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