A Simplicial Canonical Piecewise Linear Adaptive Filter

Abstract

A new adaptive nonlinear filter realization is presented based on a canonical piecewise linear (CPWL) approach. This filter realization consists of a linear part represented by a finite impulse response filter and a zero-memory nonlinear part implemented as a CPWL map. The resultant structure requires fewer parameters than other realizations found in the literature with comparable modeling capabilities. As a consequence, the proposed nonlinear filter, in addition to its simple description, has low computation and implementation costs. Some results related to convergence properties and implementation of the adaptive algorithm associated to this new realization are presented. The performance of the proposed filter is illustrated through simulation examples.