SAMPLING THEORY FOR NOT NECESSARILY BAND-LIMITED FUNCTIONS - A HISTORICAL OVERVIEW

被引：151

作者：

BUTZER, PL

STENS, RL

机构：

[1] Rheinisch-Westfalische Technische, Hochschule Aachen, Aachen

来源：

SIAM REVIEW | 1992年 / 34卷 / 01期

关键词：

SHANNON SAMPLING THEOREM; COMMUNICATION AND INFORMATION THEORY; INTERPOLATION; APPROXIMATION BY LINEAR EXPRESSIONS; DEGREE OF APPROXIMATION;

D O I：

10.1137/1034002

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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.

引用

页码：40 / 53

页数：14

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