## Correlation Analysis

Correlation analysis applies only to stationary stochastic processes (§C.1.5).

### Cross-Correlation

Definition: The cross-correlation of two signals and may be defined by

 (C.24)

I.e., it is the expected valueC.1.6) of the lagged products in random signals and .

### Cross-Power Spectral Density

The DTFT of the cross-correlation is called the cross-power spectral density, or cross-spectral density,'' cross-power spectrum,'' or even simply cross-spectrum.''

### Autocorrelation

The cross-correlation of a signal with itself gives the autocorrelation function of that signal:

 (C.25)

Note that the autocorrelation function is Hermitian:

When is real, its autocorrelation is symmetric. More specifically, it is real and even.

See §6.4.

### Power Spectral Density

The Fourier transform of the autocorrelation function is called the power spectral density (PSD), or power spectrum, and may be denoted

When the signal is real, its PSD is real and even, like its autocorrelation function.

### Sample Power Spectral Density

See §6.5.

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