Laguerre filters: an introduction

Abstract

In this tutorial paper we present a generalization of the transversal filter, called Laguerre filter, and study someof its more remarkable properties. This filter is obtained byreplacing each delay of the transversal filter by a first orderall-pass section, and by applying a first order low-pass filter(with the same pole used in the all-pass sections) to the filter’sinput signal. Both the transversal and the lattice forms of theLaguerre filter are discussed. We also deduce the stationarityconditions of the mean-square error of a Laguerre filter(transversal or lattice) with respect to its pole position.