On eigenvalues distribution of correlation matrices

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 optimimum 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.