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william wu
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Sampling Theorem Argument
« on: Oct 24th, 2004, 5:19pm » |
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(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
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| « Last Edit: Oct 24th, 2004, 5:21pm by william wu » |
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towr
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Some people are average, some are just mean.
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Re: Sampling Theorem Argument
« Reply #1 on: Oct 25th, 2004, 1:41am » |
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::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.
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