From: Ingraham, Andrew (Andrew.Ingraham@compaq.com)
Date: Tue Apr 03 2001 - 06:49:49 PDT
> I guess the important take away is that
> this sampling theory applies only to a true sine
> waveform signal not "Periodic Signals" as I mentioned
> in my first mail.
It does not require either sine waves or periodic signals.
Sampling theory certainly does not require pure sine waves. Complex
waveforms with harmonics are perfectly acceptable ... as long as the sample
points are appropriate for the highest frequency or harmonic present.
A true square wave (a physical impossibility, BTW), ideal trapezoidal wave,
triangle wave, etc. do contain infinite harmonic series; but the world is
full of quasi square waves or whatever, that are band-limited.
But when the fundamental frequency's period starts approaching the Nyquist
limit, you don't have room left for any harmonics so then you are talking
about sine waves.
Neither is periodicity required.
It can get a little funky mathematically, though.
As long as the frequency content is less than half the sampling rate, no
information is lost and the original waveform ... however non-sinusoidal or
non-periodic it is ... can be reconstructed.
> I always remembered Fourier series
> form my freshman year but did not establish the mental
> correlation between "periodic" and "band limited".
There is no correlation between them.
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