Correlation AnalysisCorrelation analysis applies only to stationary stochastic processes (§C.1.5).
Definition: The cross-correlation of two signals and may be defined by
I.e., it is the expected value (§C.1.6) of the lagged products in random signals and .
Cross-Power Spectral DensityThe DTFT of the cross-correlation is called the cross-power spectral density, or ``cross-spectral density,'' ``cross-power spectrum,'' or even simply ``cross-spectrum.''
cross-correlation of a signal with itself gives the autocorrelation function of that signal:
Note that the autocorrelation function is Hermitian:
Fourier transform of the autocorrelation function is called the power spectral density (PSD), or power spectrum, and may be denoted
Random Variables & Stochastic Processes