Bowtie factors of Toeplitz matrices by means of split algorithms

Author

Demeure, C.J.

Author_Institution

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

Volume

37

Issue

10

fYear

1989

fDate

10/1/1989 12:00:00 AM

Firstpage

1601

Lastpage

1603

Abstract

The bowtie factorization of a Toeplitz correlation matrix R and its inverse is introduced. The term bowtie describes the pattern of the factoring matrices. Several mathematical properties of bowtie matrices are described, including their close relation with block triangular matrices. The bowtie factors of the inverse R can be computed using a vector version of the split Levinson algorithm, restricted to orders with the same parity as n, the dimension of R. The bowtie factors of R can be computed using split vector versions of the Schur algorithm. The orthogonal factorization of the underlying data matrix Y can also be computed by the split versions of the lattice algorithm, producing a bowtie orthogonal factor of Y

Keywords

matrix algebra; Schur algorithm; Toeplitz correlation matrix; block triangular matrices; bowtie factors; bowtie matrices; data matrix; factoring matrices; inverse Toeplitz correlation matrix, linear prediction; lattice algorithm; orthogonal factorization; split Levinson algorithm; Acoustics; Correlation; Covariance matrix; Filters; Lattices; Prediction algorithms; Prediction theory; Reflection; Signal processing algorithms; Symmetric matrices;

fLanguage

English

Journal_Title

Acoustics, Speech and Signal Processing, IEEE Transactions on

Publisher

ieee

ISSN

0096-3518

Type

jour

DOI

10.1109/29.35401

Filename

35401