Klarinet Archive - Posting 000710.txt from 1997/11

From: Jonathan Cohler <cohler@-----.net>
Subj: RE: Nyquist and analog
Date: Thu, 20 Nov 1997 07:56:34 -0500

Ian Dilley wrote:

>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.

You will get a different set of samples, but you will still be able to
precisely reconstruct the original waveform. This is what is so important
about the sampling theorem.

> 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!

This is true, however, the probability of this happening is precisely 0.
In practical applications, one general takes samples at somewhat greater
than the Nyquist frequency.

> At the other extreme
>you can get a series of +n, -n, +n, -n ... where n is the amplitude of
>the signal.
>

Again the probability of this happening is 0, and therefore has no
practical consequences.

------------------
Jonathan Cohler
cohler@-----.net

   
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