On a generalization of the Szego-Levinson recurrence and its application in lossless inverse scattering

Author

Delsarte, P. ; Genin, Yves

Author_Institution

Philips Res. Lab., Brussels, Belgium

Volume

38

Issue

1

fYear

1992

fDate

1/1/1992 12:00:00 AM

Firstpage

104

Lastpage

110

Abstract

Predictor polynomials corresponding to nested Toeplitz matrices are known to be connected by the Szego-Levinson recurrence relation. A generalization of that result, where the relevant reduction process for Toeplitz matrices (of decreasing order) is defined by an elementary one-parameter linear transformation, is addressed. The descending and ascending versions of the corresponding generalized Szego-Levinson recurrence relations are discussed in detail. In particular, these relations are shown to be essentially the same as the extraction formulas for canonical Schur and Brune sections in the Dewilde-Dym (1984) recursive solution of the lossless inverse scattering problem. Some extensions of the Levinson algorithm for linear prediction and of the Schur-Cohn algorithm for polynomial stability test are presented

Keywords

filtering and prediction theory; inverse problems; matrix algebra; polynomials; Schur-Cohn algorithm; Szego-Levinson recurrence; Toeplitz matrices; linear prediction; lossless inverse scattering; polynomial stability test; predictor polynomials; Digital signal processing; Equations; Inverse problems; Mirrors; Polynomials; Prediction algorithms; Scattering; Signal processing algorithms; Stability; Testing;

fLanguage

English

Journal_Title

Information Theory, IEEE Transactions on

Publisher

ieee

ISSN

0018-9448

Type

jour

DOI

10.1109/18.108254

Filename

108254