Fast transversal filtering algorithms for pole-zero modeling

Abstract

In this dissertation, pole-zero (ARMA) modeling of discrete-time linear systems using the recursive-least-squares (RLS) fast transversal filter (FTF) algorithm is investigated. Three types of ARMA FTF algorithms are studied. First, an ARMA FTF algorithm for the unknown input case is proposed. This ARMA FTF algorithm can estimates unknown input excitation and the estimated input is used to determine the parameters of the pole-zero model. By introducing a spectral distance measure, we study the convergence characteristics of this algorithm, and show that it has rapid convergence speed. We also evaluate the performance of the proposed algorithm by applying to synthetic and natural speech spectral estimations. This algorithm accurately represents spectral peaks and valleys of speech and requires less computations than RLS lattice filters and the ARMA FTF algorithm of Ardalan and Faber(1988). Additionally, this algorithm can also be applied to other signal processing areas where the input is unknown. Second, an ARMA FTF algorithm for the known input case is proposed. This algorithm can exactly estimate unknown filter coefficients. Simulation results are presented to show the rpaid convergence speed and the numerical accuracy of the algorithm. We show that this algorithm converges more accurately than the ARMA FTF algorithm of Ardaln and Faber. This algorithm requires the same number of computations as that needed in the ARMA FTF algorithm for the unknown input case. These two algorithms are derived using geometric projections. The geometric projection approach gives insight and useful interpretation of various filters that form the algorithms. Finally, since the ARMA FTF algorithm for the known input case is numerically unstable, a numerically stable ARMA FTF algorithm is derived. This numerically stable ARMA FTF algorithm is derived using geometric projections and the error feedback procedure. This algorithm for the known input case. Simulation results are presente...