The Kolmogorov mapping theorem in signal processing

Abstract

Since the publication in 1957 of the work of Andrei Kolmogorov 181 in mapping a function of multiple variables by means functions of a single variable, many mathematicians and engineers try , with different degree of success and not without controversy 1191. to find the direct application of it to multiple extremes problems, rooting of multivariate polynomials, neural networks and pattern recognition. This paper revisits the theorem from the optic of a generalised architecture for signal processing 1281. It is envisaged the high potential of the theorem to handle either linear or non-linear processing problems. A specific implementation following the main guide-lines of the theorem is reported, as well as some preliminary results concerning the design, implementation and performance of non-linear systems. The applications cover non linear transmission channels for communications, instantaneous companders and prediction of chaotic series.Peer ReviewedPostprint (published version