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        riddles >> putnam exam (pure math) >> Sampling Theorem Argument
        
(Message started by: william wu on Oct 24^th, 2004, 5:19pm)

Title: Sampling Theorem Argument
Post by william wu on Oct 24^th, 2004, 5:19pm

(Some exposure to sampling theory required)

A well known and amazing result from sampling theory is that if you periodically sample a continuous time bandlimited signal at a rate greater than twice the bandwidth, you can reconstruct the original signal perfectly using a sinc interpolator. This is the "nyquist-shannon sampling theorem" in a nutshell.

Now suppose you are given a continuous time bandlimited signal that is also periodic.

Mr Jones: From the sampling theorem, if I wish to reconstruct the signal perfectly from its samples, I should take an infinite number of samples, at a rate greater than twice the bandlimit.

Mr Smith: Since the signal is periodic, I should be able to take only a finite number of samples to do the reconstruction.

Help Mr. Jones and Mr. Smith reconcile their differences. Who is right? Who is wrong?

Source: Brad Osgood

Title: Re: Sampling Theorem Argument
Post by towr on Oct 25^th, 2004, 1:41am

::[hide]If the sampling period divided by the period of the signal is a rational number, then a finite number of samples should be enough, because after a while the sequence just repeats.
I'm not sure about the other case, certainly in practise you won't need to bother with an infinite number of samples (you'd be dead long before you have them anyway) and while the sample-sequence may not be period, it should be quasiperiodic.
[/hide]::