BUILT-IN MATHEMATICA SYMBOL

# ListCorrelate

ListCorrelate[ker, list]
forms the correlation of the kernel ker with list.

ListCorrelate[ker, list, k]
forms the cyclic correlation in which the k element of ker is aligned with each element in list.

ListCorrelate[ker, list, {kL, kR}]
forms the cyclic correlation whose first element contains and whose last element contains .

ListCorrelate[ker, list, klist, p]
forms the correlation in which list is padded at each end with repetitions of the element p.

ListCorrelate[ker, list, klist, {p1, p2, ...}]
forms the correlation in which list is padded at each end with cyclic repetitions of the .

ListCorrelate[ker, list, klist, padding, g, h]
forms a generalized correlation in which g is used in place of Times and h in place of Plus.

ListCorrelate[ker, list, klist, padding, g, h, lev]
forms a correlation using elements at level lev in ker and list.

## DetailsDetails

• With kernel and list , ListCorrelate[ker, list] computes , where the limits of the sum are such that the kernel never overhangs either end of the list.
• For a one-dimensional list ListCorrelate[ker, list] is equivalent to ListConvolve[Reverse[ker], list].
• For higher-dimensional lists, ker must be reversed at every level.
• Settings for and are negated in ListConvolve relative to ListCorrelate.
• Common settings for in ListCorrelate are:
•  {1,-1} no overhangs (default) {1,1} maximal overhang at the right-hand end {-1,-1} maximal overhang at the left-hand end {-1,1} maximal overhangs at both beginning and end

## ExamplesExamplesopen allclose all

### Basic Examples (4)Basic Examples (4)

Correlate a kernel with a list of data:

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Make a cyclic correlation the same length as the original data:

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Align element 2 in the kernel with successive elements in the data:

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Pad with instead of using the data cyclically:

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Two-dimensional correlation:

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