A split-Levison approach to autoregressive modeling

Abstract

The classical Levinson-Durbin linear prediction formulas for real valued input sequences are examined and compared to the recently proposed split-Levinson formulas. Both the autoregressive linear predictor model and the adaptive lattice model are used to formulate the new split-Levinson algorithms. A brief introduction to the theory of symmetric polynomials is presented to form the basis of the new algorithms. Computer simulations are used to test and compare the computational accuracy of the new algorithms for AR filter coefficient estimation, parameter estimation for a moving average process, and spectral estimation of sinusoids in white noise. Research results indicate that the new algorithms reduce the number of real multiplications required for a k sub th order AR filter problem by one-half, and they are applicable to both the extended Prony method of spectral estimation of moving average parameters. Keywords: Text processing, Word processing, Theses. (kr)