28 Feb
2001
28 Feb
'01
5:31 a.m.
You're right in that this isn't a forum for signal processing, but it's worth
notice that the sample rate deterines the top-end cutoff frequency for the
sample, and the epsilon (the difference between 2x the cutoff frequency)
determines the resolution achievable with a finite length of sample. There are
more factors at work than that, however, and if one were really interested in
what's going on in processes such as this, one would simply read the Shannon
work.
Dick
----- Original Message -----
From: "Carlos Murillo" <cmurillo(a)emtelsa.multi.net.co>
To: <classiccmp(a)classiccmp.org>
Sent: Wednesday, February 28, 2001 12:08 PM
Subject: RE: RZ,nI: Claude Shannon
At 12:24 PM 2/28/01 -0500, you wrote:
Of course, of course. In reality, you need to sample at 2ws+epsilon.
But then again, while mathematically you just need any epsilon > 0,
in reality as epsilon -> 0 the reconstruction process needs filters
of higher and higher order, and in the end the reconstructor needed
is no longer causal. You're right when checking my epsilons, but on the
other hand this is not a systems theory forum.
carlos.
Some of
Shannon's better known known theorems include
the Sampling Theorem, which indicates that a bandwidth-limited
signal can be reconstructed only if sampled at least at twice
the frequency of the highest-frequency spectral content.
Take a 1 Vpp@40Hz Sinewave, highest-frequency spectral content is 40Hz,
sample it at twice this frequency, 80Hz, sample at 0 and 180 degrees (0Vpp
Amplitude), the reconstructed sinewave will be 0Vpp at 0 Hz. Oh well, guess
Shannon's theorem is incorrect...
steve