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From: shmulevi@tukkasotka.tut.fi (Ilya Shmulevich)
Newsgroups: comp.dsp
Subject: Re: Nyquist Rate
Keywords: nyquist
Message-ID: <1991Mar3.191056.9334@funet.fi>
Date: 3 Mar 91 19:10:56 GMT
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Organization: Tampere University of Technology
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> In a pervious post, someone brought up the theoretical problem that you
> sample a sine wave with frequency f at exactly 2*f, but your first sample
> is perfectly lined up at t=0. Thus it would seem that your sample stream
> would then be all zeros makeing it impossible to reconstruct the original 
> sine wave.
> 
> I have tried to reconcile this, but to no ava as of yet. Does anyone else
> have any ideas on this? 
> 
> Doug Reynolds

  I think the problem seems to stem from the fact that the Nyquist rate
must be GREATER than (and not greater than or equal to) twice the highest
frequency component of your signal. Try to imagine a bandlimited signal
x(n) with a non-zero component at the highest frequency. Also, assume that 
the signal x(n) is real, so its Fourier Transform is conjugate symmetric.
When sampled at exactly twice the highest frequency, the replicas of the
spectrum WILL overlap at odd multiples of the highest frequency. This will
obviously introduce distortion. 
  Although this is not the same problem, it again demonstrates that the
sampling rate must be greater than the highest frequency component.

-- 
Ilya Shmulevich
shmulevi@tut.fi
Signal Processing Laboratory
Tampere University of Technology, Finland