Approximation of Myopic Systems Whose Inputs Need Not BeContinuous

Authors:
Irwin W. Sandberg;Lilian Xu
Affiliations:
Department of Electrical and Computer Engineering, The University of Texas at Austin, Austin, Texas 78712. E-mail sandberg@uts.cc.utexas.edu;Department of Electrical and Computer Engineering, The University of Texas at Austin, Austin, Texas 78712
Venue:
Multidimensional Systems and Signal Processing
Year:
1998

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Abstract

Our main result is a theorem that gives, in a certainsetting, a necessary and sufficient condition under which multidimensionalshift-invariant maps with vector-valued inputs drawn from a certainlarge set can be uniformly approximated arbitrarily well usinga structure consisting of a linear preprocessing stage followedby a memoryless nonlinear network. The inputs considered neednot be continuous, and noncausal as well as causal maps are addressed.Approximations for noncausal maps for which inputs and outputsare functions of more than one variable are of current interestin connection with, for example, image processing.