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Sampling Theory for Not Necessarily Band-Limited Functions: A Historical Overview

P. L. Butzer and R. L. Stens
SIAM Review
Vol. 34, No. 1 (Mar., 1992), pp. 40-53
Stable URL: http://www.jstor.org/stable/2132784
Page Count: 14
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Sampling Theory for Not Necessarily Band-Limited Functions: A Historical Overview
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Abstract

Shannon's sampling theorem is one of the most powerful results in signal analysis. The aim of this overview is to show that one of its roots is a basic paper of de la Vallee Poussin of 1908. The historical development of sampling theory from 1908 to the present, especially the matter dealing with not necessarily band-limited functions (which includes the duration-limited case actually studied in 1908), is sketched. Emphasis is put on the study of error estimates, as well as on the delicate point-wise behavior of sampling sums at discontinuity points of the signal to be reconstructed.

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