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Interesting Papers re temporal resolution
saratoga
post Jul 29 2009, 16:19
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QUOTE (NullC @ Jul 29 2009, 00:48) *
QUOTE (Mike Giacomelli @ Jul 28 2009, 12:08) *
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?


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!

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andy_c
post Jul 29 2009, 16:52
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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.
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Axon
post Jul 29 2009, 17:01
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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.
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krabapple
post Jul 29 2009, 17:04
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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.

This post has been edited by krabapple: Jul 29 2009, 17:06
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Axon
post Jul 29 2009, 17:11
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QUOTE (andy_c @ Jul 29 2009, 10:52) *
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.
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.

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

QUOTE
An enormous time (of the order of two years) and effort were spent to develop the instrumentation and the methods for checking for artifacts. For example, for just the Fourier spectrum shown in Fig. 4, it took a few months to develop the instrumentation setup and to write the C code (FFT was not used). To measure one such spectrum takes over a week.


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.
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andy_c
post Jul 29 2009, 17:27
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QUOTE (Axon @ Jul 29 2009, 10:11) *
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.


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.

This post has been edited by andy_c: Jul 29 2009, 17:31
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Canar
post Jul 29 2009, 18:18
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QUOTE (Axon @ Jul 29 2009, 09:01) *
So, on that note.... an off topic comment. I just realized that every chiptunes/NSF/etc player probably has a broken square wave generator.
Sweet! I get to pester kode54! biggrin.gif We'll see how far I can go with this. happy.gif


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kode54
post Jul 29 2009, 20:22
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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.
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Axon
post Jul 29 2009, 20:41
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Well, I'm thinking more specifically of the theoretical case, where the harmonics decay at An=1/n, so to get -96db down....
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squid
post Jul 29 2009, 23:15
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QUOTE (Woodinville @ Jul 29 2009, 00:20) *
QUOTE (NullC @ Jul 28 2009, 21:48) *
…Because other sampling methods don't require band-limited signals?



Oh, what sampling methods are we talking about here?


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

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saratoga
post Jul 30 2009, 03:46
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QUOTE (squid @ Jul 29 2009, 18:15) *
QUOTE (Woodinville @ Jul 29 2009, 00:20) *
QUOTE (NullC @ Jul 28 2009, 21:48) *
…Because other sampling methods don't require band-limited signals?



Oh, what sampling methods are we talking about here?


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?


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.

QUOTE (squid @ Jul 29 2009, 18:15) *
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.


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

QUOTE (squid @ Jul 29 2009, 18:15) *
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"?


"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.
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squid
post Jul 30 2009, 08:55
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QUOTE (Mike Giacomelli @ Jul 29 2009, 18:46) *
QUOTE (squid @ Jul 29 2009, 18:15) *
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"?


"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.


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".
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gnypp45
post Jul 30 2009, 10:37
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QUOTE (ncdrawl @ Jul 30 2009, 06:43) *
QUOTE (krabapple @ Jul 29 2009, 12:04) *
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.


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.
thanks.


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.
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Canar
post Jul 30 2009, 16:55
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QUOTE (ncdrawl @ Jul 29 2009, 21:43) *
Could you please stop being confrontational and rude??
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.


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Woodinville
post Jul 30 2009, 23:50
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QUOTE (ncdrawl @ Jul 30 2009, 11:29) *
I am a member of the sphile forum, and do not appreciate his attacks.

................and we shall know them by the fruits that they bear.


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.


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Woodinville
post Jul 31 2009, 00:45
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QUOTE (ncdrawl @ Jul 30 2009, 11:29) *
um...no. you are wrong.. he was implying that the peer review Dr. Kunchur has gotten thus far was bogus (as indicated by his quotes around the words "peer review")...


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


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MichaelW
post Jul 31 2009, 01:43
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QUOTE (ncdrawl @ Jul 31 2009, 06:29) *
QUOTE
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


I am a member of the sphile forum, and do not appreciate his attacks.


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.
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krabapple
post Jul 31 2009, 06:13
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QUOTE (ncdrawl @ Jul 30 2009, 00:43) *
QUOTE (krabapple @ Jul 29 2009, 12:04) *
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.


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.




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.

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Audible!
post Jul 31 2009, 08:36
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QUOTE (ncdrawl @ Jul 30 2009, 23:07) *
QUOTE (krabapple @ Jul 31 2009, 01:13) *
blah snip blah


what are your credentials?

One need not be a scientist to recognize rudeness. You are acting like a jerk. I could be an illiterate fool and still be spot on about your being antagonistic.


it was pointed out over there, and now I am pointing it out here.

this place is a canoe club of sorts so you may get by with it more... but ill call a spade when I see it...Herr Spade.


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

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Canar
post Jul 31 2009, 08:38
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QUOTE (ncdrawl @ Jul 30 2009, 23:13) *
I am not upset. I was simply pointing out the guy's personality flaws.
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.


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benski
post Jul 31 2009, 15:39
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QUOTE (Nick.C @ Jul 28 2009, 08:13) *
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?


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.

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2Bdecided
post Jul 31 2009, 16:33
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QUOTE (benski @ Jul 31 2009, 15:39) *
QUOTE (Nick.C @ Jul 28 2009, 08:13) *
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?

It still aliases, just that the aliased harmonics overlap onto other valid harmonics, so the distortion doesn't sound as bad.
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.
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benski
post Jul 31 2009, 16:39
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QUOTE (2Bdecided @ Jul 31 2009, 11:33) *
QUOTE (benski @ Jul 31 2009, 15:39) *
QUOTE (Nick.C @ Jul 28 2009, 08:13) *
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?

It still aliases, just that the aliased harmonics overlap onto other valid harmonics, so the distortion doesn't sound as bad.
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.

This post has been edited by benski: Jul 31 2009, 16:50
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2Bdecided
post Jul 31 2009, 17:13
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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.
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ncdrawl
post Jul 31 2009, 17:15
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QUOTE (Canar @ Jul 31 2009, 03:38) *
QUOTE (ncdrawl @ Jul 30 2009, 23:13) *
I am not upset. I was simply pointing out the guy's personality flaws.
Let's keep the ad hominem to a minimum. Behavior like this from either side is unacceptable, especially in the "Scientific Discussion" forum.


I have no problem complying with that, assuming that the SOP is enforced in an even-handed manner.

I love seeing healthy discussion though, my entire reason for posting the papers..





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