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44 KHz (CD) not enough !? (Nyquist etc.), plethora of distortion frequencies?
zephirus
post May 11 2003, 17:40
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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:

____________

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 donīt have a 96 KHz soundcard. But the example with 11024 Hz surely looks rather disturbing (when looking at the waveform) and doesnīt 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 (itīs 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
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zephirus
post May 20 2003, 17:44
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QUOTE (2Bdecided @ May 19 2003 - 07:02 AM)
QUOTE (zephirus @ May 17 2003 - 04:37 PM)

QUOTE (KikeG @ May 14 2003 - 05:04 AM)

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! wink.gif 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).

QUOTE
QUOTE

I compared the Cool Edit upsampling algorithm with several of itīs 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.

QUOTE
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.

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

I better agree here smile.gif

zephirus

This post has been edited by zephirus: May 20 2003, 18:54
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Posts in this topic
- zephirus   44 KHz (CD) not enough !? (Nyquist etc.)   May 11 2003, 17:40
- - tigre   44.1KHz is enough to represent everything below 22...   May 11 2003, 22:59
- - mrosscook   The most recent thread to flog this issue is here....   May 12 2003, 04:32
- - 2Bdecided   QUOTE (zephirus @ May 11 2003 - 04:40 PM)I ha...   May 12 2003, 12:08
- - zephirus   QUOTE (tigre @ May 11 2003 - 01:59 PM)The add...   May 12 2003, 13:07
- - zephirus   QUOTE (mrosscook @ May 11 2003 - 07:32 PM)The...   May 12 2003, 13:14
- - KikeG   QUOTE (zephirus @ May 12 2003 - 01:07 PM)Iīm ...   May 12 2003, 13:33
- - tigre   QUOTE (zephirus @ May 12 2003 - 04:07 AM)......   May 12 2003, 14:16
- - zephirus   QUOTE (KikeG @ May 12 2003 - 04:33 AM)QUOTE (...   May 12 2003, 14:23
- - zephirus   QUOTE (tigre @ May 12 2003 - 05:16 AM)OK. Fin...   May 12 2003, 17:12
- - zephirus   QUOTE (2Bdecided @ May 12 2003 - 03:08 AM)QUO...   May 12 2003, 18:22
- - zephirus   While my original dubious claims obviously had a v...   May 12 2003, 20:54
- - _Shorty   I thought that's what over-sampling DACs were ...   May 12 2003, 21:42
- - zephirus   QUOTE (_Shorty @ May 12 2003 - 12:42 PM)I tho...   May 12 2003, 22:39
- - Doctor   An oversampling DAC still needs to lowpass the sig...   May 12 2003, 22:54
- - Doctor   The distortions you believe in are probably either...   May 12 2003, 22:57
- - KikeG   QUOTE (zephirus @ May 12 2003 - 08:54 PM)The ...   May 13 2003, 07:54
- - Canar   QUOTE (KikeG @ May 12 2003 - 04:33 AM)If you ...   May 13 2003, 08:10
- - tigre   To approximate the waveform between two samples S[...   May 13 2003, 11:15
- - 2Bdecided   zephirus, You were right about the 1kHz tone in th...   May 13 2003, 11:24
- - tigre   Nice link you provided, 2Bdecided. So it seems li...   May 13 2003, 11:42
- - Canar   QUOTE (2Bdecided @ May 13 2003 - 02:24 AM)Can...   May 14 2003, 07:35
- - zephirus   Doctor, KikeG: Thanks for your explanations! ...   May 14 2003, 12:23
- - SikkeK   I think your snippet has alot of frequence compone...   May 14 2003, 12:36
- - DonP   QUOTE (zephirus @ May 14 2003 - 06:23 AM)The ...   May 14 2003, 13:00
- - morelli   it's all too complex for me to understand. but...   May 14 2003, 13:06
- - zephirus   QUOTE (SikkeK @ May 14 2003 - 03:36 AM)I thin...   May 14 2003, 13:39
- - 2Bdecided   Someone do a search. I'm too lazy. But I'v...   May 14 2003, 13:40
- - KikeG   From zephirus: QUOTE A continuous signal of 21800 ...   May 14 2003, 14:04
- - DonP   For an example of this frequency vs time resolutio...   May 14 2003, 14:26
- - zephirus   QUOTE (DonP @ May 14 2003 - 04:00 AM)A pure s...   May 14 2003, 14:40
- - mrosscook   Zephirus, Harry Nyquist formulated his sampling t...   May 14 2003, 15:07
- - DonP   QUOTE (zephirus @ May 14 2003 - 08:40 AM)...   May 14 2003, 15:21
- - budgie   QUOTE (mrosscook @ May 14 2003 - 06:07 AM)I...   May 14 2003, 16:07
- - zephirus   QUOTE (2Bdecided @ May 14 2003 - 04:40 AM)Aft...   May 14 2003, 18:07
- - ye110man   QUOTE (DonP @ May 14 2003 - 06:21 AM)The Nyqu...   May 14 2003, 21:46
- - DonP   QUOTE (ye110man @ May 14 2003 - 03:46 PM)i th...   May 14 2003, 22:22
- - KikeG   QUOTE (budgie @ May 14 2003 - 04:07 PM)20 bit...   May 15 2003, 00:03
- - budgie   QUOTE (KikeG @ May 14 2003 - 03:03 PM)I don...   May 15 2003, 08:51
- - dillee1   Prove of Nyquist theory always use stationary sign...   May 17 2003, 10:44
- - DonP   QUOTE (dillee1 @ May 17 2003 - 04:44 AM)Prove...   May 17 2003, 13:11
- - zephirus   QUOTE (KikeG @ May 14 2003 - 05:04 AM)This sn...   May 17 2003, 17:37
- - zephirus   QUOTE (mrosscook @ May 14 2003 - 06:07 AM)Har...   May 19 2003, 15:05
- - KikeG   If I could have access to some 24/96 music in wav ...   May 19 2003, 15:48
- - budgie   QUOTE (zephirus @ May 19 2003 - 06:05 AM)A ma...   May 19 2003, 15:58
- - 2Bdecided   QUOTE (zephirus @ May 17 2003 - 04:37 PM)QUOT...   May 19 2003, 16:02
- - KikeG   QUOTE (2Bdecided @ May 19 2003 - 04:02 PM)If ...   May 19 2003, 16:39
- - Pio2001   QUOTE (KikeG @ May 19 2003 - 06:39 PM)I have ...   May 19 2003, 20:00
- - Pio2001   QUOTE (zephirus @ May 19 2003 - 05:05 PM)The ...   May 19 2003, 20:16
- - budgie   QUOTE (2Bdecided @ May 19 2003 - 07:02 AM)P.S...   May 20 2003, 11:12
- - 2Bdecided   QUOTE (budgie @ May 20 2003 - 10:12 AM)You ca...   May 20 2003, 17:34
- - 2Bdecided   QUOTE (KikeG @ May 19 2003 - 03:39 PM)I don...   May 20 2003, 17:35
- - zephirus   QUOTE (2Bdecided @ May 19 2003 - 07:02 AM)QUO...   May 20 2003, 17:44
- - zephirus   QUOTE (KikeG @ May 19 2003 - 06:48 AM)If I co...   May 20 2003, 21:48
- - mrosscook   @2Bdecided -- You mentioned in your post that you ...   May 21 2003, 00:04
- - budgie   2Bdecided: Nice post, but it proves nothing, sad ...   May 21 2003, 08:33
- - KikeG   David (2Bdecided): I find your report interesting...   May 21 2003, 10:18
- - 2Bdecided   budgie, I agree that this has no relevance in the...   May 21 2003, 10:24
- - KikeG   QUOTE (zephirus @ May 20 2003 - 09:48 PM)The ...   May 21 2003, 10:25
- - 2Bdecided   QUOTE (mrosscook @ May 20 2003 - 11:04 PM)@2B...   May 21 2003, 10:34
- - 2Bdecided   QUOTE (KikeG @ May 21 2003 - 09:18 AM)David (...   May 21 2003, 11:02
- - KikeG   QUOTE (2Bdecided @ May 21 2003 - 10:34 AM)As ...   May 21 2003, 11:13
- - KikeG   QUOTE (2Bdecided @ May 21 2003 - 11:02 AM)Whi...   May 21 2003, 11:20
- - 2Bdecided   QUOTE (KikeG @ May 21 2003 - 10:13 AM)Then, a...   May 21 2003, 11:30
- - mrosscook   2Bdecided, Do you recall whether the setup of Demo...   May 21 2003, 15:15
- - DickD   With 24-bit there's enough thermal noise in th...   May 21 2003, 19:45
- - DonP   QUOTE (2Bdecided @ May 21 2003 - 05:30 AM)Now...   May 21 2003, 20:36
- - Pio2001   QUOTE (KikeG @ May 21 2003 - 01:13 PM)Also, I...   May 21 2003, 22:07
- - budgie   QUOTE (2Bdecided @ May 21 2003 - 01:24 AM)Tot...   May 22 2003, 09:09
- - towolf   QUOTE (Pio2001 @ May 21 2003 - 11:07 PM)There...   May 24 2003, 00:43
- - KikeG   QUOTE (Pio2001 @ May 21 2003 - 10:07 PM)There...   May 24 2003, 12:54


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