# Autocorrelation matrix eigenvalues and the power spectrum

### David G. Messerschmitt

###
EECS Department

University of California, Berkeley

Technical Report No. UCB/EECS-2006-90

June 27, 2006

### http://www.eecs.berkeley.edu/Pubs/TechRpts/2006/EECS-2006-90.pdf

Thus tutorial report derives many properties of the autocorrelation matrix of a WSS random process, such as the distribution of eigenvalues, and relates them to the power spectral density. It especially relates these properties asymptotically as the dimension of the matrix approaches infinity. Along the way, it relates the matrix eigenvalue and linear time-invariant system transfer function principles, their parallels lying at the heart of the later results. This serves to explain some famous results from linear algebra in a way that is easy to understand from an engineering perspective.

BibTeX citation:

@techreport{Messerschmitt:EECS-2006-90, Author = {Messerschmitt, David G.}, Title = {Autocorrelation matrix eigenvalues and the power spectrum}, Institution = {EECS Department, University of California, Berkeley}, Year = {2006}, Month = {Jun}, URL = {http://www.eecs.berkeley.edu/Pubs/TechRpts/2006/EECS-2006-90.html}, Number = {UCB/EECS-2006-90}, Abstract = {Thus tutorial report derives many properties of the autocorrelation matrix of a WSS random process, such as the distribution of eigenvalues, and relates them to the power spectral density. It especially relates these properties asymptotically as the dimension of the matrix approaches infinity. Along the way, it relates the matrix eigenvalue and linear time-invariant system transfer function principles, their parallels lying at the heart of the later results. This serves to explain some famous results from linear algebra in a way that is easy to understand from an engineering perspective.} }

EndNote citation:

%0 Report %A Messerschmitt, David G. %T Autocorrelation matrix eigenvalues and the power spectrum %I EECS Department, University of California, Berkeley %D 2006 %8 June 27 %@ UCB/EECS-2006-90 %U http://www.eecs.berkeley.edu/Pubs/TechRpts/2006/EECS-2006-90.html %F Messerschmitt:EECS-2006-90