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I just found out that the original version of Nyquist-Shannon sampling theorem differs from the modern version..

In the original version, it states that the bandlimited signal $x(t)$ can be constructed by the sampling rate of $2B$ when $B$ is the highest frequency content of the signal.

However, the modern version states that the signal can be constructed by the sampling rate of $2B$ when the signal's highest frequency content does not exceed or equal to $B$.

So, is the original version wrong? Or are there any reasons why these two came to differ?

Thanks.

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2 Answers 2

up vote 2 down vote accepted

Take the signal $f(t) = \sin 2\pi Bt$. Sample at a $2B$ rate, ie, at the time points $t_k = \frac{k}{2B}$. Then you have $f(t_k) = 0$, $\forall k$. So the signal $f$ cannot be reconstructed from the samples (it is indistinguishable from the zero function at these samples).

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that's what I thought.. Wikipedia says that Shannon's original statement was as mentioned, so that's why I was curious... –  user27515 May 10 '12 at 6:28

What you call the modern version is the classical version. Your original version is wrong, as copper.hat explained, and the really modern version is studied under compressed sensing.

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