Klarinet Archive - Posting 000722.txt from 1997/11

From: Jonathan Cohler <cohler@-----.net>
Subj: Re: Nyquist and Analog
Date: Thu, 20 Nov 1997 11:18:16 -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

>You are absolutely correct, mostly. The Nyquist criterion says > 2X the
>highest frequency therefore there will always be two sample points per
>waveform period.

This is incorrect. The Nyquist theorem says "greater than or equal to" the
highest frequency component of the original continuous analog waveform.

Please stop spreading your misinformation, Jerry. These are matters of
fact. And you stand corrected. Leave it at that.

>
>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.
>

Saying it over and over doesn't make it so, Jerry. The citation I
mentioned (which by the agrees precisely with every other published
citation I have ever seen) is correct. I would be happy to give dozens of
other citations to whomever is interested.

If you have even one peer reviewed citation, which differs, please present
it. And stop talking about "they" and the "DSP engineers at your company"
and all of these other mystical club members. Facts are facts.

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