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From: mat@hou4b.UUCP (Mark Terribile)
Newsgroups: net.audio
Subject: Re: CD Reflections
Message-ID: <1278@hou4b.UUCP>
Date: Wed, 16-Jan-85 14:10:13 EST
Article-I.D.: hou4b.1278
Posted: Wed Jan 16 14:10:13 1985
Date-Received: Thu, 17-Jan-85 14:00:37 EST
References: <1420@hplabs.UUCP>
Organization: AT&T Information Systems Laboratories, Holmdel, NJ
Lines: 54

Oversampling:

	Yes, there is a certain sampling rate on the CD.  (Gee, didn't we do
this a while ago ...?)  The player inserts either one or three samples IN
BETWEEN the ones it gets.  These are created by a mathematical process from
the existing samples, and the lower bit (or two bits) of the sample get
removed.

	The data is then processed by digital and analog filters as though
it were created at the higher rate.  This raises by an octave or two the
frequency at which the anti-aliasing filters must cut off.  That in turn
changes the guardband (between the highest frequency of interest and the
alias that must be removed) from a couple of kHz to tens of kHz.  The filters
can then be designed for minimal phase damage and amplitude deviation in the
pass band ... but that pass band can extend up to (above) the new sampling
frequency.  This allows the filter designer (correct me on this, Bill Mitchell)
a place where he can put the anomalies in the filter's response (which MUST
occur).

	Y'see, there are a bunch of things that are just incompatable in
filter design.  The proper design of filters includes the usual kind of
engineering tradeoffs on these things, which are:

	Even response in the passband

	Slope of the filter (how quickly it cuts off)

	Quality of cut-off in the stop-band (if you need to get 100 dB S/N,
	you can't let lots of crud leak out here)

	Phase shifting of frequencies in the passband.

	Minimal noise created by the filter (the more electronics you add,
	the more noise you get).

If you can make the transition between passband and stopband big, you get
room to trade the other stuff off.

	Without oversampling, your top frequency of interest is 21 kHZ, your
sampling rate is 44 kHz, your alias frequencies begin at 23 kHz.  That gives
the filter designer just 2 kHz to play with on frequencies of 21 kHz.  Quite
a challenge!

	With 4x oversampling, your sampling rate goes to 176 kHz, and your
alias frequences begin at 155 kHz, but the top frequency of interest is
still 21 kHz.  We've gone from a guardband that was less than one-tenth the
bandwidth of the highest signal requency to one that is over seven times that
bandwidth!  Or, as a wise mathematician once wrote: ``somewhere ... a miracle
occurs''
-- 

	from Mole End			Mark Terribile
		(scrape .. dig )	hou4b!mat
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