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From: sullivan@harvard.ARPA (John Sullivan)
Newsgroups: net.audio
Subject: Re: Oversampling techniques
Message-ID: <164@harvard.ARPA>
Date: Wed, 21-Nov-84 11:07:19 EST
Article-I.D.: harvard.164
Posted: Wed Nov 21 11:07:19 1984
Date-Received: Fri, 23-Nov-84 03:09:27 EST
References: <645@watdcsu.UUCP>
Organization: Aiken Computation Laboratory, Harvard
Lines: 30

My understanding of oversampling is that they do a linear interpolation
between successive samples on the disk.  The general idea is to thereby
have digital filtering instead of analog filtering, and get better phase
relationships at high frequencies.

As has been discussed before, at some point you have to filter out frequencies
above 22kHz.  If this is done with a simple analog cut-off filter, the phases
of frequencies around 20kHz get changed a lot.  If you put in a square wave
signal, you have to get some kind of ringing, but with this simple filter
it will be asymmetric--at the rising edge, the output is flat until the
input goes high, and then it rings quite a bit.  This is basically because
the filter cannot anticipate the change that is about to occur.  A perfect
22kHz cutoff filter that did not change phases would have symmetric output.
Look in any book on Fourier series for sample pictures of partial sums of
the series for a square wave.  This waveform has the same frequency components
as the one from the analog filter, but the high frequency's phases haven't
been shifted.

The digital filter (or oversampling) essentially can anticipate changes,
because it looks at the n+1st input before giving you the interpolated values
between n and n+1.  Given a square wave, it will output a square wave with
sloped edges.  This will then still need analog filtering, but that is less
severe, and has less effect on the phases.

I have not read details of the methods actually used--this is just what
I guess they must be doing.  If anyone has more information, please let me
know.

	John M. Sullivan
	{ihnp4,allegra,decvax}!harvard!sullivan