RZ,nI: Claude Shannon

From: Carlos Murillo <cmurillo_at_emtelsa.multi.net.co>
Date: Wed Feb 28 13:08:02 2001

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...

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.

Received on Wed Feb 28 2001 - 13:08:02 GMT

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