RZ,nI: Claude Shannon

From: Richard Erlacher <edick_at_idcomm.com>
Date: Wed Feb 28 13:31:20 2001

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_at_emtelsa.multi.net.co>
To: <classiccmp_at_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:
> >> 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_at_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
>
> 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.
>
>
Received on Wed Feb 28 2001 - 13:31:20 GMT