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 positive 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.
- Solomon W. Golomb, and Guang Gong. Signal design for good correlation: for wireless communication, cryptography, and radar. Cambridge University Press, 2005.
- M. Soltanalian. Signal Design for Active Sensing and Communications. Uppsala Dissertations from the Faculty of Science and Technology (printed by Elanders Sverige AB), 2014.