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ListConvolve
ListConvolve[ker, list]
forms the convolution of the kernel ker with list.
ListConvolve[ker, list, k]
forms the cyclic convolution in which the k
element of ker is aligned with each element in list.
ListConvolve[ker, list, {kL, kR}]
forms the cyclic convolution whose first element contains 
and whose last element contains 
.
ListConvolve[ker, list, klist, p]
forms the convolution in which list is padded at each end with repetitions of the element p.
ListConvolve[ker, list, klist, {p1, p2, ...}]
forms the convolution in which list is padded at each end with cyclic repetitions of the 
.
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.
ListConvolve[ker, list, klist, padding, g, h, lev]
forms a convolution using elements at level lev in ker and list.
Details
- 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. - ListConvolve[ker, list] gives a result of length Length[list]-Length[ker]+1.
- ListConvolve[ker, list] allows no overhangs and is equivalent to ListConvolve[ker, list, {-1, 1}].
- ListConvolve[ker, list, k] is equivalent to ListConvolve[ker, list, {k, k}].
- The values of
and 
in ListConvolve[ker, list, {kL, kR}] determine the amount of overhang to allow at each end of list. - Common settings for
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 - With maximal overhang at one end only, the result from ListConvolve is the same length as list.
- ListConvolve[ker, list, {kL, kR}, padlist] effectively lays down repeated copies of padlist, then superimposes one copy of list on them and forms a convolution of the result.
- Common settings for padlist are:
-
p pad with repetitions of a single element {p1,p2,...} pad with cyclic repetitions of a sequence of elements list pad by treating list as cyclic (default) {} do no padding - ListConvolve works with multidimensional kernels and lists of data.
- ListConvolve[ker, list, {{kL1, kL2, ...}, {kR1, kR2, ...}}] forms the cyclic convolution whose
element contains 
, and whose 
element contains 
. 
is taken to be equivalent to 
. - 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.
- ListConvolve works with exact numbers and symbolic data as well as approximate numbers.
