## 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 value*(§C.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:

*symmetric*. More specifically, it is

*real and even*.

### Sample Autocorrelation

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

### Sample Power Spectral Density

See §6.5.**Next Section:**

White Noise

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Random Variables & Stochastic Processes