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autocorrelation matrix : ウィキペディア英語版
autocorrelation matrix
The autocorrelation matrix is used in various digital signal processing algorithms. It consists of elements of the discrete autocorrelation function, R_(j) arranged in the following manner:
:\mathbf_x = E() = \begin
R_(0) & R^
*_(1) & R^
*_(2) & \cdots & R^
*_(N-1) \\
R_(1) & R_(0) & R^
*_(1) & \cdots & R^
*_(N-2) \\
R_(2) & R_(1) & R_(0) & \cdots & R^
*_(N-3) \\
\vdots & \vdots & \vdots & \ddots & \vdots \\
R_(N-1) & R_(N-2) & R_(N-3) & \cdots & R_(0) \\
\end

This is clearly a Hermitian matrix and a Toeplitz matrix. If \mathbf is wide-sense stationary then its autocorrelation matrix will be positive definite.
The ''autocovariance matrix'' is related to the autocorrelation matrix as follows:
:
\mathbf_x = \operatorname (- \mathbf_x)(\mathbf - \mathbf_x)^H )
=
\mathbf_x - \mathbf_x\mathbf_x^H

Where \mathbf_x is a vector giving the mean of signal \mathbf 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.
* 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.

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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