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From: ertas@athena.mit.edu (Mehmet D Ertas)
Newsgroups: sci.electronics,sci.physics
Subject: Re: A question about the Nyquist theorm
Message-ID: <1991Feb15.173133.29237@athena.mit.edu>
Date: 15 Feb 91 17:31:33 GMT
References: <91046.095459F0O@psuvm.psu.edu> <1751@manta.NOSC.MIL>
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In article <1751@manta.NOSC.MIL>, north@manta.NOSC.MIL (Mark H. North) writes:
|> In article <91046.095459F0O@psuvm.psu.edu> F0O@psuvm.psu.edu writes:

|> >     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.


And just for ther sake of completeness, here's how you recover your
original signal:

Take your samples, pass them through an A-D converter and LPF the outcoming
signal with cutoff freq. 0.5 times the sampling frequency. There you go!

|> 
|> >     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.
|> 

That's correct; you cannot recover the amplitude of a frequency comp.
exactly half the sampling frequency.

|>   
|>  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

Another useful reference may be "Digital Signal Processing" by Oppenheim &
Schafer.

M. Deniz Ertas