Laguerre Filters: An Introduction

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

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