On eigenvalues distribution of correlation matrices

Author

Farhang-Boroujeny, B.

Author_Institution

Dept. of Electr. Eng., Nat. Univ. of Singapore, Singapore

fYear

1991

fDate

11-14 Jun 1991

Firstpage

1251

Abstract

The distribution of the eigenvalues of the correlation matrices of stochastic processes is addressed. A filtering view of the eigenproblem of the correlation matrices is given. It is shown that eigenvectors of a correlation matrix may be thought of as the coefficients of a set of optimum finite-impulse-response (FIR) filters that may be designed through an optimization procedure. It is shown that the eigenvalues of the correlation matrix of a transversal filter may be obtained by averaging its output power when the complex conjugate of its corresponding eigenvectors is used as its tap-gain vector. This results in an effective mathematical tool that may be readily used for estimation of the eigenvalues of the correlation matrices under many conditions of interest

Keywords

correlation methods; digital filters; eigenvalues and eigenfunctions; filtering and prediction theory; matrix algebra; optimisation; signal processing; stochastic processes; adaptive signal processing; complex conjugate; correlation matrices; eigenvalues distribution; filtering; optimization; optimum FIR filter coefficients; stochastic processes; tap-gain vector; transversal filter; Design optimization; Eigenvalues and eigenfunctions; Equations; Finite impulse response filter; Frequency; IEEE members; Power generation; Random processes; Stochastic processes; Transversal filters;

fLanguage

English

Publisher

ieee

Conference_Titel

Circuits and Systems, 1991., IEEE International Sympoisum on

Print_ISBN

0-7803-0050-5

Type

conf

DOI

10.1109/ISCAS.1991.176596

Filename

176596