Title :
On eigenvalues distribution of correlation matrices
Author :
Farhang-Boroujeny, B.
Author_Institution :
Dept. of Electr. Eng., Nat. Univ. of Singapore, Singapore
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;
Conference_Titel :
Circuits and Systems, 1991., IEEE International Sympoisum on
Print_ISBN :
0-7803-0050-5
DOI :
10.1109/ISCAS.1991.176596
