Linear systems and half-line integral representations

Authors:
Irwin W. Sandberg
Affiliations:
Department of Electrical and Computer Engineering, The University of Texas at Austin, Austin, Texas
Venue:
Math'04 Proceedings of the 5th WSEAS International Conference on Applied Mathematics
Year:
2004

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Abstract

We give an expression for the most general input-output map associated with the members of a certain important large family of causal time-invariant linear systems. This expression is a uniform limit of a convolution. We also give a necessary and sufficient condition under which the limit can be written as a convolution, and we relate this to the concepts of an impulse response and a q-response limit, and to the flawed concept of the Dirac impulse function.