Symmetric solutions and eigenvalue problems of Toeplitz systems

Author

Huang, Dawei

Author_Institution

Sch. of Math., Queensland Univ. of Technol., Brisbane, Qld., Australia

Volume

40

Issue

12

fYear

1992

fDate

12/1/1992 12:00:00 AM

Firstpage

3069

Lastpage

3074

Abstract

Algorithms and properties of symmetric solutions of a Toeplitz system are studied. It is shown that the numbers of positive and negative eigenvalues associated with symmetric (antisymmetric) eigenvectors are the same as the numbers of positive and negative predictor errors of symmetric (antisymmetric) filters. Based on the odd symmetric solutions and the property that all roots of symmetric and antisymmetric filters are on the unite circle, a method for Pisarenko´s decomposition is introduced. Compared with some other methods, it reduces the number of iterations and the computational cost in each iteration considerably

Keywords

eigenvalues and eigenfunctions; filtering and prediction theory; matrix algebra; signal processing; Pisarenko´s decomposition; Toeplitz matrix; antisymmetric filters; eigenvalue problems; eigenvectors; iteration; predictor errors; signal processing; symmetric filters; symmetric solutions; Cities and towns; Computational efficiency; Costs; Digital filters; Eigenvalues and eigenfunctions; Mathematics; Polynomials; Signal processing algorithms; Stability; Symmetric matrices;

fLanguage

English

Journal_Title

Signal Processing, IEEE Transactions on

Publisher

ieee

ISSN

1053-587X

Type

jour

DOI

10.1109/78.175752

Filename

175752