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From: gs@mit-eddie.UUCP (Gordon Strong)
Newsgroups: net.audio
Subject: Re: CD Reflections
Message-ID: <3411@mit-eddie.UUCP>
Date: Sat, 12-Jan-85 03:25:34 EST
Article-I.D.: mit-eddi.3411
Posted: Sat Jan 12 03:25:34 1985
Date-Received: Sun, 13-Jan-85 07:08:56 EST
References: <15100001@hpfcmp.UUCP>
Organization: MIT, Cambridge, MA
Lines: 26
Re: a 2x sampling rate is not good enough to reconstruct a sine wave.

I'm afraid it is.  The 2x rate is called the Nyquist Rate and is
the minimum sampling rate necessary to prevent aliasing.  It has
been proven rigorously that any waveform sampled at or above twice
the highest frequency can be reconstructed.  This is part of the
sampling theorem and is the basis of much of modern communication
theory.  Since this is the accepted minimum, it is not the same
2x rate that is usually referred to in the CD literature.  The
highest audio frequencies are 22.1KHz, so the sampling rate must
be 44.2KHz.  When CD manufacturers refer to a sampling rate of 2x,
they usually mean 88.4KHz (that's what Yamaha says for my CD-2).

The use of a higher sampling rate (oversampling) is used
so that the low pass filter used to reconstruct the original 
waveform need not have a severe slope in the transition band.
The claim is that a gentler slope reduces phase and group delay
effects.  For those that care, the CD-2 using 2x oversampling
requires a 7th order filter to reconstruct the signal.  That's
still a bit steep for some.  Several manufacturers offer CD
players that use 4x oversampling.  I haven't heard of any that
use anything higher.  I don't know if anyone has anything in
the works or even what the theoretical limit is.  If anyone
has some information on this, I'd like to hear it.

Gordon Strong
{decvax!genrad, ihnp4}!mit-eddie!gs
GS@MIT-XX