Estimation of Noise Models by Means of Discrete Laguerre/Kautz Filters

Abstract Autoregressive (AR) modelling is generalized by replacing the delay operator by discrete Laguerre or Kautz filters. The motivation is to reduce the number of parameters needed to obtain useful approximate models of stochastic processes, without increasing the computational complexity. The key observation is that Tooplitz strucure of covariance matrix of the regression vector (normal equations) for AR estimation also holds for Laguerre/ Kautz models. This result enables several AR estimation results to be generalized to the Laguerre/Kautz case. The potential of Kautz models for modelling of narrow-band signal is discussed. The Laguerre/Kautz estimation technique is illustrated by simple examples.