Klarinet Archive - Posting 000658.txt from 1997/11

From: Ian Dilley <imd@-----.uk>
Subj: RE: Nyquist and analog
Date: Wed, 19 Nov 1997 13:01:03 -0500

Here is the disputed definition of Nyquist's theorom

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.

Well, I'm no expert but I can immediately see a case where this is not
going to be true. Take as an example a 20 KHz sine wave sampled at 40
KHz. According to the above definition the samples will contain enough
information to perfectly reconstruct the 20 KHz sine wave.

Surely you are going to get different results depending on the relative
phases of the sampling and the sine wave itself. In one extreme case
you could get a set of samples that are all 0. This occurs because the
wave crosses the 0 point every 1/2 it's period. From that you aren't
going to be able to reconstruct very much at all! At the other extreme
you can get a series of +n, -n, +n, -n ... where n is the amplitude of
the signal.

Jerry, Jonathon - am I missing something obvious?

Ian Dilley

   
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