Shannon's sampling theorem in a distributional setting
Functional Analysis
2013-04-25 v2 Information Theory
math.IT
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).
Keywords
Cite
@article{arxiv.1208.6493,
title = {Shannon's sampling theorem in a distributional setting},
author = {Amol Sasane},
journal= {arXiv preprint arXiv:1208.6493},
year = {2013}
}
Comments
This paper has been withdrawn by the author due to an error in a claim about singular supports in the proof