Probability, Random Variables, and Random Processes: Theory and Signal Processing Applications

5.20 CORRELATION AND COVARIANCE MATRICES

Consider random vector consisting of N random variables {Xn}.

Definition: Autocorrelation Matrix The autocorrelation matrix of random vector is

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The (m, n)th component is where m is the row and n is the column.

Let consist of M random variables {Ym}.

Definition: Cross-Correlation Matrix The cross-correlation matrix of random vectors and is

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Assume that the random variables of a random vector are mutually correlated to some degree. The elements of a random vector can be transformed via multiplication by a matrix to a new set of random variables that are uncorrelated. Consider the transformation Y = AX, where so that

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The ...