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From: marshall@elric.dec.com (Hunting the Snark)
Newsgroups: sci.electronics,sci.physics
Subject: Re: A question about the Nyquist theorm
Message-ID: <20408@shlump.nac.dec.com>
Date: 21 Feb 91 15:09:49 GMT
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Followup-To: sci.electronics
Organization: Digital Equipment Corporation
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In article <4402@eastapps.East.Sun.COM>, gsteckel@vergil.East.Sun.COM (Geoff Steckel - Sun BOS Hardware CONTRACTOR) writes...
>In article <883@idacrd.UUCP> mac@idacrd.UUCP (Robert McGwier) writes:
> From article <6607@healey>, by grayt@Software.Mitel.COM (Tom Gray):
> > The shape of the wave is preserved within the sampling pulse. This
> > information allows representation of a signal at exactly 1/2
> > the Nyquist freqency.
> 
> I pose the following question.  Suppose you are sampling at rate N samples
> per second, and you see a constant value V for your A/D sample.  Is the
> frequency of the signal which produced those samples 0 or N/2?  Since
> 
>AARRGGGHHH!  The Nyquist criterion requires that sampling be GREATER
>THAN the highest frequency of interest.  

Wrong answer. The answer to the question posed is that you are sampling a DC
signal. if it was N/2 then the sign of the samples would alternate. The only
time you can't distinguish DC and N/2 is when you just happen to sample at the
zero crossings of the N/2 frequency signal. 

The way to get around this degenerate case is to random sample with an
_average_ sample rate of N samples per second. Actually, you do not even need
to be randomly sampling, you could for instance instead of sampling with a 50%
duty cycle you could use a 25% duty cycle and still meet the Nyquist criteria.



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               \>                                        Steven Marshall

"Hard to say Ma'am. I think my cerebellum just fused" -- Calvin


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