ListConvolve

ListConvolve[ker, list] gives a convolution of list using kernel ker.

Examples

ListConvolve[{1, 2, 1}, {1, 4, 8, 10, 8, 4, 1}]

ker = {1, 2, 1};
data = ListConvolve[ker, {1, 0, 0, 0, 1}];
data

Please visit the official Wolfram Language Reference for more details.

2D example

ker2 = {{1, 2, 1}, {2, 4, 2}, {1, 2, 1}};
data2 = {{1, 0, 0, 0}, {0, 1, 0, 0}, {0, 0, 1, 0}, {0, 0, 0, 1}};
ListConvolve[ker2, data2]

Padding and alignment

The third argument controls alignment and cyclic behavior, while explicit padding is supplied as the fourth argument. For example, ListConvolve[ker, list, k] makes a cyclic convolution aligning the k-th element of ker with each element of list, and ListConvolve[ker, list, {kL, kR}] specifies left/right alignment.

To pad the input at each end use a padding argument p (a single value) or a list of padding values. For example, padding with zeros:

ListConvolve[{1, 2, 1}, {1, 0, 0, 0, 1}, {2, 2}, 0]

Or supply a list of padding values that will be repeated cyclically:

ListConvolve[{1, 2, 1}, {1, 0, 0, 0, 1}, {2, 2}, {a, b}]

See the Wolfram Language reference for additional forms (generalized convolutions and level specifications).