From: MATGBB@LURE.LATROBE.EDU.AU (BYRNES,Graham)
Newsgroups: rec.audio.high-end
Subject: Re: Digital processing of sound
Date: Mon, 16 Nov 1992 01:23:45 GMT
Organization: La Trobe University
	id AB03036; Mon, 16 Nov 1992 12:24:12 +1100 (from news@lugb.latrobe.edu.au)
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In <1drc7hINNl9q@uwm.edu> wood@uk.tele.nokia.fi writes:
[cut ...]

> I think we all agree that digital audio only works at all because a brick
> wall filter is inserted at around 22kHz in the recording process.  This is
> necessary for Nyquist's results to be valid.  Therefore no frequencies above
> this can possibly be recorded.  No problem, say the proponents, you can't
> hear above this frequency anyway.
> 
> However, we may be able to show that the process of filtering at 22kHz can
> inject substantial noise and distortion back down into the audio band.
> Consider a tone of 20kHz, being amplitude modulated at 7kHz.  This might be a
> _very_ simple representation of a cymbal.  Ignoring the time domain, the
> spectrum of this signal (a 20kHz tone regularly varying in amplitude) will
> consist of three spikes - one at 20kHz, where we would expect, and one at
> each of 20kHz +/- 7kHz, ie 13kHz and 27kHz.
> 
Yes, exactly! The ORIGINAL signal has a spectral component at 13kHz.

> In the ordinary course of events, playing back these three signals will
> result in the original signal. This happens in the human sensing mechanism,
> because the body is still sensitive to the 27kHz tone,
Is it? I think this debate has been run before, with the people who have done
the experiment saying quite strongly that the body is NOT sensitive to 27kHz.

 it combines all three
> and we 'hear' the original cymbal.
> 
> However, pass this signal through a brick wall filter at 22kHz, and we now
> have only two tones, one at 20kHz and one at 13kHz.  No matter how well these
> are then reproduced by the playing equipment, there is no 27kHz sideband to
> combine with the 13kHz sideband to modulate the 20kHz carrier.  The result is
> a distorted version of the original 20kHz tone, and a new and completely
> unrelated 13kHz tone that wasn't in the original signal!
You said above that it was in the original signal. Please revise your Fourier
theory: A modulated tone is precisely the same thing as the central tone
and the two sidebands, otherwise AM radio wouldn't work! So the cymbal in fact
produced 3 tones, one of which we cant hear. When recorded digitally, the one
we cant hear is not present. Talking about AM is just using the wrong
analytical tools for the problem and confusing the issue.
> 
> Proponents of Nyquist (but who haven't studied his work) will say that his
> theorem states that all signals up to half the sampling frequency can be
> reproduced. This is precisely what's happening in this case, but the
> information content of the signals below half the sampling frequency is being
> eroded, and noise is being added.

No. The noise added is a result of the discretisation, not the sampling rate.
Remember these are separate issues... if it were possible to sample with
infinite precision, there would be no extra noise in the pass band.

I presume from your put-down that you have studied Nyquist's work. So please
tell me where he says there will be erosion of the information content in
band? Exact reconstruction of the signal means just that: exact reconstruction.
It is a mathematical theorem, not a matter of opinion, so unless you can find
fault with the maths, I think you are obliged to accept it
> 
> It is this injection of noise back into the audio band that is subjectively
> the most objectionable component of digital sound.
Well, perhaps it is, but it is not as bad as your erroneous example above
suggests: The noise is down around the digital noise floor, ie -96dB,
which is much lower than the surface noise on a record. What I think you are
trying to get at is that the spectral nature of the noise is important.
A very low level tone is percievable, but white noise at the same level
is more acceptable (more analogue?) but here I'm heading into hear-say,
so I'll leave it alone. 

My opinion, for what it is worth, is that it is the LACK of noise in digital
that offends people, because it leaves lots of things to be heard which
are inaudible not only in analogue recordings, but often in live performance
(especially if you are at the back of the hall). So what do tube amps put back?
Thermal noise....
                 Amiably yours (please!)
                  Graham