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From: newton2@ucbtopaz.CC.Berkeley.ARPA
Newsgroups: net.audio
Subject: Re: CD Reflections - 44.1k?
Message-ID: <651@ucbtopaz.CC.Berkeley.ARPA>
Date: Thu, 17-Jan-85 13:35:42 EST
Article-I.D.: ucbtopaz.651
Posted: Thu Jan 17 13:35:42 1985
Date-Received: Sun, 20-Jan-85 01:48:17 EST
References: <15100001@hpfcmp.UUCP> <3411@mit-eddie.UUCP> <1420@hplabs.UUCP>, <755@clyde.UUCP>
Organization: Univ. of Calif., Berkeley CA USA
Lines: 32

Here's a way to think about how the sampling theorem works, without needing to believe that "eventually" you need to sample a continuous repetitive waveform
"everywhere" to be sure you get its peak amplitude. Actually, two ways:

First, disabuse yourself of the notion that because music is transient-ridden
or is characterized by an envelope that modulates (multiplies) a steady-state
excitation, that therefore this implies the need for infinite bandwidth in
a digital audio system. Yes, an impulse or discontinuous sinewave has a 
continuous spectrum that is not bandlimited, *but* the *premise* of the
sampling theorem is that the signal is bandlimited to <1-2X the sampling rate.
Thus, even if  the acoustic signal is a spectral smear with non-zero 
magnitude in the nuclear phonon realm, *assume* that no significant 
components are present at more than <1-2X the sample rate. In practice, we
use a big bad low-pass filter to attenuate such out-of-band signals
sufficiently so the aliases resulting from their presence are less than
an arbitrarily-decided bound.

Second, even assuming continuous sinewaves, the system doesn't have to wait
until it's tasted every chunk of a sinewave to know what frequency and
magnitude it represents- this is the role of the complementary anti-imaging
filter, which outputs, for example, a damped sinewave when excited by
a pulse, or a continuous sinewave when excited by a pulse train, and
selects only the first of the repeated ensemple of imaged spectra implied by 
discrete or stepwise output of the D/A.
The real answer to nagging uncertainties about the propriety of hacking up
the silken-smooth continuity of music is to settle on a bandwidth that is
acceptable and then hack away; everything will bne provably copacetic
*within those agreed-upon constraints*. It's not fair to keep coming back
and claiming that things fall through cracks that never troubled anyone
when we depended on even narrower-band media before digital.

Regards, 
Doug Maisel