample, but not the raw 192kHz sample, verified by ears and spectrograms.

Ok, I have re-generated them again and am going to re-upload.

In the meantime, does anyone see any flaws here?



PS This is the source code of Sox' square wave generator.

Don't even bother using a square wave generator in an audio editor - in order to ensure that the aliasing is below a 16-bit noise floor, you'd need 65536x oversampling....

Instead, construct the square wave by hand using additive synthesis based on the Fourier series expansion:

Amplitude(n) = 1/n, odd n; 0, even n
Phase(n) = 0

(Or, if you are sure your audio editor uses a technique immune to aliasing issues, like this one, use it.)

Such techniques are well documented - it's quite a shame that so many audio applications (and Dr. Kunchur, and other audiophiles) continue to use bad code.

Yes, I asked myself why Adobe would even include such a broken feature. It is very obviously broken and they should have seen that. Sox' results look fine to me now, though. If not, I'm open for feedback.



I thought that Kunchur had used an analog square wave generator?

I only skimmed the paper, but IIRC tried a digital one couldn't get it to work (for unspecified reasons) and then used an analog one. I presumed it was because he had a high end analog synthesizer handy (they're pretty common in labs since people used them for all sorts of stuff in the days before cheap digital DAQs).

Now the WAV files won't load in foobar2000...

Edit: Hacked around with them, got them loading in foobar2000, but all of them have subharmonics well under 7000Hz. At first I thought I was just hearing some weird IMD, but the subharmonics are there.

Edit 2: Synthesized my own versions, using Axon's cited additive synthesis technique:
http://benjamincook.ca/441.wav - 44.1kHz square, harmonics at 7k (gain 1) and 21k (gain 1/3).
http://benjamincook.ca/192-441.wav - 44.1kHz square, harmonics at 7k (gain 1) and 22k (gain 1/3), resampled to 192kHz using sox 441.wav 192-441.wav rate -v 192000
http://benjamincook.ca/192.wav - 192kHz square, harmonics at 7k (gain 1), 21k (gain 1/3), 35k (gain 1/5), ..., 91k (gain 1/13)

These really don't look square in any editor, but they should be mathematically-acceptable. I really can't ABX these. It hurts my ears, and I don't have a DAC that handles 192kHz nicely.

Edit 3: For the curious, this is simply the <math.h> sin function, at 32-bit floating-point precision. Fixed some numbers in Edit 2.

Kunchur's claims were introduced here at HA by moi two weeks ago:

http://www.hydrogenaudio.org/forums/index....mp;#entry646398

and yes, rpp3po , he is saying the Redbook is broken in terms of transparency.

Hence the uproar on Stereophile's forum, where it's delightful to see what fulsome respect the letters 'PhD' can garner from audiophiles when they really want to believe.

Just as an aside, no, that's not the case.

In order to contain the bandwidth of a signal, you have to filter it. It is possible (i.e. it is done with ridiculous filters which I cheerfully stipulate are not useful in any real sense) that filters might have a slight, tiny effect, maybe, kinda sorta, PERHAPS, at 44.1. Even less likely at 48, and not at all at 64. Nobody has shown this with sensible filters, by which I mean filters that have decent transition bandwidth (i.e. not as tight as humanly possible), ripple, and stopband rejection.

And, of course, if Dr. K's argument is mistaken, that shows nothing, for or against.

Could anybody enlighten me why a sine function, that supposedly outputs something that is not square (can't check - files are offline right now), should be a better approximation of a square wave than successive sequences of -x,-x,-x,-x,-x,-x,-x,-x,+x,+x,+x,+x,+x,+x,+x,+x values and x being a constant?

Not a sine, but a sum of sines:

is 1*sin(f*x) + 1/3*sin(3*f*x) + 1/5*sin(5*f*x) + ... + 1/N*sin(N*f*x), where N*f < 2*pi*Nyquist_frequency.


Because of aliasing. Take analog square wave and sample it without lowpassing it at Nyquist freq. You'll get that square digital wave; it contains frequencies below Nyquist limit and aliases of frequencies above it.

Why not just just create a 7.35kHz square wave "manually", i.e. for 44.1kHz sample rate 6x 32767 followed by 6x -32768 <repeat>; 15x for 110.25kHz and 24x for 176.4kHz?

The sum of sins approach is exact for a band limited square wave (since a band limited square wave is by definition the Fourier series of a non-limited square wave truncated at the band limit). Flipping between +/- x and then low pass filtering is only an approximation thats limited by the quality of the filtering applied.

Because that places unacceptable restrictions on the desired wavelength.

OK, so, my paper is taking a little too long to get out the door, so I will provide an executive summary here. I am trying as fast as possible to get it out, but the discussion is about to pass me by, soooo...

• His definition of the power difference at 14Khz, ΔLp(2), is not derived. When one derives it, one discovers that he fails to correctly sum the 14kHz components resulting from the (7+7) and (21-7) terms - in fact, he explicitly treats the calculation of ΔLp(2) as a "peak" level difference, when in fact the summed component quite obviously has a constant level. (That Dr. Kunchur makes such a basic trig error is profoundly disturbing to me.)
• His definition of ΔLp(2) also uses the theoretical values of Δφ instead of the values he already documented in his own measurements.
• When these issues are corrected, the values of ΔLp(2) for the RC-filter experiment fall from 1.4db down to the 0.2-0.3db range, and do not materially differ between the 3.9us and 4.7us cases. It therefore becomes extremely difficult to justify the results of the RC filter test due to nonlinear mixing.
• Paradoxially, Dr. Kunchur never mentions nonlinear mixing as a theoretical justification for his other test (speaker alignment), and in fact explicitly ascribes the results to an unknown cause. But when the corrected ΔLp(2) calculation is run, the values found are even larger than for the RC filter test, and vary quite substantially between test configurations (2.9mm: 0.76db; 6.2mm: 1.71db; 10.3mm: 3.59db). The bizarre conclusion that must be reached is that Dr. Kunchur's analyses are mutually contradictory between his two later papers (Acta Acoustica/Technical Acoustics). Either nonlinear mixing is the cause (which means the RC filter results are unexplained), or it's not (which means the RC filter's results are incorrectly justified).
• When ΔLp(2) is restated in terms of the before/after level difference of the 21khz level, and ignoring the differences in 7khz before/after levels, one finds that ΔLp(2) is strongly correlated with changes in 21khz level. If Dr. Kunchur truly wishes to justify audibility based on nonlinear mixing, and above ΔLp(2) being above a threshold, he must also admit that arbitrarily raising the 21khz level must also raise ΔLp(2) further above threshold, leading to arbitrarily lower measured temporal resolutions.
• The choice of 7khz square wave is unusually, profoundly rich in ultrasonics: The 21khz level is only 10db below fundamental, where the vast majority of tonal musical instruments have ultrasonic components far below that. That is: the input signal is entirely unrepresentative of actual music.
• Putting the above two points together yields quite possibly the most important objection to make here: Kunchur's results advocating a 5us temporal resolution are completely meaningless, because the process he uses to generate that result ought to be extended indefinitely to generate arbitrarily low resolutions. These results have no basis in psychoacoustic reality because they rely on signals further and further disconnected from realistic situations.
• Even if one discounts the nonlinear mixing justification for all of this there are still extremely good reasons to believe that the measured resolutions are inversely proportional to ultrasonic level. For instance, if one adopts a level- or peak-detection model, a signal with faster rise time ought to result in a lower measured resolution - but this faster rise time must be accomplished with increased high frequency components (keeping signal amplitude constant).
• Furthermore, his choice of 7khz square wave, far from being representative, is very carefully tuned. Any lower of a frequency would result in the 3rd harmonic becoming audible, which would invalidate his listening tests involving the manipulation of that component. Any higher of a frequency would move the 2nd harmonic further up in frequency, where human hearing is that much less sensitive; the risk becomes too great that the component would be made completely inaudible. In other words, results obtained for this type of input cannot be generalized for arbitrary music signals.

Of course, I'm only listing the comments here that relate to Dr. Kunchur's main thesis - I'm leaving out the rest of the points relating to his comments on 44.1khz digital audio, on signal synthesis, on high-end audio, etc...

ncdrawl, hold off on sending these to Kunchur just yet - I'll be able to give you/him a nicely typeset LaTeX file pretty soon with all of these points more fully fleshed out.

If I may grossly oversimplify your argument Axon, you're partially arguing that he's choosing an extreme edge case to test. However, if his intent is to map the boundaries of audibility, wouldn't an edge case be acceptable? I find the conclusion that ultrasonics are perceptible fascinating, and if he's found a case in which they actually are audible, should we not hear it out? Even though it does not represent most cases, if they are truly audible in this case, isn't that worth considering?

As an archivist, I want transparency in all cases, so I don't have to worry about the edge cases. That's why I use FLAC and not MP3. If there is any case where 44.1kHz is not sufficient, isn't that worth devising solutions for?

The use of a 7khz square wave as an input here, in this context, seems particularly unrepresentative to me, as a -10db ultrasonic third harmonic, with a signal completely absent of energy at 14khz from other sources, is a profoundly special case. It's not merely that it's an edge case - it is way, way over the edge to begin with. It's like arguing that 16 bits is insufficient because you can hear the noise with the gain raised ~20db above normal (as even shown by Meyer/Moran). Of course you can - but that situation never actually happens in the real world, where music is normalized near 0dbFS and released for an audience that actually wishes to listen to it. More generally, Kunchur never really justifies that input signal very well, and without careful delineation, nothing's stopping anybody from boosting 21khz levels arbitrarily high to get arbitrarily low measured thresholds (like with, for instance, a bipolar pulse train).

In the final reduction ad absurdum, it's hard to tell apart his conclusions apart from a claim that (say) 200khz bandwidth is necessary for audio, because if you play extremely powerful 200khz and 202khz tones, the inevitable intermodulation is audible. The existence of any form of intermodulation, combined with the existence of an ultrasonic bandwidth, necessarily implies that some classes of signals will show audible differences when filtered before distortion. Morevoer, this audibility will exist at any amount of filtering greater than zero, because I'll always be able to hand you a signal that will break threshold at the intermodulation frequency.

A test with ultrasonic content at ranges more representative of real situations would restore validity, but I think that is not going to save his conclusions. In that case, if audibility is shown in the first place, it will almost certainly be above 22us. And at that point it no longer has anything to do with time resolution. But it would be a convincing proof of CD's insufficiency - but before that point is reached, the question is, how would that be possible when every prior attempt has failed?

I think his results are really interesting, but to an archivist, they're not relevant until they're shown to apply to something approaching actual audio. After all if you just want to store square waves, you shouldn't be using PCM in the first place because of its nasty requirement that signals be band limited . . .

…Because other sampling methods don't require band-limited signals?

For archival purposes there is a decent argument for going beyond redbook "just in case" ... Perhaps the lizard people who will take over the earth after we nuke ourselves will have decent ultra-sonic hearing and want the full experience? It's not like the behaviours of professional archivists have much relationship to the behaviour of normal people anywhere else. (Or will you be micro-scribing my message onto a nickel plate?)

Sampling a square wave is silly. Just store the frequency, duty cycle, phase and amplitude. 4 numbers and you don't have to band limit it!

I'd like to add a few comments regarding the "Temporal resolution of hearing probed by bandwidth restriction" paper.

One potential issue is the second-harmonic contribution of the test setup. Since this contribution is within the audible band (14 kHz), special attention needs to be paid to it. Of course, an ideal square wave has no even-order harmonics by virtue of its half-wave symmetry, i.e. f(t +/- T/2) = -f(t). But there are ways that the second harmonic can creep back in. Two ways I can think of are the duty cycle of the square wave not being exactly 50 percent, and second-harmonic distortion of the test setup's transducers and electronics. Either of these situations will eliminate the half-wave symmetry and introduce even-order harmonics. The text below figure 1 states "The acoustic output from the transducer is devoid of even numbered harmonics because of the square-wave signal fed to it". Of course, in the real world, that signal can't be entirely devoid of second harmonic, and indeed figure 4 shows its presence. Oddly, figure 4 shows the frequency components in terms of power, where dB would have been better if clarity were the intent. In any case, the power ratio of second harmonic to fundamental is shown as 1e-6, giving a voltage ratio of 1e-3 (-60 dB) at the mic preamp output where this measurement was presumably taken.

One interesting thing that can be done is to make the generous assumption that the electronics and transducers have zero second-harmonic distortion, and assume this second-harmonic component is due entirely to the duty cycle of the square wave not being exactly 50 percent. One could then derive the Fourier series coefficients of a rectangular wave having duty cycle d, where 0 < d < 1. Then one could figure out what values of d correspond to a second-harmonic component 60 dB down from the fundamental. This would correspond to a "best case" scenario, because with electronics and transducers having non-zero second-harmonic distortion, the tolerance on the duty cycle of the square wave would have to be even tighter to take into account those additional second-harmonic components. Suppose we have a rectangular wave with a symmetrical voltage swing of +/- Vp and a duty cycle d. It's not too hard to show that the Fourier series coefficients vn of this function are:

vn = (4Vp/(pi*n)) sin(pi*d*n) for n >= 1 (i.e. this excludes the DC term)

The ratio r of the second harmonic to the fundamental is:

r = (1/2) sin(2*pi*d)/sin(pi*d)

Now we can solve numerically for the value of d that makes r = +/- 1e-3. This will give two answers - one slightly less than 0.5 and one slightly greater. Plugging this into MathCad, we get r1 = 0.49968 and r2=0.50032. So the allowable range of the duty cycle is 50 +/- 0.032 percent. This is an extremely stringent requirement, and yet this number is optimistic for two reasons. The first is the previously mentioned assumption that the electronics and transducers have no second-harmonic distortion. The second is that real-world square wave generators use nonlinear circuits which in general will have slightly asymmetric rise and fall characteristics. The Fourier series coefficients assume zero rise and fall times. I'm finding it hard to believe that he actually achieved this number, especially with two transducers involved (the headphones and microphone). So let's look at table 1, where he lists the harmonic components of the transducer output to see what he actually measured for the second harmonic in each condition. Well, those measurements aren't there, only the fundamental and the third and fifth harmonics. The entire issue is papered over with the statement "The acoustic output from the transducer is devoid of even numbered harmonics because of the square-wave signal fed to it". Since changes in this second harmonic value could explain the experimental results without needing some hypothesis regarding the alleged ability of the ear to detect signals above the frequency limit of human hearing, it's essential to include these data. Yet he fails to do so.

So, on that note.... an off topic comment. I just realized that every chiptunes/NSF/etc player probably has a broken square wave generator.

I checked the source code for one (nosefart) and it just does the naive synthesis. I checked blapp's libraries, which are used in many places, including foo_input_gep, and go to some trouble to ensure bandlimited synthesis... If I make an NSF with nothing but an A#7 square wave, and decode it through that library, it only rejects the 26khz harmonic to the tune of -50db!

It's kind of comical that the "high quality" players support oversampling... like, say, to 96khz. Whereas to get the aliasing under the 16-bit noise floor, one would have to sample at 1.45Ghz.

That's just barely infuriating enough for me to consider hacking together a player that relied entirely on additive synthesis.

It may well be that Dr. Kunchur's audio work is getting more thorough 'peer review' here than he's gotten so far. ;>

It shall be interesting to see the response.

Well, given that he actually measured the acoustic field at the listening position and no even harmonics were observed at that point, I figure that is reasonable enough evidence that they do not exist... but read on.

In his first paper (to Proceedings of Meetings on Acoustics) Kunchur explicitly rejects the use of FFTs in the power spectrum analysis:



IIRC, when questioned about this he said the implementation was an "elementary" one derived from textbook sources. I assert that anything using a power spectrum that can't use an FFT is unquestionably not elementary.

Figure 4 is evidence that they do though. This is not a surprise in any way. Ever try to get clean square waves to a scope from a pulse generator through a cable as short as 1m? A coworker of mine years ago thought his pulse generator was defective because of all the ringing and other artifacts observed on a scope when doing this. He was going straight into the high-impedance input of the scope. What he didn't know was that the cable had to be terminated in its characteristic impedance at the scope end. Once that's done, a "textbook" square wave is obtained. Otherwise, it's an awful-looking mess.

When the theory shows the second harmonic component to be so strongly dependent on tiny changes in the duty cycle, it raises concerns as to whether that was really controlled adequately. I don't see evidence of any such precautions having been taken.

Sweet! I get to pester kode54! We'll see how far I can go with this.

Where did you come up with that 1.45GHz figure? The 5A02 was clocked at closer to 1.6MHz, and thus produced sound at about that rate.

Well, I'm thinking more specifically of the theoretical case, where the harmonics decay at An=1/n, so to get -96db down....

I may be incorrect, but assuming a signal model different from the traditional (sum of sines), isn't it possible to come up with better sampling and reconstruction functions than the (time-domain) sinc? If yes, each time-domain sample could potentially be multiplied with a non-band-limited function (as opposed to the sinc) and thus produce a non-band-limited reconstructed signal.

In the square-wave case, certainly one could come up with better reconstruction rules given a signal model where square-waves have a high probability, mitigating e.g Gibbs issues.

Btw. does anyone know of references to more genereal work in this field? How to find the optimal sampling and reconstruction functions given a signal model that is less trivial than just "band-limited"?

/Pontus

You are correct. PCM is general, but typically not optimal if you have extensive prior information about a signal. In this case, as I hinted before since you know theres only one type of signal you (perfect square waves) you can perform exact non-bandlimited sampling while using a finite (and absolutely tiny) number of measurements.



Correct again. Technically PCM doesn't even work for square waves since they're not band limited.



"Compressed sensing", "compressed sampling" and "sparse sampling" are wildly used in engineering and optics to refer to other modes of sampling apart from Nyquist-Shannon. If you google you can find texts covering various approaches.

Why you insist on spewing such counterproductive nonsense is beyond me. I have spoken with Dr. Kunchur personally (via phone) and know that his work has been rigorously reviewed by authorities in many fields. He describes this process/experience in great detail in his writings.

so....Could you please stop being confrontational and rude?? I mean...firs the jab at the Stereophile forum, now another jab at Dr. Kunchur.
If you aren't going to be polite(like the rest have), please do not pollute this thread as you have elsewhere.

your comments have added nothing.

thanks.

Thanks for your answers and the pointers. I've studied those concepts briefly and they seem to consider mostly the case of modifying both the sampling and reconstruction functions. However I haven't found any literature describing how to modify the reconstruction function, given standard (uniform Dirac pulses) sampling but a signal model other than "band-limited".

OK, OK... But I must say I find nothing rude in Krabapples comment. In fact (without prior knowledge of the case at hand) it seems plausible.

I'm not implying anything w.r.t. Dr. Kunchur's papers here, but in my experience peer review process can mean very different things in practice. Factors such as journal ranking, mood, interest and workload of reviewer in combination with reputation of author (or co-authors), novelty of research field etc. can influence the process. After all, reviewers are human beings and can have a bad day.

Sometimes you get a very thorough review with lots of constructive comments, sometimes the reviewer just seems to have made a few read-throughs with minor remarks and that's it. Sometimes you may even find errors in your own output which passed unnoticed through the peer-review process. From my graduate student years (semiconductor laser physics) I remember seeing a few papers every now and then in rather prestigious journals (e.g. Appl. Phys. Lett.) that I would never have let through myself.

So, the fresh eyes provided by Axon and others here at HA may see things from another angle and discover things unnoticed by the peer reviewers. It can only be a good thing.

He might have been so elsewhere, but there's really little to critique about his posts in this thread. Your response is more "confrontational and rude" than his initial post. He was just commenting that he expects to see some engaging peer-review here, which is a very valid belief.

I think it's reasonable to question the peer review of some of the quotes that you guys over there have mined, because they are just wrong.

It may not have been what the Dr. intended to mean, but nipping that kind of misapprehension is a substantial part of what reviewing and editing is on about.

The quotes wherein the Dr. is alleged to have said that amplitude resolution has no bearing on time resolution in a PCM signal is also cause for questioning. Now, I wasn't there, I don't know exactly what the good Dr. said, but if he said that, he's sorely mistaken.

I read his reply. It is equivocation, plain and simple. The words have defined, specific meanings in the field, and part of peer review is making sure that the author uses words in such a fashion. So, when that does not happen, that's yet another reason to be concerned about the review process and the reported results.

There is a distinct possibility it was reviewed by the wrong set of "peers', I must say.

Bismarck, or someone, said that you'd not feel the same about laws or sausages if you'd seen them being made. Add to that list PhDs. Some PhDs, of course, are awarded for outstandingly original work; most, for good solid stuff which shows that the candidate has learned how to do research (in the specified field); some are awarded for no visible reason. Feynman once said that he didn't supervise PhDs because the degree was awarded for work by a member of faculty completed under particularly trying circumstances. Harsh, but everyone who's supervised PhDs laughs when they hear it. Rule of thumb: anyone who makes a big deal of their doctorate, for any reason other than trying to get upgraded on an airline, is to be viewed with suspicion.

Based on talking to Dr. Kunchur, *you* are convinced his work has been thoroughly vetted by relevant authorities.

Your confidence might matter to me if you can answer 'yes' to all of the following questions:

Are you demonstrable expert in the fields related to the audio work Dr. Kunchur has published?

And if not,

Are you a scientist? Are you familiar with peer review -- its potential and demonstrated strengths and flaws? Are you equipped to even begin to assess the bona fides presented for a scientist's work, e.g. his CV, the list of conferences he's presented it at, the journals he's published it in? Would you even know how to gauge their relevance to a particular bit of his published research? How to determine if he publishes in 'good' journals or not? How to find out what esteem his work is held in by people working in the same field?

If you can't answer that last set in the affirmative, what is *your* confidence supposed to mean to me, someone who *can* answer yes to all of those?

I am a scientist . Not famous, not especially accomplished. My field is not digital audio signal processing or psychoacoustics. But I have certain skills to investigate claims from a field outside my own. These aren't unusual skills for scientists; you pick them up of necessity. And looking into where he's presented , and where he's published, I'm not 100% convinced Dr. Kunchur's audio work has gotten rigorous peer review from properly targeted reviewers.
I might add my own proverb that when a scientist publishes well outside his or her main field of expertise, as Dr. Kunchur has done with his audio work, he or she stands a good chance of either finding something fresh...or making a fundamental error. Some people here who are pretty well versed in matters closely related to his work, appear to think he's done the latter. That gives me pause.

If you find that 'impolite' maybe you need to attend a few scientific conferences yourself, or try being part of a peer review process. It's not for the faint of heart or for those with a romantic idea of how science gets done ('how the sausage gets made')

But even if you disagree, it should be clear even to you that there is vastly more detailed and substantive review of Dr. Kunchur's audio work being offered here at HA that on offer from certain braying asses on Stereophile's forums who merely keep repeating HOW DARE YOU!! LOOK AT THE LIST OF CONFERENCES!!! LOOK AT THE PHD!!! LOOK HE HAS TWO PAPERS!! SO SHUT UP, DR KUNCHUR RULEZ!!!!

So as I said: I look forward to Dr. Kunchur's responses and debate on the technical critiques offered here...assuming he reverses his decision that all substantive issues have already been addressed.

Yikes.
I'm an employed scientist (honestly, I'd be tempted to say we're 'technical professionals' on the production side, since original research isn't the primary thrust) as well, and looking at the questions posed on some of the other forums, and the response from Dr. Kuncher, I'd say he has a good point or three even assuming badly forged credentials scrawled with blunt crayons on toilet tissue.
What are your credentials and how is your core specialty relevant to psychoacoustics and signal processing?

To be perfectly honest, my credentialed competencies don't relate directly to these topics, but I do have an amateur interest and the circumstances here are interesting. The researcher of the (possibly revelatory, if documented accurately and actually reproducible) work in question here has called an end to participation in even cursory internet discussions (with numerous apparently relevant unanswered questions, some posed by figures known in the specific field) and taken his ball and gone home to his core competency. There is no doubt in my mind that talented superconductivity researchers are a much needed force in society (buddha knows we could use some nice 250mph maglev trains here on the west coast), but phonon dynamics have at best a tangential relevance to this topic. Given the sweeping conclusions one might be tempted to draw from Kuncher's statements regarding this research, I'm a bit befuddled as to his reticence to engage in discussion.

Therefore, with all due respect, pimping Dr. Kuncher's general scholastic record is less interesting and vastly less relevant than actually addressing the specific technical questions posed.
There is also an apparent 'context' here, which colors both Kuncher's work and is reminiscent of that surrounding some of his references (re: ultrasonics).

edit: formatting, redundancy

Let's keep the ad hominem to a minimum. Behavior like this from either side is unacceptable, especially in the "Scientific Discussion" forum.

This thread is for technical discussion of the paper put forward by Dr. Kunchur. I may not personally have a doctorate in a related field, but that is a goal of mine. This discussion is basically a form of peer review. There are quite a few people here that have significant degrees of understanding in this field, ncdrawl. Many professionals, scientists, passionate amateurs, and everywhere in-between.

It still aliases, just that the aliased harmonics overlap onto other valid harmonics, so the distortion doesn't sound as bad. You can get better square wave approximation through other means like minimum-phase bandlimited steps (minBLEP), band-limited impulse trains (BLIT), or windowed sinc method (BLIT-SWS). But only exact synthesis (sum of sines) is going to be exact.

In this case, either the fundamental and harmonics end up at the amplitude they should be, or they don't.

Are you saying that they don't?

Of course you end up with something where the phase relationship between the square wave and the sampling instants is specific and fixed - but can't you get exactly the same thing by summing sines? (or nearly the same thing, assuming the comparison is with this "square" wave run through a decent but real world oversampling DAC).

Cheers,
David.

Sorry for the confusion. I meant that, if the sampling rate is a multiple of the square wave's fundamental frequency, then the aliased harmonics will have the exact frequency as a non-aliased harmonic.

That is, if a square wave has harmonics at f1 through f<infinite>, nyquist frequency (fn) will also be a harmonic, and every harmonic fn+1 will alias to fn-1 which is also a harmonic.

It's still aliasing distortion, but it "sounds" OK because it is still harmonic. Just that the spectral distribution of the waveform will be different than a proper sampled (or properly synthesized) version.

A real unaliased square wave, when digitized, will have gibbs effect during the transitions at all frequencies (and the length of ringing is frequency-invariant), because the impulse in the analog domain turns into a sinc wave in the digital domain.

And, to clarify. Yes, a "naive" digital square wave will have the wrong amplitude for its harmonics even when the sampling rate is a multiple of the fundamental frequency.

Yes, I see it now (having tried it!), it's looks (after the DAC) and sounds almost the same, but there's too much of the high frequency harmonics because the aliases are added in.

Cheers,
David.