A non-linear approach to signal processing bymeans of vector measure orthogonal functions

Abstract

Sequences of real functions that are orthogonal with respect to a vector measure are a natural generalization of the orthogonal systems with respect to a parametric measure. In this paper we develop a new procedure to construct non linear approximations of functions by de fining orthogonal series in spaces of square integrable functions with respect to a vector measure which Fourier coeffi cients are also functions. We study the convergence properties of these series, defi ning a convenient approximation structure for signal processing involving time dependence of the measure. Some examples regarding classical orthogonal polynomials are given.