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ListConvolve

FilledSmallSquare ListConvolve[ker, list] forms the convolution of the kernel ker with list.

FilledSmallSquare ListConvolve[ker, list, k] forms the cyclic convolution in which the k element of ker is aligned with each element in list.

FilledSmallSquare ListConvolve[ker, list, , ] forms the cyclic convolution whose first element contains list[[1]] ker[[]] and whose last element contains list[[-1]] ker[[]].

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

FilledSmallSquare ListConvolve[ker, list, klist, , , ... ] forms the convolution in which list is padded at each end with cyclic repetitions of the .

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

FilledSmallSquare ListConvolve[ker, list, klist, padding, g, h, lev] forms a convolution using elements at level lev in ker and list.

FilledSmallSquare With kernel and list , ListConvolve[ker, list] computes , where the limits of the sum are such that the kernel never overhangs either end of the list.

FilledSmallSquare Example: ListConvolve[x,y, a,b,c] LongRightArrow.

FilledSmallSquare ListConvolve[ker, list] gives a result of length Length[list]-Length[ker]+1.

FilledSmallSquare ListConvolve[ker, list] allows no overhangs and is equivalent to ListConvolve[ker, list, -1, 1].

FilledSmallSquare ListConvolve[ker, list, k] is equivalent to ListConvolve[ker, list, k, k].

FilledSmallSquare The values of and in ListConvolve[ker, list, , ] determine the amount of overhang to allow at each end of list.

FilledSmallSquare Common settings for , are:

FilledSmallSquare Examples: ListConvolve[x,y, a,b,c, 1,1] LongRightArrow.

FilledSmallSquare ListConvolve[x,y, a,b,c, 1,-1] LongRightArrow.

FilledSmallSquare With maximal overhang at one end only, the result from ListConvolve is the same length as list.

FilledSmallSquare ListConvolve[ker, list, , , padlist] effectively lays down repeated copies of padlist, then superimposes one copy of list on them and forms a convolution of the result.

FilledSmallSquare Common settings for padlist are:

FilledSmallSquare ListConvolve works with multidimensional kernels and lists of data.

FilledSmallSquare ListConvolve[ker, list, , , ... , , , ... ] forms the cyclic convolution whose 1,1,... element contains ker[[, , ... ]] list[[1,1,... ]] and whose -1,-1,... element contains ker[[, , ... ]] list[[-1,-1,... ]].

FilledSmallSquare , is taken to be equivalent to , , ... , , , ... .

FilledSmallSquare When a function h is specified to use in place of Plus, explicit nested h expressions are generated with a depth equal to the depth of ker.

FilledSmallSquare ListConvolve works with exact numbers and symbolic data as well as approximate numbers.

FilledSmallSquare See Section 3.8.5.

FilledSmallSquare Implementation Notes: see Section A.9.4.

FilledSmallSquare See also: ListCorrelate, Partition, Inner, CellularAutomaton, PadLeft.

FilledSmallSquare New in Version 4.

Further Examples