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Path: utzoo!linus!decvax!ittvax!dcdwest!sdcsvax!bmcg!asgb!mike
From: mike@asgb.UUCP
Newsgroups: net.audio
Subject: Re: Logarithmic CD encoding
Message-ID: <563@asgb.UUCP>
Date: Tue, 30-Oct-84 19:01:39 EST
Article-I.D.: asgb.563
Posted: Tue Oct 30 19:01:39 1984
Date-Received: Thu, 1-Nov-84 03:21:36 EST
Organization: Burroughs Corporation, Boulder Colo.
Lines: 29


In reference to the 8 bit logarithmic representation described by
Richard Schooler (inmet!schooler):  he suggested an 8 bit
representation with a sign bit and a seven bit fixed point exponent
with three fraction bits.  This gives a dynamic range of
2^(+-(15+7/8)) or 96 dB and "an absolute S/N of 93 dB, and an
instantaneous S/N (precision, roughly) of 32 dB."

This representation does not however, consider waveform fidelity.  At
each sampling point, the signal must be quantized to one of the values
represented by the encoding scheme.  In the 8 bit scheme, each quantum
level is greater than the previous by a factor of 1.09.  A 9% jump
between levels and a maximum quantizing error of 4.5%.  This error due
to the lack of precision does not yield a greater S/N, it's DISTORTION. 
True, filtering techniques can minimize the distortion, but 4.5% isn't
quite a high fidelity source to begin with.

This encoding does have the interesting characteristic that the
difference between quantizing levels is a constant factor.  In the
current CDs 16 bit encoding, the error varies from 50% (!) between 0
and 1 to .00075% between 65534 and 65535.  If a 16 bit logarithmic
representation was used, the error would be a constant .024%.  I don't
know if this is a significant characteristic, but it at least has a
nice consistency to it.

Mike Rosenlof                  ...hplabs!sdcrdcf!\
                                                  -bmcg!asgb!mike
                              ...allegra!sdcsvax!/
Burroughs Advanced Systems Group              Boulder, Colorado