Lecture Notes on Eigen-analysis of Autocorrelation and Power Spectrum Density Function

Eigen-analysis is a quite important tool in signal processing, from which we can analyze the random signal. In this paper, the eigen-analysis of the autocorrelation function and power spectrum density are analyzed using Einstein-Wiener-khintchine relationship, LTI system, AR model, etc. The relationship between the two is illustrated. The eigen-analysis of the autocorrelation function of the random signal and power spectrum density can be derived from each other. We hope that the results of this lecture notes can give some inspiration to students who are studying digital signal processing.