I read something rather interesting today. I browsed through the
headphone amp designs available at headwize.com and found this (http://headwize2.powerpill.org/projects/showproj.php?file=meier4_prj.htm) article.
Look at figure 1. The guy explains why 44.1kHz isn't fast enough to
sample a 21kHz signal. Nyquist was completely wrong!
Now.. if you look more closely at the second picture of figure 1, you
will notice a flaw in the "21kHz image-signal" picture. He simply
performs a linear interpolation between every point. (!)
How could such an intelligent guy makes such a mistake? I mean, read
the article.. you will see this guy is far from being stupid.
Am I missing something?!?!
I am in no means qualified to really discuss this... it seemed logical to me though. In what sense do you feel he was incorrect though? How would you draw it differently?
I've never read such a crock of lard in my life. Nyquist would be scandalized. Clearly this character doesn't know the first thing about oversampling, sigma delta modulation, and decimation filtering. Instead, he advocates using a less-than-brickwall analog filter to "warm up" the sound in the passband. Hey - let's add some phase distortion (among other types) to the passband and completely ignore the fact that converters these days make it unnecessary to filter out the narrow gap between the edge of the passband and 22.05kHz. This fellow's project was a museum piece back in the mid eighties when the first 4X oversampling machine hit the stores.
Why can't people who think they know what they're talking about take a bit of effort to read up on DSP fundamentals...
:x
edit: I'm backing out of this conversation while I still can
I am in no means qualified to really discuss this... it seemed logical to me though. In what sense do you feel he was incorrect though? How would you draw it differently?
If I didn't know I was dealing with sines, I could use a quadratic, cubic, Nth order polynomial function to approximate what really was the function (the data between the two points). A linear approximation is really crude.
Knowing I am dealing with sines, well... that's even easier. There is mathematically one and only one way to represent a sine given two points (with only two points you can represent it perfectly.. frequency wise and amplitude wise). I am not inventing anything here. This has been discussed amply.
So why does he say you cannot represent a 21kHz sine (well.. he says anything beyond 15kHz I think) correctly when sampling at _only_ 44.1kHz? His linear interpolation is debatable to say the least.
I am not saying 16/44.1 is perfect. Don't want to go there either. I was just wondering if I was missing his point or something...
Exactly. The shortest distance between two points is not a straight line when dealing with a band-limited signal. By drawing straight lines, he completely misses the point and introduces spanking brand new harmonics to the original sampled signal outside the passband. I think we learned not to draw straight lines on the first or second day of my 4th year Discrete Time Systems course...
:x
Phony. The guy takes the sampling of a 41.5 kHz wave, and since it's like a 2.5kHz wave, he extrapolates backwards and says that's a problem at 21kHz, which it's not.
I see. I would really like to learn about this stuff, starting from a pretty ignorant background - any tips as to a good website or book? I thought his description was pretty easy to follow, too bad it is apparently bulls**t
I don't think Meier adequately (or correctly) described why the ringing occurs in the first place, and therefore I can see why you all are missing the point. It is definitely not because DSP algorithms use linear approximations. His picture is misleading. Series (Fourier, Laplace, etc) are often used to represent analog signals (mathmatically sound by the way).
Some sort of low-pass filtering must be used for digital conversion; you notice CDs cut off around 22kHz (44.1kHz /2, according to Nyquist's formula). Ringing occurs when an infinite series is truncated (discontinuous), and occurs with any practical digital filter. This is known as Gibbs phenomenon and is mentioned in the article. According to Meier this ringing is most pronounced in the case of a hard cut-off (or brick-wall filter). Meier's filter apparently uses a method to ease this hard cut off, and thus lessen the effect of Gibbs phenomena (according to Meier). I have to admit I haven't taken enough signal processing classes to say if it would work or not, or even if common modern digital filters are inadequate in this regard.
Because this ringing is due to the filter, it doesn't make sense to say Nyquist's formula is wrong.
lol
Maybe he just put the linear-approximation diagram on the page to encourage people to buy his $260 Analoguer. The rest of the post might at first seem reasonable, though (to an undergraduate EE student like myself): the more gradual the low-pass, the less ringing present. For people with poor high-frequency hearing such as Meier, high-frequency attenuation won't hurt, so you get rid of the ringing "for free".
But from what I've read in my digital audio books, modern low-pass filters don't suffer from significant ringing, even with relatively sharp filtering. And even then, if the brick-wall filter introduces high-frequency ringing (I think that was what Joe Bloggs briefly mentioned at the beginning of this thread (http://www.hydrogenaudio.org/forums/index.php?act=ST&f=1&t=3472)), Meier won't notice it, because he has already admitted that he can't hear high frequencies. What's the point of filtering out something you can't hear? If there is aliasing present in the recording, a high-pass filter won't fix it without removing the frequencies that should be present. Perhaps I'm committing a serious fallacy here, but to me, the Analoguer appears to be pretty useless.
And also, some of this was discussed in an ancient thread (http://www.hydrogenaudio.org/forums/index.php?act=ST&f=1&t=210) back in 2001...
@MTRH: this isn't an FB2K discussion (http://www.hydrogenaudio.org/forums/index.php?act=ST&f=27&t=8069) (that was appalling). Try not to post such useless comments.
It should also be noted that this ringing occurs in the frequency domain, not the time domain (Meier's article makes it look the other way). That is, it creates a ripple on the amplitude of the frequency response close to the point of discontinuity, and graduately evens out as frequency decreases. Check out the animation on this page (http://www.sosmath.com/fourier/fourier3/gibbs.html) for an illustration of this effect.
Jebus: Meier's explanation for why there is ripple (and what kind of ripple) seems to be incorrect, and does not give credibility to his design.
SometimeWarrior: (off-topic) You go to UCSB? I'm at Cal Poly, computer engineering...
SometimeWarrior: (off-topic) You go to UCSB? I'm at Cal Poly, computer engineering...
Yes, I'm a computer engineering student at UCSB. They've somehow avoided teaching me what a Fourier series is, after two years. Maybe I should have attended SLO instead?
I'll dig up my math book and look again at your link in a couple of days, thanks. I'll probably end up eating my words...
Don't torture yourself man! We didn't get to Fourier analysis until the end of our second year, and it was not the most exciting thing in the world. I've been avoiding my next signal analysis class like the plague. I avoided looking at the equations on that page; the animation was the part I found interesting.
But hey, I'd have to say that SB just may have more hotter women - but it's a close call. Can't wait 'till it summer weather B)
Phony. The guy takes the sampling of a 41.5 kHz wave, and since it's like a 2.5kHz wave, he extrapolates backwards and says that's a problem at 21kHz, which it's not.
No no, I don't think it's phony. He sampled a 21kHz wave @ 44kHz (which is okay), but then he interpolated linearly (which is the problem).
Except for that incorrect example though, I think this paper is (mostly) correct.
Question 1: would that 21kHz wave be accurately reconstructed after the 44kHz sampling, if correct interpolation were used (ie: sinc) ? Nyquist says yes.
Question 2: for transients, what is more important: the shape or the curve, or the precise harmonic content ?
A little question: would the wave be accurately reconstructed after the 44kHz sampling, if correct interpolation were used (ie: sinc) ?
The problem occurs when a low-pass filter is introduced, and this is the issue Meier is trying to address. A sine wave at a fixed frequency of 21kHz should be able to be reproduced accurately, and so would a sine wave at a fixed frequency of 19KHz. The real problem is that they may have inaccurate amplitudes. The problem is in the frequency response, and it's not clear if Meier even realizes this. It would be nice if he labeled the axis of his graphs. He describes a picture of a sine wave at a fixed frequency of 21KHz wobbling; this is not correct as I understand it.
So the answer to your question: depends on the quality of the filter. But there is an ongoing debate of whether 44.1kHz is high enough to begin with - so there may be no easy answer.
freakngoat:
I can understand that the ringing problem makes sense, if the ear is more sentitive to the graphical shape of transients than to their harmonic content (which is very possible...).
About sampling, though, I had always thought that any [0Hz .. 22kHz[ tone could be reproduced exactly when using 44kHz sampling and no quantization. Well, it seems that any such tone can be reproduced, but not always accurately ? Or, is his interpolation solely at fault ? Would "sinc" solve that problem ? I don't understand that..
Right: here are the facts.
A brick wall low pass filter should ring. You see his first criticism - that the 21kHz sine wave is amplitude modulated? The ringing removes the amplitude modulation. It's the ringing that fills in the gaps between the sample points, and also maintains the 21kHz wave at the correct amplitude in the regions where the samples appear to be low in amplitude. Without the ringing, you'll get the amplitude modulation. Pick your poison!
This begs an obvious question: if the "correct" filter rings on and on like this, surely that causes problems when the 21kHz sine wave stops. Surely, in this system, it can't just "stop dead"? Correct!
The thing is, if a 21kHz sine wave just "stops", it will generate a click, which has frequencies WAY above 22kHz (the nyquist limit). You can't have a sine wave that stops dead, but has no higher frequency components at the stopping point. It's a fundamental of audio (and other areas too!) - you can even try it practically in Cool Edit! So, nyquist implies that a 21kHz tone can't stop dead, because this would mean it contained frequencies way above 21kHz - i.e. above the nyquist limit.
This means that, the nearer the frequency is to the nyquist limit, the poorer the time resolution is (in terms of cycles taken for the sine wave to decay to some fraction of it's former amplitude) - but this isn't a fault - it's just the physics of bandlimitting the signal.
All he's doing in the article is making a gentle filter. There's no magic. A gentle filter won't ring as much. This means that either:
a) you allow frequencies higher than the nyquist limit through - which will give you apparent amplitude modulation of the 21kHZ tone (he didn't show you that his box still does that, but it may!), or
B) remove frequencies below the nyquist limit. This will give a dull sound. Also, because there's almost no 21kHz signals left after you've killed them with the gentle filter, you're less likely to notice any ringing that may remain.
He's doing both. In a way, this is ideal. With higher sampling rates, you can use a gentler filter, and there will be no ringing or amplitude modulation to speek of. BUT at 44.1kHz, it's a difficult compromise. But it's not magic. You can either:
a) keep all the frequencies up to nyquist, kill all the ones above, and have lots of ringing at the nyquist frequency, or
B) compromise this, reducing ringing, but letting more frequencies above nyquist through, or reducing the amplitude of some frequencies below nyquist that may be audible.
You shouldn't be able to hear ringing at 22kHz - but that's with perfect equipment and old ears. There's a theory that when the energy of an impulse is stretched in time, even though the stretching is only at inaudible frequencies, that it make an audible difference. This is because real audio equipment (especially speakers) produces distortion with all sounds, but not with silence. So, you're adding distortion before and after all sounds. Thinking about how sensitive we are to pre-echo (think about mp3!), and how long a true brick-wall filter will ring for (infinity!) - if the equipment makes this inaudible ringing become audible, then it could be a real problem.
In practice, it's all very subtle stuff, creating very subtle effects. But it's one argument for higher sampling rates - you can use gentle filters and avoid any possible compromise. The best thing at 44.1kHz seems to be to filter gently, starting at around 18kHz, making sure it's nearly dead by 22kHz. Because of the compromise, it makes designing good "sounding" nyquist digital filters as much of an art, as it is a science.
Coming back to the original article, in his box, one of the filters is 2dB down at 10kHz and 4dB down at 15kHz - it's hardly surprising that it makes things sound "less harsh" - try this filtering in Cool Edit and things will sound less harsh too!
Cheers,
David.
NumLOCK: I've just been reviewing my books, and yes, mathematically it can be proven that a 44.1kHz sampling rate is able to recover the exact original waveform with a bandwidth of 22kHz (Nyquist's theorem) so you are correct.
Perhaps the basis for the debate on whether 44.1kHz is high enough has to do with the effect of ringing from the lowpass filters being used. (48kHz would allow a bandwidth of 24kHz and more diminished ringing in the audible range). Or maybe it's because various alterations to the waveform typically being applied these days (effects, equalizers) diminish the original signal less at higher sampling rates. Unfortunately I don't know the answer.
Strictly speaking, all approximation by the analog to digital process is done in the quantization step as long as Nyquist's theorem is satisfied. This is where more bits help.
A brick wall low pass filter should ring. You see his first criticism - that the 21kHz sine wave is amplitude modulated? The ringing removes the amplitude modulation. It's the ringing that fills in the gaps between the sample points, and also maintains the 21kHz wave at the correct amplitude in the regions where the samples appear to be low in amplitude. Without the ringing, you'll get the amplitude modulation. Pick your poison!
I don't see any reason why the sampling process would add amplitude modulation to the original waveform. The whole idea is to reproduce the original waveform, and this can be done precisely since 44KHz > 2*21kHz. Certainly the sampling process is not used as a demodulation step. Therefore I can see no reason why ringing would ever be desirable.
Also, you talk about how "long" a filter will ring for. I'm not sure what you mean by this. Do you mean the bandwidth of frequencies which produce noticable ringing? It is my understanding that this ringing is in the frequency domain, not the time domain - however I am going to research this further.
As far as the click at a sudden cutoff, you may be right, but it is not discussed in any of the papers, books, or webpages I have read so far. Since a true brick-wall filter would have a slope of infinity and therefore be non-differentiable at the cut-off point, practical ones do not exist and therefore my be a non-issue. All practical filters have some slope. From what I've read the biggest problem with a very steep filter is the ringing effect. You are right in that if you can't increase the sampling rate some sort of softer filter is needed to reduce ringing. I don't think the answer is to have a filter transisition beyond the Nyquist limit, since this will introduce aliasing errors. My guess is that some sort of gentle filter starting around 20kHz would be good and would not audibly dull the sound.
My question is, what type of filters are typically being used these days for audio? Maybe we're talking about something so slight that it doesn't even make an audible difference. It would be nice to hear some samples.
Just a side note: This is not just a problem in audio, this is also a problem in digital imaging as well, and there are well known filters (Lanczos, cubic) to reduce the same ringing we've been talking about due to Gibbs Phenomenon.
I don't see any reason why the sampling process would add amplitude modulation to the original waveform.
Sampling does exactly this to frequencies near the nyquist limit -
if you look at the sample points themselves, rather than the reconstructed waveform. It's what he's trying to show in his first figure.
At the DAC, before the low pass filter, the spectrum extends to infinity (theoretically), each sample having infinite height, infinitely short duration, with an area equal to the amplitude value. That's the theory. In practice, the samples are often reproduced as a staircase waveform - this still has a near-infinite spectrum (just as a "real" square wave has an infinite spectrum). Most importantly, from 22-44kHz, this spectrum is a mirror image of the real spectrum from 0-22kHz.
That's what causes the "amplitude modulation" if you just look at the sample points themselves. For a 21kHz tone, there's also a 23.1kHz alias - without a filter, the two beat - that's what you see in his first figure.
Also, you talk about how "long" a filter will ring for. I'm not sure what you mean by this. Do you mean the bandwidth of frequencies which produce noticable ringing? It is my understanding that this ringing is in the frequency domain, not the time domain - however I am going to research this further.
I read this earlier up the thread, but forget to comment - the ringing is in the time domain. Frequency domain wobbles in the filter response have little to do with this discussion. So, by length, I mean duration.
As far as the click at a sudden cutoff, you may be right, but it is not discussed in any of the papers, books, or webpages I have read so far.
That's because I haven't written any yet Seriously, this is advanced stuff. The ideas come from some backround research which I did for a post doctoral research project which never happened! They're not all my ideas - I spoke to a lot of clever people.
Since a true brick-wall filter would have a slope of infinity and therefore be non-differentiable at the cut-off point, practical ones do not exist and therefore my be a non-issue.
Yes - infinite slope = infinite duration. Impossible. Rather than thinking about making a finite slope, and seeing what the result will be in the time domain, it's easier to take the infinite length time domain filter (a sinc function) - chop it (or window it) down to a sensible length (e.g. a few thousand samples), and see what the result is in the frequency domain. It's the practically the same either way, but I find it easier to think about it this way. You can do it all in Cool Edit with an impulse (drag one sample up), the FFT filter, and the frequency analysis window.
All practical filters have some slope. From what I've read the biggest problem with a very steep filter is the ringing effect. You are right in that if you can't increase the sampling rate some sort of softer filter is needed to reduce ringing. I don't think the answer is to have a filter transisition beyond the Nyquist limit, since this will introduce aliasing errors. My guess is that some sort of gentle filter starting around 20kHz would be good and would not audibly dull the sound.
Yes. Though, in the analogue world (I know we're not talking about the analogue world, but anyway...) a filter which drops from 0 to -90dB within 1/10th of an octave isn't called "gentle"!
My question is, what type of filters are typically being used these days for audio? Maybe we're talking about something so slight that it doesn't even make an audible difference. It would be nice to hear some samples.
I can't help you there (how would you listen to them anyway?!) - but you can read...
http://www.dcsltd.co.uk/papers.htm (http://www.dcsltd.co.uk/papers.htm)
- the second paper addresses the issue of energy smearing, which is caused by (and, in effect,
is) ringing.
"typical" filters are a compromise, and are usually realsed as cheaply as possible. You can download specifications from several companies e.g.
http://www.analog.com/UploadedFiles/Datash...892AD1855_b.pdf (http://www.analog.com/UploadedFiles/Datasheets/578404892AD1855_b.pdf)
Just a side note: This is not just a problem in audio, this is also a problem in digital imaging as well, and there are well known filters (Lanczos, cubic) to reduce the same ringing we've been talking about due to Gibbs Phenomenon.
Though the best compromise is vastly different in image processing. Images look OK with the kind of aliasing that would sound terrible in audio. Conversely, audio sounds OK with the kind of ringing that would look awful in images!
We discussed about all this some time ago: http://www.hydrogenaudio.org/forums/index....2957#entry29125 (http://www.hydrogenaudio.org/forums/index.php?act=ST&f=1&t=2957#entry29125)
Quoting myself, here are my views:
Ringing in filters happens whenever there is an abrupt discontinuity in the frequency response of the filter. If there is sonic "content" in the original signal at the frequency this discontinuity exists, pre or post ringing will appear. The more abrupt the discontinuity (~ higher slope, or steeper filter), the greater the time-domain ringing.
In CD brickwall filters, the discontinuity happens near 22 KHz. So, if there is any ringing, it will appear at these frequencies. Also, for this ringing to appear, the signal must have content at these frequencies.
Thinking a little bit more about this, in a properly recorded cd signal, there should be no content at these frequencies, because it must have been filtered at the AD stage in order to avoid aliasing. However, this AD pre-filtering can also produce ringing, if there was any content at the filtering frequencies in the original signal. So, if there is any ringing, it is already present in the recorded signal, and (most likely) not produced by the cd player brickwall filter. I say most likely because if the CD player filters at a lower frequency than the AD filter, it will eliminate the AD filter ringing, but will introduce its own. However, I don't think this is likely to be the case. Also, in the case of same synthetic generated signals, there can be no AD stage, then the ringing would happen due to the player filter, but I also think this is not very common, or likely to happen in commercial CD's.
So, there can be ringing in the cd signal, but this ringing will be near 22 KHz, which is inaudible. Also, using a proper not ultra-steep AD filtering, this ringing time duration can be minimized.
Although 22 KHz is not audible, if there are nonlinearities in the playback path at this frequencies, this 22 KHz ringing might intermodulate with other signals and produce intermodulation products which fall into the audible band of frequencies, and in fact "became" audible. However, and as recapitulation, for this intermodulation products to happen and be audible (which is our "final" main concern now), some conditions have to be satisfied:
- There must be signal content in the original signal at 22 KHz. For the ringing to have audible significance, this 22 KHz content must be of relatively high amplitude, and of "transient" type, that is, of very short attack or decay times.
- The AD stage pre-filtering must be quite steep. I believe that with a relatively "soft-edge" filter, the ringing duration and amplitude can be quite minimized. However, I don't know how steep are actually the filters commonly used.
- The playback chain (mostly speakers or headphones) must be able to reproduce this 22 KHz signals, and also be quite nonlinear a this frequencies. I think that good speakers of headphones capable of reproducing such high frequencies are not likely to be very nonlinear. However, I could be wrong.
So, I think that this ringing in CD audio is very, very difficult to be noticeable, and even if it was a real problem, could be effectively adressed using proper AD pre-filtering.
I think that usual FIR filters at players have quite short pre-ringing, due to the limited number of taps used.
Edit: corrected wrong link.
Question 1: would that 21kHz wave be accurately reconstructed after the 44kHz sampling, if correct interpolation were used (ie: sinc) ? Nyquist says yes.
I'm not an expert in signal processing (yet), but i think the problem is cardinal (sinc) interpolation is practically impossible to do in real-time, since you should know the amplitude of samples which are after the ones you're processing (in the time domain). Someone correct me if I'm saying bulls**t.
Norman
WTF are you guys talking about!!!!!
I thought Chemistry was difficult!!
auldyin
I'm not an expert in signal processing (yet), but i think the problem is cardinal (sinc) interpolation is practically impossible to do in real-time, since you should know the amplitude of samples which are after the ones you're processing (in the time domain).
Yeah, that's why FIR filters cause pre-ringing: they begin to output filtered signal *before* the actual signal has come out of the filter. They work realtime by delaying the signal a few ms., they need to take data in advance, in order to work. I don't know if I've explained myself very well...
I thought Chemistry was difficult!!
If fact I used to find chemistry more difficult than these things...
We discussed about all this some time ago: http://www.hydrogenaudio.org/forums/index....=ringing&st=50& (http://www.hydrogenaudio.org/forums/index.php?act=ST&f=20&t=3390&hl=ringing&st=50&)
Actually, it was the Shibach EQ (http://www.hydrogenaudio.org/forums/index.php?act=ST&f=1&t=2957#entry29125) thread where you said this.
I did a search for "filter AND ringing" before posting, but I
knew I should have also filtered by your username, KikeG. I mean, with 775 posts, I was sure you had addressed this issue before, I just couldn't find where.
If fact I used to find chemistry more difficult than these things...
Yeah, so did I. I guess it just comes down to what you're interested in.
Anyway, this is a facinating topic. I'll have to come back to it after I take my next signal analysis class (this fall). It's funny though, because this topic relates to a lot of things. We were discussing Fourier series, as well as Nyquist's and Shannon's formulas in my networks class today; I was on top of it.
Actually, it was the Shibach EQ (http://www.hydrogenaudio.org/forums/index.php?act=ST&f=1&t=2957#entry29125) thread where you said this.
Yep, true, it seems that I made a mistake when cutting and pasting. I've corrected it, thanks.
I mean, read
the article.. you will see this guy is far from being stupid.
Am I missing something?!?!
He's trying to sell his stuff?
I'd propose that in the future this kind of thread gets renamed or split quicker. It contains a lot of usefull information, but my first reaction on seeing the title was 'sigh' and closing it.
He's trying to sell his stuff?
I'm afraid so. The pity is that surely some people bought it.
Either this Jan Meier thinks that he's smarter than Nyquist (when in fact he doesn't understand him), or he is just taking advance of people ignorance, or a mix of both things. I wonder how much he charges for his "analoger" tha tin fact is just a very simple analog delay line.
Be careful with those "audiophile"-style products and explanations!!
No, I'm not an idiot, I don't feel like an audio-guru either, and I don't like to sell equipment using "audiophile" style explanations. Actually, I have a PhD in physics and a profound professional experience in (digital) signal analysis.
Yes, the linear interpolation as shown in the article is a rather simplified one. Not because I don't understand, but because of didactic reasons. "Popular" articles always have to be written in such a way that the layman can understand without a throurough knowledge of the underlying theory. You always have to choose a certain balance between detail and simplification.
However, the beating effect is much closer to the truth than people at this forum seem to think. For a newer version of the article, with a slightly more elaborate discussion on the "beating" phenomenon I suggest people take a look at my home-page: www.meier-audio.com. Simply click at the "analoguer"-button and enjoy.
Cheers,
Jan
Yes, the linear interpolation as shown in the article is a rather simplified one... You always have to choose a certain balance between detail and simplification.
I'd say, in case of your article, it is balance between "wrong" and "right" explanation.
However, the beating effect is much closer to the truth than people at this forum seem to think.
I see you have tried to disguise the effect you talk with new fancy graphics and explanations. The fact is that they are still *wrong*. The beating you talk about is a nonlinear type of distortion. Sinc() filtering, which is the filtering used in DACs, won't cause any kind of nonlinear distortion, no matter how short the filter. A short filter will result just in a less sharp filter, but will cause *zero* distortion or beating. Beating is amplitude modulation, which translates into the addition of sidebands to the original signal. The inexistence of this phenomenon can be easily verified with any decent soundcard, just play and record a 20 KHz tone, and analyze it. Result? No beating or sidebands.
As to other assertions you do, good ADCs/DACs introduce minimal phase distortion at high frequencies, just see PCAVTech phase analysis of the LynxTwo, it is close to nothing. Maybe you SACD is one of those esoteric ones that in fact are not close no anything neutral. As to pre-ringing, I explained why it is not important in this case, at a previous post in this thread.
I have a PhD in physics and a profound professional experience in (digital) signal analysis.
This is just basic theory signal. I guess you need an introductory course, or just some real-world measurements that show any of this.
Edit: added more explanations.
No, I'm not an idiot, I don't feel like an audio-guru either, and I don't like to sell equipment using "audiophile" style explanations. Actually, I have a PhD in physics and a profound professional experience in (digital) signal analysis.
Yes, the linear interpolation as shown in the article is a rather simplified one. Not because I don't understand, but because of didactic reasons. "Popular" articles always have to be written in such a way that the layman can understand without a throurough knowledge of the underlying theory. You always have to choose a certain balance between detail and simplification.
However, the beating effect is much closer to the truth than people at this forum seem to think. For a newer version of the article, with a slightly more elaborate discussion on the "beating" phenomenon I suggest people take a look at my home-page: www.meier-audio.com. Simply click at the "analoguer"-button and enjoy.
Cheers,
Jan
I think the main argument against the analoguer in the posts above was not the linear interpolation in the explanation, but rather that it solves one 'problem' by introducing several others.
PS. I don't know about where you live, but here biomedical engineering is a quite different discipline from physics.
Yes, the linear interpolation as shown in the article is a rather simplified one. Not because I don't understand, but because of didactic reasons. "Popular" articles always have to be written in such a way that the layman can understand without a throurough knowledge of the underlying theory. You always have to choose a certain balance between detail and simplification.
That doesn't wash if the simplification is what introduces the problem you are trying to explain.
The inexistence of this phenomenon can be easily verified with any decent soundcard, just play and record a 20 KHz tone, and analyze it. Result? No beating or sidebands.
Should this apply if the 20 kHz tone is played by a different soundcard (clock shift -> beating) ?
The inexistence of this phenomenon can be easily verified with any decent soundcard, just play and record a 20 KHz tone, and analyze it. Result? No beating or sidebands.
I've analised the output of several CD players and DACs, using a tone 1kHz below nyquist, and an external spectrum analyser (an old HP machine which had 70dB range, and a frequency response from DC to either 100kHz or 200kHz - I forget which). They all showed this effect to some degree. Two of the DACs cost over $1000, so we're not talking cheap junk here!
As you reminded me, we've been through this before. Since we have, we must have discussed (and I'm sure you know) that a shorter filter gives rise to a less steep frequency domain response. The less steep response let's more of the nyquist +1kHz alias through - which beats with the 1kHz below nyquist tone.
Outside the theoretical limits, both sampling and quantisation are totally non-linear. They become linear over a specified range with correct filtering and dither.
FWIW I would rather perform the function of the analoguer using Cool Edit Pro (or a DSP board with 24-bit output) and a good DAC running 2 or 4x (e.g. 88.2kHz or 176.4kHz - it may oversample further internally). Having tried with CEP and the audiophile 2496 (which may not count as a good DAC) I can't say that I hear a difference, but (using a 21kHz sine wave) I can certainly measure one.
I must try ABXing the frequency response of the analoguer - I bet that the high frequency filtering of setting "5" is ABXable, using most normal DACs. This would probably improve the sound of most harsh recordings - but is it really any better than just EQing them to match your own personal taste? That's the fun of Cool Edit
et al - we can all be audio engineers in our own bedrooms!
Cheers,
David.
2Bdecided:
We would have to distinguish between issues due to real-world implementation, ideal implementation, and theory. We could split this into 3 levels. In reverse order:
-In theory, when reconstructing sampled information in a pure, limitation-free, mathematical way, without quantization levels, there should be no problems (beating, noise, etc) at all, the reconstructed signal would be identicall 100% to the band-limited original signal. This is what Nyquist says, and I believe that Jan Meier agrees too, at least in his second version of the page.
- Going into a more real-world version of a DAC, we could consider a model that uses quantized, fixed-resolution sampled data, and digital reconstruction filters of fixed length, but that would have no real-wold analog parts inside that could cause any linear or nonlinear distortion or noise by themselves. This is how real-world DACs are, with the exception of the analog components inside them. A DAC of this kind can be perfectly modelled and simulated inside a computer.
Here is where things start to differ. Jan Meier says that in this case, there would be "beating" (nonlinear distortion) due to the use of fixed-length reconstruction filters. False. If you simulate a DAC inside a computer this way, it will still be distortion-free, given that you use dithering as needed. There would only appear quantization noise, depending exclusively on the data size of the samples at the adquisition (ADC) and the reconstruction (DAC) stages. Depending on the implementation of the filter, there would be for sure some images of the reconstructed signal (aliases, although it is not a proper definition of this) remaining above Nyquist frequency, specially if the filter is short and those images are not well attenuated. But, there would be still no distortion below the Nyquist frequency, just reflected attenuated "images" of the signal, above this frequency, due to this possible limitation of the digital filters.
- Now, if we go into a real-world DAC, there is a possibility that due to the non-linear limitations of analog components, that ultrasonic remaining information ("aliases", or better say "images" of the signal over Nyquist frequency) could intermodulate with the reconstructed signal, appearing intermodulation products into the audible band (below Nyquist frequency). This is the only way that this beating can happen, due to analog limitations (linear and nonlinear distortion, noise) of real-world, solid-state, components. But this non-linearity has no direct relationship with the lenght of the filters used at the reconstruction process, or the frequency of the sampled signal, as Jan Meier tries to imply. It can be a non-direct consequence of it, but depends exclusively on the nonlinearity of the system, not the reconstruction sampling process, and will happen equally when playing lower frequency signals.
Now:
I've analised the output of several CD players and DACs, using a tone 1kHz below nyquist, and an external spectrum analyser (an old HP machine which had 70dB range, and a frequency response from DC to either 100kHz or 200kHz - I forget which). They all showed this effect to some degree. Two of the DACs cost over $1000, so we're not talking cheap junk here!
I find this quite strange. This is a loopback recording of my $150 card playing two tones of 19 KHz and 20 KHz.
(http://www.kikeg.arrakis.es/measurements/M-Audio%20Audiophile%202496%20ASIO%2024bit/imd.png)
As you see, there are minuscule intermodulation products at around -115 dBFS. However, those are result of the intermodulation of the two played tones, not of the tones plus aliased information over fs/2 (Nyquist frequency). See, the intermodulation products of those -12 dBFS tones fall at -115 dBFS. For sure, the intermodulation products of these tones with the aliased ones will be much lower, since those aliases will be of significant lower amplitude, due to the filtering of these frequencies over fs/2 that any DAC performs.
If I repeat that same measurement with a single 20 KHz tone, I bet that intermodulation products will be minuscule, if measurable at all. Maybe the effect you saw was due to the old HP anayzer you used?
Outside the theoretical limits, both sampling and quantisation are totally non-linear. They become linear over a specified range with correct filtering and dither.
Well, if you use proper dither, the system will be perfectly linear below Nyquist frequency, in the sense of that there will be just quantization noise added, but no distortion at all.
Here is where things start to differ. Jan Meier says that in this case, there would be "beating" (nonlinear distortion) due to the use of fixed-lenght reconstruction filters. False. If you simulate a DAC inside a computer, it will still be distortion-free, given that you use dithering as needed. There would only appear quantization noise, depending exclusively on the data size of the samples at the adquisition (ADC) and the reconstruction (DAC) stages. Depending on the implementation of the filter, there would be for sure some images of the reconstructed signal (aliases, although it is not a proper definition of this) remaining above Nyquist frequency, specially if the filter is short and those images are not well attenuated.
If you have a real tone at 22kHz, and an image of that tone at 22.1kHz, the two will beat, won't they? If they're the same amplitude (unlikely in this case, but just imagine...), you'll see a classic beat waveform, with the amplitude envelope going from minimum to maximum in a regular pattern - in this case 100 times per second. Just what Jan shows on his site.
But, there would be still no distortion below the Nyquist frequency, just above, due to this possible limitation of the digital filters.
This is the key to the problem. What you say here is true. "If we look at this very carefully, and if we only consider frequencies
below the nyquist limit, then they have not been harmed or changed in anyway." That's true - but in saying it,
you are incorporating a perfect low pass filter into your hypothetical viewpoint.
"there would be still no distortion below the Nyquist frequency" = if I have a perfect filter, there is no distortion.
To "see" that there is no distortion, you have to look through a filter. In your viewpoint, you are removing all the components above 22.05kHz; then from this viewpoint, everything looks fine.
(If you use a spectrum analiser, with a long FFT setting, you can see that there are two tones - one above the nyquist limit, and one below - you're saying we ignore the one above - fair enough - but ignoring everything above a certain frequency is imposing a low pass filter on your view. That's not a useful way of looking at it...)
Now, back to reality: Let's say that we can hear 22kHz. I can't. I doubt most people can. But let's say we find someone who can. I think it's quite likely that, if your hearing extends to 22kHz, it'll also extend to 22.1kHz. Therefore, when you listen to the 22kHz tone, reproduced by this DAC which allows a (smaller) 22.1kHz image through, what you'll hear is a rough, beating tone, with a frequency of around 22.05kHz.
There you go - no analogue electronics involved, but a hiedous non-linear effect.
I've analised the output of several CD players and DACs, using a tone 1kHz below nyquist, and an external spectrum analyser (an old HP machine which had 70dB range, and a frequency response from DC to either 100kHz or 200kHz - I forget which). They all showed this effect to some degree. Two of the DACs cost over $1000, so we're not talking cheap junk here!
I find this quite strange. This is a loopback recording of my $150 card playing two tones of 19 & 20 KHz.
OK - first, I'm not talking about intermodulation - I'm just talking about the presence of the image tones.
Then, second, your looped back sound card doesn't work at a high enough frequency to capture the image tones of itself - the only way to do that it to run one soundcard playing at 44.1kHz, and another recording at (say) 96kHz.
If we repeat that same measurement with a single 20 KHz tone, I bet that intermodulation products will be minuscule, if measurable at all. Maybe the eefect you saw was due to the old HP anayzer you used?
You can see the beating between a 22kHZ and 22.1kHz tone on a 'scope. But I think we're talking at cross purposes - this all goes back to the fact that I think having an image tone is a bad thing (despite it being above nyquist) whereas you don't.
You're right - the effect at 20kHz is probably tiny.
(goes away, looks round the office, opens a box from university)
I've dug out the results of the experiment. I checked 3 DACs on a 'scope, and more using the spectrum analyser. All checked using 16-bit 44.1kHz test signals generated in CEP.
On the scope, I measured the beating, or amplitude modulation, in volts - peak to trough.
Meridian DAC, ref: 1kHz tone Vpp=6.4V
22.0kHz: 1.35V
21.0kHz: 0.32V
20.0kHz: <0.02V
Digilog DAC, ref: 1kHz tone Vpp=7.6V
22.0kHz: 2V
21.0kHz: 0.6V
20.0kHz: 0.1V
10.0kHz: ~0.02V
Sony DAC, ref: 1kHz tone Vpp=7.2V
22.0kHz: 0.96V
21.0kHz: 0.08V
20.0kHz: <0.02V
Then, on the scope, I measured the relative amplitudes of the real and image tones:
SME DAC
20.0kHz: +1.62dB > no image above -78dB
20.5kHz: +1.57dB > 23.6kHz: -50dB
21.0kHz: +1.24dB > 23.1kHz: -27dB
21.5kHz: -0.20dB > 22.6kHz: -13.31dB
22.0kHz: -3.95dB > 22.1kHz -5.09dB
Sony DAC
1.00kHz: +2.21dB
10.0kHz: +2.37dB
15.0kHz: +2.19dB
20.0kHz: +1.98dB > no image above -78dB
20.5kHz: +1.54dB > 23.6kHz: -51.5dB
21.0kHz: +0.12dB > 23.1kHz: -31.01dB
21.5kHz: -2.92dB > 22.6kHz -18.11dB
22.0kHz: -8.11dB > 22.1kHz: -9.45dB
CardD+ sound card
1.00kHz: -4.05dB
10.0kHz: -4.14dB
15.0kHz: -4.22dB
20.0kHz: -4.34dB
20.5kHz: -4.38dB > 23.6kHz: -66dB
21.0kHz: -4.52dB > 23.1kHz: -40.15dB
21.5kHz: -5.62dB > 22.6kHz: -22.03dB
22.0kHz: -9.76dB > 22.1kHz: -11.17dB
Digilog DAC:
1.00kHz: +2.96dB
This DAC has terrible filtering - even the 1kHz tone gives:
~43kHz: -57.8dB
~45kHz: -59.2dB
~87.2kHz: -60.4dB
~89.2kHz: -60.7dB
Similar rubbish for 10 and 20k, then for the main ones:
20.5kHz: +2.62dB > 23.6kHz: -21.59dB
21.0kHz: +1.88dB > 23.1kHz: -12.67dB
21.5kHz: +0.41dB > 22.6kHz: -6.74dB
22.0kHz: -2.05dB > 22.1kHz: -2.69dB
Meridian DAC
1.00kHz: +1.74dB > ~43kHz: -66.9dB (I hadn't checked this high for the other DACs before the one above)
10.0kHz: +1.32dB > ~34kHz: ~64dB
15.0kHz: +1.67dB > 29.1kHz: ~-65.5dB
20.0kHz: +1.54dB > 24.1kHz: -52.7dB
20.5kHz: +1.08dB > 23.6kHz: -29.75dB
21.0kHz: -0.01dB > 23.1kHz: -18.61dB
21.5kHz: -2.03dB > 22.6kHz: -11.21dB
22.0kHz: -5.25dB > 22.1kHz: -6.08dB
At the time, I dumped these numbers into Excel and plotted graphs of the image rejection filter response in each of these DACs - not quite the brick walls I was expecting before I performed these measurements. The Digilog DAC from Musical Fidelity was very old, but both the Meridian DAC and the SME DAC were recent, and generally thought to be excellent.
I did these tests because of an AES paper by Richard Black (I think) who suggested that these image frequencies were a real problem. He doubted that we could hear them, but he pointed out that they are not harmonically related to anything within the true audio spectrum - hence any intermodulation caused by amplifiers or speakers could create some nasty inharmonic components within the audible range. I'm not sure the numbers add up to a huge problem for typical music, but he had a point - it is possible that there is an audible effect.
Cheers,
David.
If you have a real tone at 22kHz, and an image of that tone at 22.1kHz, the two will beat, won't they? If they're the same amplitude (unlikely in this case, but just imagine...), you'll see a classic beat waveform, with the amplitude envelope going from minimum to maximum in a regular pattern - in this case 100 times per second. Just what Jan shows on his site.
Not exactly. The output of a DAC goes through a filter (in practice, it's one digital filter with over-sampling plus an alalog filter) that makes sure there's nothing left above 22.05 kHz. Depending on your hardware, it may start cutting at 20 kHz to achieve that (in which case, you'll likely lose the 22 kHz tone), as long as nothing's left above Nyquist frequency. Now for your example, it's quite possible to make a filter that would have its transition band between 22.01 and 22.05 kHz, in which case you'd get the signal correctly. In the case of a normal soundcard, trying to play a 22 kHz tone would probably result in no output at all.
jmvalin,
Have you read the rest of the thread?
Actually, just the rest of the post that you quoted will do - especially the part where a 22kHz tone comes out of a soundcard at only 5.71dB less than a 1kHz tone - that's hardly "no output at all". :;
Hope this doesn't sound harsh - I'm just trying to stop the thread discussion from looping back to the start!
And though it sounds like I think I know all the answers, I actually learn something more about this subject every time it comes around - so I'm not having this discussion with KikeG to say "I'm right, you're wrong" because I've learnt things from what he's said in the past. Just hads to put this bit because it's very easy to sound argumentative in typed things when you don't mean to be.
Cheers,
David.
Actually, just the rest of the post that you quoted will do - especially the part where a 22kHz tone comes out of a soundcard at only 5.71dB less than a 1kHz tone - that's hardly "no output at all". :;
Well, it has nothing to do with 44.1 kHz not being enough to sample a 21 sine wave. It just shows that the DAC's you analyzed aren't behaving the way a "standard DAC" ought to do. I'm guessing that they just didn't really bother filtering the exact way because you don't really hear above 20 kHz anyway. I don't think it's really worth discussing what each individual DAC does.
The main thing here is that people keep saying "Nyquist was wrong" when they're just completely mis-interpreting the sampling theorem. So far I've seen:
- I use linear interpolation between samples and it doesn't look like the original.
- My soundcard doesn't work with a 22.0499 kHz tone.
- I can sample a 1 MHz tone at 50 kHz and still get perfect reconstruction, Nyquist was wrong. (no you can just compensate the aliasing which is OK as long as you don't have other stuff in the baseband)
this is obviously cannot be a discussion whether nyquist was right or wrong. this discussion is basicly a 'theory vs. practice' discussion..
theory : nyquist wasn't wrong. the sampling function is a one-to-one function iff (if and only if) the sampling-rate is equal or higher than twice the bandwidth of the source signal. in this case (one-to-one), there exist an inverse function.
practice : implementing the inverse function (reconstruction filter) is a problem.
i wonder what's your opinion about an alternative approach :
process your digital signal through a digital upsampler from 44.1khz to 88.2khz (cs8420 (http://www-test.cirrus.com/en/products/pro/detail/P53.html), for instance, can do this directly on spdif traffic), and then use a lousy anti-aliasing reconstruction filter with cut-off frequency at 88.2khz.
edit : typo
i wonder what's your opinion about an alternative approach :
process your digital signal through a digital upsampler from 44.1khz to 88.2khz (cs8420 (http://www-test.cirrus.com/en/products/pro/detail/P53.html), for instance, can do this directly on spdif traffic), and then use a lousy anti-aliasing reconstruction filter with cut-off frequency at 88.2khz.
Well, of course you can get almost as close to the Nyquist limit you like by spending more on hardware. As for up-sampling, that's of course the logical thing to do, although you still need a sharp filter at 22 kHz. The only difference is that the filter can be implemented numerically, which is easier. In theory, you could have a transition band of only 1 Hz. The down side is that the (huge) filter would introduce a delay of several seconds.
Anyway, I still don't understand the point of this thread.
This thread deserves to be pinned one and for all times IMHO. What i do understand is that even the most intelligent experts here are slowly coming to the point where i have been at almost 5 years ago ( and i dont understadn at least half of what is said here, being a low-level electrical engineer with bad results in the DSP courses :
Its much easier to drop the old 16/44.1 standard and concentrate on 24/96 instead, to make sure we have a digital frontend that is superior to the human ear under all circumstances, instaed of discussing endlessly if maybe 16/44.1 iss good enough or not, and then tweaking the old standard with expensive equipment to make the best out of it.
F..ck ( censored ), any crappy DVD can hold up to 5 hours of 24/96 recorded Stereo music today, so whats the bloody point in defending the usage of 16/44.1 still ? The necessary ADC/DAC's to record in 24/96 are no miracles anymore, and for low cost equipment you simply downsample to 16/48 and the user of this unit will still be more than happy .....
The mere feeling of being on the safe side does justify the using of higher sampling rates already IMHO, especially with respect to the fact that its technically feasible today !! There is only one reason why DVD-Video with 24/96 has not found broad usage already, and that is because Chesky was the only one to release music on this standard, while Panasonic and SONY are still trying with huge amounts of money to push SACD and DVD-A .. sad but true .... every crappy DVD-player out there ( and there are billions already ) has to be able to play 24/96 audio tracks on DVD-Videos ( somehow ), that makes it even more sad ....
This thread deserves to be pinned one and for all times IMHO. What i do understand is that even the most intelligent experts here are slowly coming to the point where i have been at almost 5 years ago ( and i dont understadn at least half of what is said here, being a low-level electrical engineer with bad results in the DSP courses :
Its much easier to drop the old 16/44.1 standard and concentrate on 24/96 instead, to make sure we have a digital frontend that is superior to the human ear under all circumstances, instaed of discussing endlessly if maybe 16/44.1 iss good enough or not, and then tweaking the old standard with expensive equipment to make the best out of it.
F..ck ( censored ), any crappy DVD can hold up to 5 hours of 24/96 recorded Stereo music today, so whats the bloody point in defending the usage of 16/44.1 still ? The necessary ADC/DAC's to record in 24/96 are no miracles anymore, and for low cost equipment you simply downsample to 16/48 and the user of this unit will still be more than happy .....
The mere feeling of being on the safe side does justify the using of higher sampling rates already IMHO, especially with respect to the fact that its technically feasible today !! There is only one reason why DVD-Video with 24/96 has not found broad usage already, and that is because Chesky was the only one to release music on this standard, while Panasonic and SONY are still trying with huge amounts of money to push SACD and DVD-A .. sad but true .... every crappy DVD-player out there ( and there are billions already ) has to be able to play 24/96 audio tracks on DVD-Videos ( somehow ), that makes it even more sad ....
Hey, keep in mind that with Speex, I'm still trying to convince people to switch from 8 kHz to 16 kHz . My opinion is that 96/24 is overkill. While I agree that 44.1 kHz might not be enough (even then, I'm not completely sure), 48 kHz should be enough. It's not only a matter of storage but processing too. In many cases, processing at 96 kHZ is just 100% overhead. As for 24 bits, I think it's usful if you're going to do some processing, but just for playback, I don't think it makes much of a difference when taking into account compression (even at high bit-rate) and the rest of the sound system. I have yet to see a power amp (or even a 24-bit soundcard) with 144 dB SNR.
2Bdecided:
Ok, I must admit I've been trying to explain the wrong thing, and that didn't totally understand what this beating effect consisted of. What mislead me was Jan Meier suggestion of that this was an audible phenomena and for that reason, I assumed it happened below Nyquist frequency. My explanation holds true if you assume that signals above 20 KHz or 21 KHz are not audible. But, as you say:
This is the key to the problem. What you say here is true. "If we look at this very carefully, and if we only consider frequencies below the nyquist limit, then they have not been harmed or changed in anyway." That's true - but in saying it, you are incorporating a perfect low pass filter into your hypothetical viewpoint.
That's all true, from the point of view of the whole signal, there is distortion. But assuming that our "natural" lowpass filter will filter out all frequencies close to Nyquist frequency and above, it still holds.
If you have a real tone at 22kHz, and an image of that tone at 22.1kHz, the two will beat, won't they?
...
There you go - no analogue electronics involved, but a hiedous non-linear effect.
True. Doing a short-time analysis of the signal, as our ear does, in this case there would be obvious amplitude modulation.
OK - first, I'm not talking about intermodulation - I'm just talking about the presence of the image tones.
Now I see. For the reasons explained before I thought this was an intermodulation problem, so I just analyzed below Nyquist frequency.
this all goes back to the fact that I think having an image tone is a bad thing (despite it being above nyquist) whereas you don't.
The measurement data you have provided is very interesting. I have done some quick audibility tests based on the image rejection data, but with audible test tones of 15 KHz instead. According to those, assuming that we could hear above 20 KHz, this beating effect would be audible just near 22 KHz. At 21.5 KHz, the attenuation of the images is of around 15 dB, and 1.1 KHz over the original tone. In this case, my tests suggest (using 15 KHz plus 16.1 KHz "image" tone, both audible by themselves in my case) that the image tone wouldn't be audible, because the beating effect dissapears when the frequencies are distant enough, and because the image gets masked from the original tone.
At the time, I dumped these numbers into Excel and
I did these tests because of an AES paper by Richard Black (I think) who suggested that these image frequencies were a real problem. He doubted that we could hear them, but he pointed out that they are not harmonically related to anything within the true audio spectrum - hence any intermodulation caused by amplifiers or speakers could create some nasty inharmonic components within the audible range. I'm not sure the numbers add up to a huge problem for typical music, but he had a point - it is possible that there is an audible effect.
I think this could only be verified via blind tests. I think that over 16 KHz or so, many of the audible content of music is usually of percusive type (drums, cymbals, transients, etc) and of inharmonic content then, too. On the other side, this beating effect would happen just over, say, 21.5 KHz (being pesimistic), where usually ADCs start rolling off and there's less signal content recorded. I think very plausible the idea that intermodulation products due to high-frequency image signals would be small in comparison with the intermodulation effects on this non-harmonic percusive content over 16 KHz.
And though it sounds like I think I know all the answers, I actually learn something more about this subject every time it comes around - so I'm not having this discussion with KikeG to say "I'm right, you're wrong" because I've learnt things from what he's said in the past.
Thanks, I'm happy to have helped you on those occasions. That same thing has happened to me sometimes from you in the past too, and has happened in this this particular case.
While I agree that 44.1 kHz might not be enough (even then, I'm not completely sure), 48 kHz should be enough.
I still think that, given limitations of human hearing, 44.1 KHz is enough. Maybe for some 0.1% of young bat-eared people there could be a difference using a higher sampling rate, and just on critical material. But even in this case, the difference I believe would be very subtle. Still, I would only be convinced form a rigorous, repeatable, blind test.
KikeG,
Hey - I think we agree!
Cheers,
David.
While I agree that 44.1 kHz might not be enough (even then, I'm not completely sure), 48 kHz should be enough.
I still think that, given limitations of human hearing, 44.1 KHz is enough. Maybe for some 0.1% of young bat-eared people there could be a difference using a higher sampling rate, and just on critical material. But even in this case, the difference I believe would be very subtle. Still, I would only be convinced form a rigorous, repeatable, blind test.
Stumbling across this discussion, I just had to jump in on some of what's being discussed.
1. Filter ringing / Impulse response
Any filter, may it be analog (electronic), digital or even mechanical, will ring around fc. The steeper the filter, the longer the impulse resonse (ringing) will be. Symmetric filters (only realizable in the digital domain) will have even distribution of pre/post ringing, creating a flat phase response.
2. Audibility of filter steepness
As it has been stated in this thread, it should be impossible to hear filter ringing with fc beyond human hearing. This is INCORRECT. It might be tempting to think so. The human hearing cannot hear steady-state sines over 20kHz. This has been concluded in millions of hearing tests all over the world. However, when listening to impulse responses, we have to take into account what is analyzing these sounds. The human ear has its own set of filters, analysis windows. Analyze a long enough impulse response with an auditory model and you will find that these filters are indeed triggered. This is why we can hear steepness of filters even when fs=96kHz and fc=47kHz.
Cheers,
Martin Saleteg
N i n j a F X
I would love to sic my college digital signals and systems professor on whoever wrote this. (His nickname was 'the hurricane') He would tear this article to shreds. Complete bullshit.
As it has been stated in this thread, it should be impossible to hear filter ringing with fc beyond human hearing. This is INCORRECT. It might be tempting to think so. The human hearing cannot hear steady-state sines over 20kHz. This has been concluded in millions of hearing tests all over the world. However, when listening to impulse responses, we have to take into account what is analyzing these sounds. The human ear has its own set of filters, analysis windows. Analyze a long enough impulse response with an auditory model and you will find that these filters are indeed triggered. This is why we can hear steepness of filters even when fs=96kHz and fc=47kHz.
It sounds like you know what you're talking about - but this is theory. What we know about the ear (and brain) are just models, and these models are more or less close to reality but not perfect - otherwise it would be no problem samples in lossy codecs.
As you probably know it's a forum rule (http://www.hydrogenaudio.org/forums/index.php?showtopic=3974) (#8) here that claims need to be backed up with evidence. So could you please either provide links to double blind tests or give a suggestion how to create test signals that sound different after 20kHz lowpass?
I did not know about any forum rules,
however, I have been looking into this problem ever since trying to create a close-to-perfect LowPass filter for the use in a samplerate converter. I simply sat down listening to various filter steepnesses for 96kHz->48kHz and 96kHz->44.1kHz conversions, and I noticed there were quite remarkable differences in imaging and transient response.
I have looked all over for papers describing this particular phenomenon, but to no luck. The problem is real and does exist though. It is in fact rather obvious.
Explanations (bio-digital? (Thanks to Jim Johnston for this)
Consider a pre-echo of an impulse that is longer than the leading edge of the cochlear filter. This pre-echo will get the inner hair cells into detection mode. This starts the outer hair cells depolarizing and going into compression mode (by detuning basilar vs. tectoral membranes). When the center of signal arrives (a transient) instead of the full level, the compression has reduced the sensitivity of the system, so the central impulse does not sound as loud.
This is an example of non-linearities introduced by tiny amounts of pre-echo.
A small test to try:
When you (like the ear does) analyze a very short section of sound (say an impulse with filter ringing around 22kHz) the signal IS NOT as narrowband as you might think. Try making a short-term Fourier Transform of a sliding window on a standard AA or AI filter. Use the fastest cochlear filter length, about 400us, as the window length.
A real world test to try:
Create a windowed sinc FIR filter with a narrow transtition band, place fc at 22kHz. Use a very good 96kHz recording, preferrably surround or stereo, playing back through a set of very good converters and speakers. Then gradually increase steepness of filter (or easier, apply the filter several times) until you can hear a difference.
Hope this clarifies a bit?
Martin Saleteg
N i n j a F X
...
Hope this clarifies a bit?
Your explanation is clear to me.
What I'm sceptical about:
Consider a pre-echo of an impulse that is longer than the leading edge of the cochlear filter. This pre-echo will get the inner hair cells into detection mode.
Sine waves at 20kHz (reasonable volume) are inaudible, so why would pre-echo/ringing of this frequency cause what you've described?
Create a windowed sinc FIR filter with a narrow transtition band, place fc at 22kHz. Use a very good 96kHz recording, preferrably surround or stereo, playing back through a set of very good converters and speakers. Then gradually increase steepness of filter (or easier, apply the filter several times) until you can hear a difference.
I guess high resolution equipment (D/A convertor) is needed for this. - Do you think there's a way to test this with "ordinary" 48kHz soundcard (+ good headphones)?
Sine waves at 20kHz (reasonable volume) are inaudible, so why would pre-echo/ringing of this frequency cause what you've described?
I have never said anything about us being able to hear beyond 20kHz. I was never referring to steady state signals. As you probably know, transients are NOT steady state signals. And a transient can NEVER be of a single frequency alone. This would be mathematically impossible. You will find more frequencies depending on the length of the analysis window used.
So:
1. We are not talking about steady state signals.
2. We are not talking about linear systems.
I guess high resolution equipment (D/A convertor) is needed for this. - Do you think there's a way to test this with "ordinary" 48kHz soundcard (+ good headphones)?
I guess it depends on the quality of your reproduction chain. No, a Soundblaster won't do it.
He would tear this article to shreds.
What article are you talking about ?
I have never said anything about us being able to hear beyond 20kHz. I was never referring to steady state signals.
<snip>
I didn't say so. I'll try to clarify:
I know that transients don't consist of one frequency, nevertheless they can be transformed to frequency domain (and back).
Your claim was:
As it has been stated in this thread, it should be impossible to hear filter ringing with fc beyond human hearing. This is INCORRECT. It might be tempting to think so. The human hearing cannot hear steady-state sines over 20kHz.
If you lowpass a transient (e.g. silence with a single 1-sample click), pre- (and post-) ringing arround fc is introduced. Making the lowpass steeper causes
- the ringing to become louder
- the ringing to last longer
- the frequency range of ringing arround fc to become wider.
I've tried this with CoolEditPro. Even if silence with a single 1-sample click is lowpassed (using fft filter) at 20kHz with a lowpass width of only 6 Hz, the frequency range of ringing is between 19500 and 20500 Hz, so still out of audible range.
So why should adding a 19.5-20.5 kHz increasing + decreasing sound to a signal change the signal noticably if we can't hear the added sound itself at all?
...
This pre-echo will get the inner hair cells into detection mode. This starts the outer hair cells depolarizing and going into compression mode (by detuning basilar vs. tectoral membranes). When the center of signal arrives (a transient) instead of the full level, the compression has reduced the sensitivity of the system, so the central impulse does not sound as loud.
I understand your explanation about the ear very well as I'm studying medicine. It's clear and a known fact that it works like this if a pre-echo (or any "sound before a sound") is audible - but is there any proof that it works like this if the pre-ringing is in a conciously inaudible frequency range? Does the sound reach the inner hair cells at all - and, if yes, do they react? Any neurological measurements done on this you know of?
1. We are not talking about steady state signals.
Well, pre-/post-ringing is not stead state, but short "steady state with fadein and fadeout". Why should this cause a difference in perception?
Two ideas to ABX (double blind test) your claim using ordinary equipment:
1.
a ) Take a sample with strong transients (e.g. castanetts sample or something artificial - suggestions welcome) (resample it to 48kHz if necessary because of not-so-decent soundcard, using SSRC or other HQ resampler)
b ) Apply the steepest available lowpass (e.g. CoolEdit's FFT filter) at 16, 17, 18, 19, 20, ... kHz and ABX if there's an audible difference
c ) Take the highest ABXable lowpass (e.g. 18kHz) and apply a less steep lowpass to the original arround this frequency (e.g. 17.5-18.5kHz) and
d ) try to ABX against the steep lowpassed.
e ) Result: If d ) works your claim is most likely true for the tested frequency (e.g. 18kHz), otherwise not. - Comparing to the highest frequency one can hear might be interesting.
2.
a ) See 1.a )
b ) Add a loud increasing high frequency tone (or similar e.g. narrow band noise) before transients manually
c ) ABX
d ) Result: see 1.e )
Volunteers?
For god's sake, don't try 2b on speakers unless you really know what you're doing !
Udial.wav have already fried some tweeters around here
For god's sake, don't try 2b on speakers unless you really know what you're doing !
Udial.wav have already fried some tweeters around here
This is sound (no pun intended) advice. I fried a pair of tweeters in my PSBs while doing some high frequency testing about 6 months ago (Madisound gets honorable mention here for excellent and affordable replacement Vifa tweeters). The rule of thumb here is that the volume control is a dangerous weapon to your tweeters when auditioning full-scale sinewaves in the upper end of the audio spectrum.
Just because you can barely hear a high frequency tone does not mean that you aren't sending tweeter coil frying energy through your speaker cables. Exercise extreme caution with this kind of testing...
For god's sake, don't try 2b on speakers unless you really know what you're doing !
Udial.wav have already fried some tweeters around here
This is sound (no pun intended) advice. I fried a pair of tweeters in my PSBs while doing some high frequency testing about 6 months ago (Madisound gets honorable mention here for excellent and affordable replacement Vifa tweeters). The rule of thumb here is that the volume control is a dangerous weapon to your tweeters when auditioning full-scale sinewaves in the upper end of the audio spectrum.
Just because you can barely hear a high frequency tone does not mean that you aren't sending tweeter coil frying energy through your speaker cables. Exercise extreme caution with this kind of testing...
Good that you care about people here (and their equipment) ...
I didn't mean to create something like udial sample (high frequency 5x amplitude of audible tone) - rather like this:
- Audible signal with transient 1/2 * max. amplitude (+/- 32768)
- "Artificial pre-ringing" something like 1/10 - 1/4 * max. amplitude
- Duration of "artificial pre-ringing" (fadein) smaller than 1/2 second
I think 1. is more reallistic anyway - it's already exagerated ("Apply the steepest available lowpass" = much steeper than necessary)
I did a 1st try:
Test signal: 1-sample-clicks, ~ 10/second, created at 48kHz sampling rate
lowpassed at 20kHz using CEP FFT filter; lowpass width (100%-0%: 5.9 Hz)
ABX'ed 8/9 but then lost focus/control/luck and gave up at 9/12...
I guess I should start with something like 16kHz lowpass and increase step by step. I just thought a quick success couldn't do any harm as listening to this sample is no nice experience at all.
Don't forget to check the resulting signal at the sample level.
SoundForge 4.5 for example completely destroys the transient when applying a lowpass, it generates new transients at both ends of the impulse response, resulting in a triple transient. Its filters seem not to work properly.
I posted about this here, but it was so long ago that I don't know what to search for.
I know that transients don't consist of one frequency, nevertheless they can be transformed to frequency domain (and back).
And what happens when you do this transformation? (just like the ear does)
So why should adding a 19.5-20.5 kHz increasing + decreasing sound to a signal change the signal noticably if we can't hear the added sound itself at all? I've tried this with CoolEditPro. Even if silence with a single 1-sample click is lowpassed (using fft filter) at 20kHz with a lowpass width of only 6 Hz, the frequency range of ringing is between 19500 and 20500 Hz, so still out of audible range.
So you agree with me, that the ringing introduced when low-passing a transient is NOT steady.
The ear analyzes this NON-STEADY ringing signal. Again, what happens when you analyze a non-steady signal with a given window length?
You will find that the ear finds energy outside of the frequency of ringing. If energy is loud and long enough, this will (as I stated before) introduce non-linearities in the ear, in other words, your perception of the transient will be different.
Any neurological measurements done on this you know of?
I have searched for papers about this for a lnog time without finding any. I know there have been some less scientific experiments done on filter steepness (one of the tests by Tom Stockham I think) and the conclusion seem to be that at fs=50kHz it is possible to create a filter that will be shorter than the ears shortest analysis window.
Well, pre-/post-ringing is not stead state, but short "steady state with fadein and fadeout". Why should this cause a difference in perception?
If a signal per definition is not steady state, it cannot be treated as such.
If you're studyiong medicine perhaps this is a very good topic for some research :-) I know a bunch of people who would be glad to have this printed black on white.
Cheers,
Martin Saleteg
N i n j a F X
Oh, I also forgot... Don't try the tests with Soundblasters, Midiman Deltas or anything in that range... The conversion process will most probably mask all of the effects.
And perform the tests at 96kHz.
Samplerate converting the source signal is not a very good way to test it either, since the samplerate converter will add an anti-imaging filter in itself. Try using 96kHz sources.
And you don't necessarily have to listen to just transients. My experiments show that stereo imaging is what is first lost when pre-echos start appearing. (Since tiny transients is what define stereo image, they get blurred -> Stereo image gets less clear)
Martin Saleteg
N i n j a F X
Azeteq: if you are still around, some blind (ABX) tests would be good to support your claims, together with the source files and some information about the characteristics of the filter used.
About pre-ringing: it is not a steady signal, but it is a narrowband signal with frequency content just around fc. I thing it is doubtful whether this signal could be heard alone, and I think it is also doubtful it having an effect in perceivability of the posterior impulse. I can think of it having an audible effect just due to nonlinearities inside the ear producing audible components. I read a post from James Johnston (JJ) about the possibility of such effect being true, but I think it could be very subtle as much. Anyway, it's something that would need to be tested.
I don't see any problems with M-Audio cards performance at 96 KHz.
We are trying to set up a blind test in order to check some of these things, see http://www.hydrogenaudio.org/forums/index....topic=12920&hl= (http://www.hydrogenaudio.org/forums/index.php?showtopic=12920&hl=)
When you (like the ear does) analyze a very short section of sound (say an impulse with filter ringing around 22kHz) the signal IS NOT as narrowband as you might think. Try making a short-term Fourier Transform of a sliding window on a standard AA or AI filter. Use the fastest cochlear filter length, about 400us, as the window length.
According to some tests I just performed, I think there is some flaw in this explanation.
I have lowpassed a 96 KHz impulse with various ringing length passband FIR filters, leaving just frequencies between 19 KHz and 21 KHz, so that the result consists just of time-enveloped ringing at cutoff frequencies. I can't hear anything when listening to this ringing. Even when it is a non-steady signal, it does not have audible components.
I think we can't hear over 20 KHz, be it with steady signals or transient signals.
I couldn't use good equipment for this test, but still I can hear 16 KHz tones clearly with it, and up to 18 KHz, but very softly. I'll repeat this test with better equipment when I have time.
I also tried to ABX a 96 KHz impulse signal filtered with a long ringing 20 KHz lowpass FIR filter, from the unfiltered version. I couldn't. I used good equipment this time. This suggests that the effect, if existing, is very subtle as much.
When someone uses statements like this: "However, using music with a substantial share of upper frequencies (soprano, hobo, upper strings) one notices that the sounds gets less brittle and that the harshness at the treble has gone." to sell something, even engineering students ought to have their BS alarm go off. The fellow who wrote the article is selling snake oil. He goes on to say that the effect is very subtle. Translation: if you do not hear the difference you are a plunk. Sounds like the emperor has new clothes to me.
This kind of prose has accompanied hustles in the audio world for all of the time I have been in it, since 1956. As a general rule, if it sounds too good too be true, it is.
L8R B)
I have lowpassed a 96 KHz impulse with various ringing length passband FIR filters, leaving just frequencies between 19 KHz and 21 KHz, so that the result consists just of time-enveloped ringing at cutoff frequencies. I can't hear anything when listening to this ringing. Even when it is a non-steady signal, it does not have audible components.
I think we can't hear over 20 KHz, be it with steady signals or transient signals.
I couldn't use good equipment for this test, but still I can hear 16 KHz tones clearly with it, and up to 18 KHz, but very softly. I'll repeat this test with better equipment when I have time.
I also tried to ABX a 96 KHz impulse signal filtered with a long ringing 20 KHz lowpass FIR filter, from the unfiltered version. I couldn't. I used good equipment this time. This suggests that the effect, if existing, is very subtle as much.
I've done similar tests when Azeteg made his statements, no success as well.
Here (http://www.hydrogenaudio.org/forums/index.php?showtopic=12920&&st=16hl=) 2Bdecided has summarized what Azeteg tried to say in quite understandable words:
If I understand him correctly, the idea is that the cochlear amplifier (ie. the active process within the cochlea, which isn't fully understood I hasten to add!) does respond to HF sound that we can't actually hear when presented as a steady state tone. This response isn't to let us hear HF sound, but to trigger a change in the cochlea tuning and dynamic compression so that audible sounds are perceived differently.
So to test this, single-sample clicks probably won't help, as they contain much audible content that will trigger the cochlea tuning anyway. I'm trying to create some samples to test this right now ...
So to test this, single-sample clicks probably won't help, as they contain much audible content that will trigger the cochlea tuning anyway. I'm trying to create some samples to test this right now ...
Maybe I misunderstood, but I think the problem with using a pure impulse to test this is the opposite to what you suggest.
A filter will only pre-/post ring when there is energy in the signal somewhere around its cut-off frequency (at least).
We're trying to test if this ringing has an audible effect on the perception of other frequencies. So, we need those other frequencies to be present. i.e. using just 18-22kHz info is no good, because there's nothing else (very) audible for it to have an impact on.
Using just an impulse isn't very good either, because it's an uninteresting signal with which to judge if the sound has "changed".
I think it would be much better to use a very high quality recording (or a codec killer maybe - what would be a pre-ring or pre-echo killer?) and add lots of pre/post-ringing to that. That would be a good test.
I've tried it with the 2496 samples from the PCABX site, using an audiophile 2496, and HD580 headphones - no luck!
But, when I heard the advantage of 2496 over CD quality, it had nothing to do with HF response - see http://www.hydrogenaudio.org/forums/index....opic=9311&st=51 (http://www.hydrogenaudio.org/forums/index.php?showtopic=9311&st=51)
Cheers,
David.
We're trying to test if this ringing has an audible effect on the perception of other frequencies. So, we need those other frequencies to be present. i.e. using just 18-22kHz info is no good, because there's nothing else (very) audible for it to have an impact on.
Yes, here I was just addresing what he said about non-steady tones having a higher bandwidth using short-time analysis, and then supposedly being possibly audible.
Using just an impulse isn't very good either, because it's an uninteresting signal with which to judge if the sound has "changed".
It depends. Naoki's superEQ has pre-ringing issues that are hard to detect using actual music, but easy to detect using an impulse signal. The potentially audible mechanism here is different, but on the other side I think that music that has transients with strong content exactly at filter cutoff (somewhere from 20 KHz to 22 KHz) is not that easy to find.
Let me try to explain more understandably:
Simplified the cochlear amplifier (CA) works like an compressor, the only difference is that it can't look ahead and it needs some time to react/adjust. So if there's a signal (consciously audible or not) that triggers CA, it takes some time until the perception of the signal afterwards is changed.
So single-click transients
a ) are probably too short to change the perception of themselves by triggering CA
b ) trigger CA by their content in audible frequency range. If >20kHz content is changed e.g. by lowpassing, adding pre-ringing etc., there won't be much "extra-trigger" caused by this.
Additionally Azeteg's claim should lead to this: Not only pre-ringing introduced by lowpassing could trigger/change CA, also the loss of high frequency content due to lowpassing could do this. So a test signal should be designed like this:
Some sublte, quiet sounds and immediately before (several miliseconds) much high frequency content, most of it in inaudible range (or arround lowpass frequency).
But looking for strong or loud sounds around the cut-off frequency is surely wrong - it's good enough that there's some sounds around this frequency - as is typical of most music.
Surely the hypothesis isn't that "certain signals with sharp transients and/or lots of ultrasonic information are affected by this", it's that "most music is affected by this". That's the bold claim that seems to have been made - isn't that what we should test?
Cheers,
David.
But looking for strong or loud sounds around the cut-off frequency is surely wrong - it's good enough that there's some sounds around this frequency - as is typical of most music.
Surely the hypothesis isn't that "certain signals with sharp transients and/or lots of ultrasonic information are affected by this", it's that "most music is affected by this". That's the bold claim that seems to have been made - isn't that what we should test?
IMO 1st we would need a proof (at least 1 successfully abxed sample) that this exists at all (or not). Testing with normal music should be a 2nd step if the 1st was successful (using samples especially created for this).
Here (http://www.hydrogenaudio.org/forums/index.php?act=ST&f=35&t=13054)'s a sample. My soundcard is just too crappy to be useful for testing this. high frequencies cause bumping background noise. I have to tweak the settings or try some other soundcards, I guess.
Something I just found about audibility of ultra-high frequencies:
From http://groups.google.com/groups?hl=es&lr=&...a%2Ben%2BGoogle (http://groups.google.com/groups?hl=es&lr=&ie=UTF-8&threadm=Pmb7b.395282%24YN5.262549%40sccrnsc01&rnum=4&prev=/groups%3Fq%3Dof%2Bauthor%253Aarny%26ie%3DISO-8859-1%26hl%3Des%26btnG%3DB%25FAsqueda%2Ben%2BGoogle)
From an AES lecture from David Griesinger:
"Adding ultrasonics to a recording technique does NOT improve time
resolution of typical signals â?? either for imaging or precision of
tempo. The presumption that it does is based on a misunderstanding of
both information theory and human physiology.
Karou and Shogo have shown that ultrasonic harmonics of a 2kHz signal
are NOT audible in the absence of external (non-human) intermodulation
distortion.
Their experiments put a limit on the possibility that a physiological
non-linearity can make ultrasonic harmonics perceptible. They find
that such a non-linearity does not exist at ultrasonic sound pressure
levels below 80dB.
All commercial recordings tested by the author as of 6/1/03 contained
either no ultrasonic information, or ultrasonic harmonics at levels
more than 40dB below the fundamentals.
Our experiments suggest that the most important source of audible
intermodulation for ultrasonics is the electronics, not in the
transducers.
Some consumer grade equipment makes a tacit admission of the
inaudibility of frequencies above 22kHz by simply not reproducing
them. Yet the advertising for these products claims the benefits of
â??higher resolution.â?
Even assuming ultrasonics are audible, loudspeaker directivity creates
an unusually tiny sweet spot, both horizontally and vertically."
More at http://world.std.com/~griesngr/ (http://world.std.com/~griesngr/) , at the end.
The lecture is available at http://world.std.com/~griesngr/intermod.ppt (http://world.std.com/~griesngr/intermod.ppt)
Among other interesting things, it says and gives some examples of how most DVD-A and SACD the writer tested were just resampled from a 48 KHz master. In other words, they had no content at all over 22-24 KHz. And of the few he found had content over 48 KHz, it was in quite small amounts (40 dB below the fundamental, as much). It also shows ultrasonic noise characteristic of SACD, but somewhat surprisingly, just in one of the SACD disks tested.There are some spectrum graphs showing all this.
Also, it says that high directivity of speakers at ultrasonic frequencies, together with high attenuation of those frequencies along the way to the inner ear, makes reception of those signals possible just at a very small spot at the listening location.
There are many other explanations and test results over intermodulation, hearing internal working and such.
I know I'm attracting flamage here, but in trying to establish exactly what is "good enough", we have to remember that the process of audio-quality refinement will inevitably reach further into the realm of intangibles. There are perceptible differences, noticeable differences, and obvious differences. Obvious differences are the ones we can talk about with any degree of confidence, e.g. "wow, that 128kbit CBR file really does ring!". Noticeable differences are those we might not be able to put into words but that still affect our appreciation of the sound's quality. There are still perceptible differences that we may not be entirely conscious of, and it's this region we're starting to stray into by comparing CD-audio with DVD-A, SACD, or even the original analog signal. The sad truth is that it's almost unavoidable that differences must exist that are not justifiable within our current, limited models of the ear and its interaction with sound. The fact that serious audio enthusiasts (and I mean that in the best possible sense ) are still today talking in terms of absolute frequency/tone response when discussing human hearing shows exactly how limited our knowledge is.
We must refrain from pooh-poohing the notion that the ear is nonlinear, because to date there is simply no good reason to suppose that our models are complete. The ear is a living subsystem, and the most essential defining feature of living systems is that their responses are nonlinear!
To summarise: just because you haven't discovered the mechanism yet, it doesn't mean it 's not there.
just because you haven't discovered the mechanism yet, it doesn't mean it 's not there.
Yes, but it means that it it doesn't affect us.
There is a difference between a fact for which we don't know the explanation, and the absence of fact ! This board's Terms of Service are strict :
8. Any statement about sound quality must be supported by the author responsible for such statements by a double blind listening test demonstrating that he can hear a difference.
This way, we have a fact to begin with, then, we can search an explanation. Without blind test results, we consider that we have no fact to explain.
For DVD-A or SACD quality, we are currently gathering facts, but they are difficult to reproduce in order to confirm them : the japanese Oohashi et al. experiment, and Listen's results (http://www.hydrogenaudio.org/forums/index.php?showtopic=17118&).
Griesinger's experiment, that Nika Aldrich and I have confirmed, doesn't necesseraly dismiss them, because we listen for intermodulation between continuous tones, while in Oohashi et al.'s experiment, the recording used was a gamelan's recording, that is a kind of metallophone. The negative result in Griesinger's experiment is that if a 90 dB (for example) ultrasound doesn't intermodulate, then the 50 dB harmonic of a music instrument certainly won't.
But we forgot that this 50 dB measured value is an average value, while the gamelan has high frequency content mostly on attacks, thus, since the high frequency content is present only for very short times, its level must be very high in order to give a 50 dB level after averaging.
In order to get the instant level, the frequency analysis should be done with the shortest possible FFT window, so as to see how loud the ultrasounds can get, compared to the other frequencies present at the same time. As long as the FFT window is longer than the attack duration, the instant level of some high frequencies may be higher than measured, if they are shorter.