Unconstrained linear combination of even mirror Fourier non‐linear filters

Abstract

In this study, the unconstrained linear combination of the outputs of even mirror Fourier non-linear filters is considered. These filters are new members of the class of causal, shift-invariant, finite-memory and linear-in-the parameters non-linear filters. Their name derives from the even symmetry of their trigonometric basis functions. Even mirror Fourier non-linear filters are universal approximators for causal, time invariant, finite-memory and continuous non-linear systems. Moreover, their basis functions are mutually orthogonal for white uniform input signals in the interval [−1, +1]. The authors show in this study how to exploit these characteristics, in the framework of the unconstrained linear combination of non-linear filters, for modelling unknown non-linear systems. In particular, they show that the filters whose outputs are combined can be adapted avoiding the choice of the step sizes, by using a simple algorithm presented in this study. The analysis of the proposed structures is accompanied by a set of simulation results that confirm the good performance obtained in different situations.