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arXiv · 1208.6493

Shannon's sampling theorem in a distributional setting

Amol Sasane
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Abstract

The classical Shannon sampling theorem states that a signal f with Fourier transform F in L^2(R) having its support contained in (-\pi,\pi) can be recovered from the sequence of samples (f(n))_{n in Z} via f(t)=\sum_{n in Z} f(n) (sin(\pi (t -n)))/(\pi (t-n)) (t in R). In this article we prove a generalization of this result under the assumption that F is a compactly supported distribution with its support contained in (-\pi,\pi).

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Amol Sasane. 2012-08-31. Shannon's sampling theorem in a distributional setting. https://arxiv.org/abs/1208.6493

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