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

Autores UPV
Año
Revista PUBLICATIONS OF THE RESEARCH INSTITUTE FOR MATHEMATICAL SCIENCES

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 coefficients 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.