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From: north@manta.NOSC.MIL (Mark H. North)
Newsgroups: sci.electronics,sci.physics
Subject: Re: A question about the Nyquist theorm
Message-ID: <1751@manta.NOSC.MIL>
Date: 15 Feb 91 16:51:29 GMT
References: <91046.095459F0O@psuvm.psu.edu>
Organization: Naval Ocean Systems Center, San Diego
Lines: 34

In article <91046.095459F0O@psuvm.psu.edu> F0O@psuvm.psu.edu writes:
>
>     I was reading an article that states the Nyquist theorm as:
>     "The sample frequency must be at least twice the highest frequency
>component within the analog signal for an accurate representation of the
>analog signal".

This is an incorrect statement of the Nyquist theorem. The sample freq
must be *greater* than twice the highest freq component...

>     I'd guess here he is talking about complex signals.  But what do you
>do with a pure sine wave?  There is only one frequency component in a sine
>wave(the fundamental), and if you sample at twice that, you're not going
>to get a good representation of the signal.

A pure sine wave is fine. As long as you sample at greater than twice its
freq. Even though it may appear that you are not getting a good represen-
tation of the signal it can be shown with Fourier analysis that the
sample set is unique to this component and hence the exact signal can
be recovered from the sample set.

>     i.e. If you have a 60HZ sine wave, and you sample at 120HZ, you're
>only going to get two points per cycle.

And imagine that those two points are phased such that they land at the
zero crossing of the 60Hz signal. All your samples are zero! This is
why you must sample at greater than 2nu.

 
 A good reference is "Digital Signal Analysis" by Samuel D Stearns. It is
 no longer in print but is available in most engr. libraries. Also there
 is a new edition of this book published by Printice Hall.

 Mark