Klarinet Archive - Posting 000690.txt from 1997/11

From: Mark Charette <charette@-----.com>
Subj: Re: Nyquist and Analog
Date: Wed, 19 Nov 1997 19:21:40 -0500

Jerry Korten wrote:
> And Mark the citation, no matter where it comes from is in error. Take it
> to a DSP engineer in your company and ask them. I have also disproved
> mathematical formulas given in biomedical engineering text books as they
> too can sometimes be printed in error.

Jerry, at this point the respect I've had for you is starting to
dimish. The reference was cited by Jonathan Cohler. _I_ took the
minimal effort to see what the reference was, something you
evidently did not. It is not a mathematical treatise on the Nyquist
Theorem. It says, verbatim (and I have been in error for many years
stating it as the Nyquist Theorem. It is properly Nyquist's theorem):

Nyquist's theorem

Nyquist's theorem: A theorem, developed by H. Nyquist, which states
that an analog signal waveform may be uniquely reconstructed,
without error, from samples taken at equal time intervals. The
sampling rate must be equal to, or greater than, twice the highest
frequency component in the analog signal. Synonym sampling theorem.

This HTML version of FS-1037C was last generated on Fri Aug 23
00:22:38 MDT 1996

This is a theorem. A mathematical construct or physical counter
example disproving any conjecture made by this theorem will cause
it to collapse. You have not presented any evidence that the
theorem is wrong. If it is wrong, it will no longer be a theorem.
It will not even be a conjecture. It will be flat wrong, it will
be discarded, and mathematicians and theoretical scientists and
physical scientists and others will go over it and possibly modify
it to become a theorem again, since it works well at what it does.
But ... it won't be Nyquist's theorem any more. It'd be a different one.

You haven't even gone so far as to present a simple conjecture that
could be construed as a counterexample.

As to whether or not Nyquist's theorem makes common sense; it seems
not to. But - it works. As far as we know at the moment.
--
Mark Charette | "This is a very democratic organization, so let's
charette@-----. All those who disagree with me, raise
Mika Systems, Inc.| their hands." - Eugene Ormandy
Webmaster of http://www.sneezy.org/clarinet, The Clarinet Pages