Summary: Computing the Poles of Autoregressive Models
from the Reflection Coefficients 1
Gregory S. Ammar 2 Daniela Calvetti 3 Lothar Reichel 4
Abstract
A new approach to the computation of the poles of a stable autoregressive system
from the reflection coefficients is proposed. Equivalently, we compute the zeros of Szeg�o
polynomials from the associated Schur parameters. The numerical method utilizes an
efficient algorithm for computing the (unimodular) zeros of a unitary Hessenberg matrix;
this step can be regarded as the computation of the poles of an associated lossless system.
These eigenvalues are then used as starting points for a continuation procedure for finding
the zeros of the desired polynomial. The procedure is efficient and parallelizable, and
may therefore be suitable for real�time applications.
1. Introduction
Autoregressive models are of fundamental importance in time series analysis and discrete�
time control. For example, in linear prediction, one is often given the autocorrelation
matrix of a wide sense stationary real�valued signal fx j g 1
j=\Gamma1
. This matrix is a real
symmetric positive definite Toeplitz matrix
M n+1 = [� j \Gammak ] n

Source: Ammar, Greg - Department of Mathematical Sciences, Northern Illinois University

Collections: Mathematics