RE: [SI-LIST] : Nyquest Sampling Rate

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From: Ingraham, Andrew ([email protected])
Date: Sat Mar 31 2001 - 14:36:37 PST

> Can any one explain to me how you can recover a
> periodic signal form only 2 samples. I can understand
> the math but I am having difficulty visualizing this.
> Draw me any 2 points in the time domain and I can make
> endless number of periodic signal go through them?
The bandwidth limit works both ways; both when sampling a signal and when
restoring it from the sampled points. Thus, given _slightly_more_than_ 2
points per cycle, you can reconstruct the one sinewave that must have been
the band-limited original. No signal other than a sinewave will do, because
any other shape has harmonic frequencies that would violate the Nyquist

However, given exactly 2 samples per cycle, indeed there are an infinite
number of sinewaves that you could draw that pass through those points,
because you don't know both the amplitude and the phase of the original.
Two samples per cycle is the borderline case. You really need slightly more
than 2 per cycle.


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