Cross-correlation

In statistics, the term cross-correlation is sometimes used to refer to the covariance cov(X, Y) between two random vectors X and Y, in order to distinguish that concept from the "covariance" of a random vector X, which is understood to be the matrix of covariances between the scalar components of X.

Related Topics:
Statistics - Covariance - Random vector - Matrix of covariances

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In signal processing, the cross-correlation (or sometimes "cross-covariance") is a measure of similarity of two signals, commonly used to find features in an unknown signal by comparing it to a known one. It is a function of the relative time between the signals, is sometimes called the sliding dot product, and has applications in pattern recognition and cryptanalysis.

Related Topics:
Signal processing - Signal - Time - Dot product - Pattern recognition - Cryptanalysis

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For discrete functions fi and gi the cross-correlation is defined as

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:(fstar g)_i equiv sum_j f^*_j,g_{i+j}

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where the sum is over the appropriate values of the integer j  and an asterisk indicates the complex conjugate. For continuous functions f (x) and g i the cross-correlation is defined as

Related Topics:
Integer - Complex conjugate

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:(fstar g)(x) equiv int f^*(t) g(x+t),dt

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where the integral is over the appropriate values of t.

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The cross-correlation is similar in nature to the convolution of two functions.

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