44 KHz (CD) not enough !? (Nyquist etc.), plethora of distortion frequencies? Options

[zephirus]

Remarks and conclusions added May 12 2003 - 1:55 PM, and edited May 14 2003 - 08:35 AM :

My dubious claims unfortunately had a very short life span due to the very successful enlightenment efforts of tigre, 2Bdecided, KikeG and mrosscook.

In short: I failed to come up with evidence that cd quality (I mean 44.1 KHz digital sampling) is somehow problematic. It basically was a story of using the wrong tools, jumping to the wrong conclusions, and not having enough of a clue about signal processing.

Nevertheless, I tried again to make less daunting claims that the 44.1 KHz digital sampling rate is not enough to represent all signals less than 22.05 KHz correctly.

And again my claims had a very short life span. This time due to further enlightenment efforts by DonP, 2Bdecided, KikeG, mrosscook and SikkeK.

The conclusion: Arguing against the technical specification of cd quality (44.1 KHz/16 bit) should not be tried by someone that severely lacks in signal processing clue (like me).

If the cd sound quality is perceived as suboptimal, it may have more to do with poor recording, poor mastering, and suboptimal reproduction equipment (i.e. cd-player and sound system/headphones).

What one still could try are listening tests:

Such tests would need to be done with one and the same high end hardware for all signals and all tests (preferably with 192 KHz resolution, with 20-24 bit, and with a DAC that is perfectly shielded and outside of any system that is rich of EM signals, like a computer, and has a near perfect analog circuitry). And when testing the 192 KHz signal against the 44.1 KHz signal, the latter would need to be a digitally downsampled version (to 44.1 KHz), which was upsampled to 192 KHz again. Using the best available algorithms (Cool Edit may do a resonable job here).

And still, asking the test persons for audible artifacts would most likely not work at all. It might be more rewarding letting them rate how the music "felt" (e.g.: more or less "relaxing" for music that should be "relaxing" but is rich in high frequency content nonetheless). This could be done in a way that is scientifically sound and statistically relevant.

My original post:
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I have to admit: This 44.1 KHz topic more or less has been discussed to death already. It also seems likely that the following problem has been discussed on Hydrogenaudio several times as well (but I had no luck with the search function).

The 44.1 KHz sampling rate (CD quality) seems to create an infinite number of "mirrors" at its harmonics. These in turn create a complex set of distortion frequencies for every frequency in the analog source.

The strongest "mirror" is at at 22.05 KHz (44.1 KHz/2). But the problem can easily be demonstrated with the one at 11025 Hz (44.1 KHz/4) as well: if one creates a sine signal of 11025-1000 = 10025 Hz in a sound editor (e.g. Audacity, using a 44.1 KHz sampling rate) and plots the spectrum, then two additional frequencies are shown: one at 1000 Hz and one at 22050-1000 = 21050 Hz. More distortion signals can be seen if the FFT resolution is increased above 1024.

The general problem seems to be that a sampling frequency of 44.1 KHz does not guarantee that frequencies below 22.05 KHz are represented faithfully (as is mostly believed). Instead it probably more or less only guarantees that in the resulting complex signal the source frequency is significantly stronger than the numerous distortion signals.

Of course, the remaining question is if these distortions are audible (they resemble pretty much amplitude modulation). I cannot really test this with 44.1 KHz since I don´t have a 96 KHz soundcard. But the example with 11024 Hz surely looks rather disturbing (when looking at the waveform) and doesn´t sound very clean as well.

Did anyone do any respective (blind) listening tests?

zephirus

PS:
The following example is very audible: When using a sampling frequency of only 2000 Hz (instead of 44100 Hz) and creating a sine frequency of 750 Hz (well below the Nyquist limit of 1000 Hz) then the result sounds pretty ugly (it´s some kind of mixed signal of 750 Hz, 250 Hz and 1250 Hz).

This post has been edited by zephirus: May 19 2003, 15:49

[zephirus]

This snippet has an only, non-ambiguous, interpretation, given that it doesn't contain any frequencies over 22050 Hz ...

It believe it does contain frequencies above 22050 Hz since I did not obtain it by properly downfiltering it (from e.g. 192 KHz). But instead by fiddling with Cool Edit in the 44.1 KHz domain.

Doh! we were doing so well! If it's sampled at 44.1kHz, it doesn't contain anything unique above 22.05kHz. Anything above this is a copy of what's below it. And anything below it that you intended to be above it, isn't!

Yes, exactly! I may have an explanation for this: Above 22.05 KHz there are no unique frequencies (as you pointed out earlier, these are mirrored and copied from below 22.05 KHz), but of course they are frequencies nonetheless. This way one can indeed represent frequencies above 22.05 KHz with a sampling frequency of 44.1 KHz. But only for the price of adding the respective (mirrored/copied) distortion frequencies below 22.05 KHz as well. And only if no filtering in the recording step is done (brickwall at 20 KHz).

I compared the Cool Edit upsampling algorithm with several of it´s filtering algorithms. I found: Doing the silence fiddling in the 192 KHz domain and then filtering out anything above 22050 Hz looks much better than doing that fiddling in the 44.1 KHz domain and then upsampling it.

There shouldn't be any difference. (...) But you should be able to get a very similar result in CEP with the right filter. Really!

Perhaps the "implicit" frequencies above 22.05 Khz (see above) help the Cool Edit filters here. But this is not relevant anyways.

P.S. CD "sound" (if there is one) is glassy, and less realistic than 24/96. This is what I heard with professional DCS convertors, comparing A>D>A at 44.1kHz and 96kHz (both 24-bits, so both are actually better than CD) with the original analogue signal. (...) I can quite believe record producers who use this equipment everyday (and who hear live music every day) when they say that, to them, the difference is significant.

One could argue that the problem here lies in the (perhaps analog part) of the A/D or D/A circuitry. And that the different sound may have nothing to do with the digital representation in principle.
What I do remember is that some people complained that stradivaris do not reproduce too well. But unfortunately this all is "anecdotic" evidence, and therefore not really scientific evidence.

But almost all of the faults I hear with CDs at home are almost certainly the fault of bad mastering.

I better agree here

zephirus

This post has been edited by zephirus: May 20 2003, 18:54