Spectral Density of Sample Covariance Matrices of Colored Noise

TL;DR

This paper investigates how the spectral density of sample covariance matrices varies with the power spectrum of multivariate signals, extending known results from white noise to colored noise signals.

Contribution

It extends the spectral density analysis of covariance matrices from white noise to colored noise signals, providing new theoretical insights.

Findings

Spectral density depends on the power spectrum of the underlying signal.

Marchenko-Pastur law applies to white noise signals.

Results demonstrated for specific colored noise signals.

Abstract

We study the dependence of the spectral density of the covariance matrix ensemble on the power spectrum of the underlying multivariate signal. The white noise signal leads to the celebrated Marchenko-Pastur formula. We demonstrate results for some colored noise signals.