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From: turk@apple.UUCP (Ken "Turk" Turkowski)
Newsgroups: sci.math,sci.physics,sci.electronics
Subject: Re: Analog/Digital Distinction
Message-ID: <277@apple.UUCP>
Date: Sat, 8-Nov-86 00:43:32 EST
Article-I.D.: apple.277
Posted: Sat Nov  8 00:43:32 1986
Date-Received: Sun, 9-Nov-86 03:10:34 EST
References: <105@mind.UUCP> <6654@think.COM> <22067@rochester.ARPA> <521@ptsfd.UUCP>
Reply-To: turk@apple.UUCP (Ken "Turk" Turkowski)
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Organization: Apple Computer Inc., Cupertino, USA
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Xref: mnetor sci.math:160 sci.physics:135 sci.electronics:59

In article <521@ptsfd.UUCP> djo@ptsfd.UUCP (Dan'l Oakes) writes:
>I think an earlier candidate hinted at the right idea and then dropped it.  The
>distinction is that a digital signal is discrete -- not so much with respect to
>amplitude as with respect to time.  An analog signal doesn't much care when you
>look at it; a digital signal has "transition" or "edge" periods which can carry
>no information, by definition.

Au contraire, the transitions contain timing information, and some disk
controllers use this information to synchronize.

Most applications don't, however.  A good digital-to-analog subsystem will
not produce signals with transitions, edges, or impulses.  The steps seen
on signals coming directly from an A/D converter are due to aliases in the
frequency domain; a lowpass filter with a sharp cutoff at half the Nyquist
rate will eliminate these steps or aliases.

As I asserted in an earlier article, the time- and band-limited nature of
practical analog signals implies the finite dimensionality of them, where
the dimension is approximately 2WT, where W is the bandwidth and T is the
duration of the signal.

 [see: Slepian, David, "On Bandwidth", Proc. IEEE, v. 64, no. 3 March 1986]

As such, analog and digital representations of bounded signals are equivalent,
as long as the digital signal has approximately 2WT samples, and amplitude
quantization error is negligible.

In particular, if the analog signal is sampled with more than 2WT samples of
infinite precision, the sampling is completely invertible.
-- 
Ken Turkowski @ Apple Computer, Inc., Cupertino, CA
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