Cross-correlation matrix: Difference between revisions

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[[File:Comparison_convolution_correlation.svg|thumb|300px|Visual comparison of [[convolution]], [[cross-correlation]] and [[autocorrelation]].]]

A '''correlation function''' is a [[function (mathematics)|function]] that gives the statistical [[correlation]] between [[random variable]]s, contingent on the spatial or temporal distance between those variables. If one considers the correlation function between random variables representing the same quantity measured at two different points then this is often referred to as an [[auto-correlationautocorrelation function]], which is made up of [[auto-correlationautocorrelation]]s. Correlation functions of different random variables are sometimes called '''cross-correlation functions''' to emphasisemphasize that different variables are being considered and because they are made up of [[cross-correlation]]s.

Correlation functions are a useful indicator of dependencies as a function of distance in time or space, and they can be used to assess the distance required between sample points for the values to be effectively uncorrelated. In addition, they can form the basis of rules for interpolating values at points for which there are no observations.