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Recent representation results for linear system maps: A short survey
Author(s) -
Sandberg Irwin W.
Publication year - 2007
Publication title -
international journal of circuit theory and applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.364
H-Index - 52
eISSN - 1097-007X
pISSN - 0098-9886
DOI - 10.1002/cta.428
Subject(s) - impulse response , bounded function , mathematics , convolution (computer science) , weighting , iterated function , integrable system , invariant (physics) , pure mathematics , representation (politics) , discrete mathematics , computer science , mathematical analysis , artificial intelligence , medicine , politics , artificial neural network , political science , law , mathematical physics , radiology
We give an expression for the most general input–output map associated with the members of a certain important large family of multidimensional linear shift‐invariant systems with bounded Lebesgue‐measurable inputs. The expression given is an iterated function‐space limit of a convolution. We also give a necessary and sufficient condition under which the limit can be written as a convolution with an integrable impulse–response function. A key role is played by a certain family of weighting operators. It is observed that for the large family of inputs and maps addressed, the Dirac impulse–response concept is in fact not the key concept concerning the representation of H , and that instead the input–output properties of H are determined, in general, by a certain type of family of responses. Some related material concerning other results, engineering education, and discrete‐space systems, is also given. Copyright © 2007 John Wiley & Sons, Ltd.