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From: spp@ucbvax.ARPA (Stephen P Pope)
Newsgroups: net.audio
Subject: Re: David Mohler is completely correct
Message-ID: <10068@ucbvax.ARPA>
Date: Wed, 21-Aug-85 19:48:24 EDT
Article-I.D.: ucbvax.10068
Posted: Wed Aug 21 19:48:24 1985
Date-Received: Sat, 24-Aug-85 14:21:05 EDT
References: <19@drune.UUCP> <4162@alice.UUCP>
Organization: University of California at Berkeley
Lines: 41
Summary: David Mohler is not completely correct


     Sorry, Dave, since you clearly know quite a bit about
signal processing, but there are some misstatements in
your recent posting.
     First off, a 14-bit quantizer, oversampled at 4x, will
give you the resolution of a 15 bit quantizer, not a 16
bit quantizer.  Each time you double the sample rate, half
as much quantization noise energy lies in-band as previously
did, so you get a 3dB S/N improvement.  A 4x oversampling
gives you a 6dB improvement, which is the same improvement
you would get from adding ONE bit to your quantizer.
A 16-bit quantizer has 12dB better S/N than a 14 bit quantizer.
     Also, you are commingling two partially related issues --
D/A implementation, and reconstruction filter design.
All consumer CD players process operate at a 44 kHz sample
rate (for obvious reasons) but some interpolate up to
a higher sample rate, filter digitally, D/A convert at this
higher sample rate, and then filter the analog signal.
The advantage of doing this is that the sharp cut-off you
need at about 20 KHz is implemented by an EXACTLY LINEAR PHASE
digital filter, while the analog filter does not have a
lot of phase shift in the audio band since its rolloff occurs
much higher.
     The implication (I'm not sure you stated it explicity)
that a CD player that implements its reconstruction filter
in this way has a higher S/N than one that has an all-analog
reconstruction filter is completely false.  The statement
that the D/A implementation might be more linear is true,
however, the D/A conversion could be performed after 
interpolation to a higher sample rate even with an all-analog
reconstruction filter.  
     To summarize:

You can eliminate most of the phase shift in a CD player's
reconstruction filter by using a sharp-cut-off, linear-phase
digital filter followed by a gradual-cut-off analog filter.
As a side benefit, this possibly allows a more linear and/or
lower cost D/A implementation; but the same D/A implementation
could be used without the digital filter.

steve pope (ucbvax!spp)