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The **autocorrelation matrix** is used in various digital signal processing algorithms. It consists of elements of the discrete autocorrelation function, arranged in the following manner:

This is clearly a Hermitian matrix and a Toeplitz matrix. If is wide-sense stationary then its autocorrelation matrix will be nonnegative definite.

The *autocovariance matrix* is related to the autocorrelation matrix as follows:

Where is a vector giving the mean of signal at each index of time.

- Hayes, Monson H.,
*Statistical Digital Signal Processing and Modeling*, John Wiley & Sons, Inc., 1996. ISBN 0-471-59431-8.