Parametric Signal Modelling using Laguerre Filters

Abstract

Autoregressive (AR) modelling is generalized by replacing the delay operator by discrete Laguerre filters. The motivation is to reduce the number of parameters needed to obtain useful approximate models of stochastic processes, without increasing the computational complexity. Asymptotic statistical properties are investigated. Several AR model estimation results are extended to Laguerre models. In particular, it is shown how the choice of Laguerre time constant affects the resulting estimates. A Levinson-type algorithm for computing the Laguerre model estimates in an efficient way is also given. The Laguerre technique is illustrated by two simple examples.