Correlation 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 Density
Note that the autocorrelation function is Hermitian:
When is real, its autocorrelation is symmetric. More specifically, it is real and even.
When the signal is real, its PSD is real and even, like its autocorrelation function.
Random Variables & Stochastic Processes