DISTRIBUTIONAL TIME-DOMAIN SYSTEM REPRESENTATIONS

被引：0

作者：

Moenich, Ullrich J. ^{[1
]}

Boche, Holger ^{[1
]}

机构：

[1] Tech Univ Berlin, Heinrich Hertz Chair Mobile Commun, D-10578 Berlin, Germany

来源：

2010 IEEE INTERNATIONAL CONFERENCE ON ACOUSTICS, SPEECH, AND SIGNAL PROCESSING | 2010年

关键词：

System representation; convolution; bandlimited signal; distribution; convergence;

D O I：

10.1109/ICASSP.2010.5495782

中图分类号：

O42 [声学];

学科分类号：

070206 ; 082403 ;

摘要：

In this paper we analyze the convergence behavior of convolution-type system representations for the Paley-Wiener space PW(pi)(1).. We completely characterize all stable linear time-invariant (LTI) systems for which we have convergence in the distributional sense by giving a necessary and sufficient condition for convergence. Furthermore, we prove that there are stable LTI systems and signals in PW(pi)(1) for which the convolution integral and the convolution sum diverge even in a distributional sense. In signal processing, distributions are often used to show convergence. Surprisingly, here we are in a situation where distributions cannot be used to justify convergence.

引用

页码：3994 / 3997

页数：4

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