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| The '''autocorrelation matrix''' is used in various digital signal processing algorithms. It consists of elements of the discrete ] function, <math>R_{xx}(j)</math> arranged in the following manner: | |||
| {{R with history}} | |||
| :<math>\mathbf{R_x} = \begin{bmatrix} | |||
| R_{xx}(0) & R_{xx}(1) & R_{xx}(2) & \cdots & R_{xx}(N-1) \\ | |||
| R_{xx}(1) & R_{xx}(0) & R_{xx}(1) & \cdots & R_{xx}(N-2) \\ | |||
| R_{xx}(2) & R_{xx}(1) & R_{xx}(0) & \cdots & R_{xx}(N-3) \\ | |||
| \vdots & \vdots & \vdots & \ddots & \vdots \\ | |||
| R_{xx}(N-1) & R_{xx}(N-2) & R_{xx}(N-3) & \cdots & R_{xx}(0) \\ | |||
| \end{bmatrix} | |||
| </math> | |||
| This is clearly a ]. More specifically because <math>R_{xx}(j) = R_{xx}(\!-j) = R_{xx}(N-j)</math>, it is a ]. | |||
| ] | |||
| == References == | |||
| * Hayes, Monson H., ''Statistical Digital Signal Processing and Modeling'', John Wiley & Sons, Inc., 1996. ISBN 0-471-59431-8. | |||
| {{Uncategorized|date=August 2010}} | |||
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