Adaptive Learning Methods for Nonlinear System Modeling

Chapter 2

Orthogonal LIP Nonlinear Filters

Alberto Carini^⁎; Stefania Cecchi^†; Simone Orcioni^{†    ⁎}University of Urbino Carlo Bo, DiSPeA, Urbino, Italy^†Università Politecnica delle Marche, DII, Ancona, Italy

Abstract

This chapter provides an overview of orthogonal linear-in-the-parameter (LIP) nonlinear filters defined in the real domain. After reviewing the classical theory of Volterra and Wiener filters, it presents different classes of real LIP nonlinear filters, whose basis functions are orthogonal for specific distributions of the input signal, under the unified framework of functional link polynomial (FLiP) filters. The class of FLiP filters includes nonorthogonal and orthogonal nonlinear filters, as the Wiener nonlinear filters, ...