Fast algorithms for computing QR and Cholesky factors of Toeplitz operators

Author

Rialan, Christophe P. ; Scharf, Louis L.

Author_Institution

Dept. of Electr. & Comput. Eng., Colorado Univ., Boulder, CO, USA

Volume

36

Issue

11

fYear

1988

fDate

11/1/1988 12:00:00 AM

Firstpage

1740

Lastpage

1748

Abstract

Levinson, Lattice and Schur recursions provide alternative ways of computing reflection coefficients for stationary time series. The authors show that when a Toeplitz correlation matrix is a product of two Toeplitz data matrices, as in the correlation method of linear prediction, then the Levinson recursions can be used to derive the Lattice recursions and the Lattice recursions can be used to derive the Schur recursions. They explore the close relation between QR and Cholesky algorithms in the Toeplitz case, and present the underlying matrix factorization

Keywords

correlation theory; matrix algebra; signal processing; Cholesky factors; Lattice recursions; Levinson recursions; QR factors; Schur recursions; Toeplitz correlation matrix; linear prediction; matrix factorisation; reflection coefficients; stationary time series; Acoustic reflection; Arithmetic; Autocorrelation; Correlation; Equations; Error analysis; Lattices; Least squares methods; Speech enhancement; Vectors;

fLanguage

English

Journal_Title

Acoustics, Speech and Signal Processing, IEEE Transactions on

Publisher

ieee

ISSN

0096-3518

Type

jour

DOI

10.1109/29.9011

Filename

9011