Mathematical Problems in Engineering
Volume 4 (1998), Issue 5, Pages 369-375

A representation theorem for linear discrete-space systems

Irwin W. Sandberg

Department of Electrical and Computer Engineering, The University of Texas at Austin, Austin 78712, TX, USA

Received 22 July 1997

Copyright © 1998 Irwin W. Sandberg. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The cornerstone of the theory of discrete-time single-input single-output linear systems is the idea that every such system has an input–output map H that can be represented by a convolution or the familiar generalization of a convolution. This thinking involves an oversight which is corrected in this note by adding an additional term to the representation.