This is documentation for Mathematica 8, which was
based on an earlier version of the Wolfram Language.

ListCorrelate

 ListCorrelateforms the correlation of the kernel ker with list. ListCorrelateforms the cyclic correlation in which the k element of ker is aligned with each element in list. ListCorrelateforms the cyclic correlation whose first element contains and whose last element contains . ListCorrelateforms the correlation in which list is padded at each end with repetitions of the element p. ListCorrelateforms the correlation in which list is padded at each end with cyclic repetitions of the . ListCorrelateforms a generalized correlation in which g is used in place of Times and h in place of Plus. ListCorrelateforms a correlation using elements at level lev in ker and list.
• With kernel and list , ListCorrelate computes , where the limits of the sum are such that the kernel never overhangs either end of the list.
• For higher-dimensional lists, ker must be reversed at every level.
 {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
Correlate a kernel with a list of data:
Make a cyclic correlation the same length as the original data:
Align element 2 in the kernel with successive elements in the data:
Two-dimensional correlation:
Correlate a kernel with a list of data:
 Out[1]=

Make a cyclic correlation the same length as the original data:
 Out[1]=
Align element 2 in the kernel with successive elements in the data:
 Out[2]=

 Out[1]=

Two-dimensional correlation:
 Out[1]=
 Scope   (5)
Use exact arithmetic to compute the correlation:
Use machine arithmetic:
Use 24-digit precision arithmetic:
Correlation of complex data:
Two-dimensional correlation:
Cyclic two-dimensional correlation:
Two-dimensional correlation with maximal overhangs and zero padding:
Use functions f and g in place of Plus and Times:
Use functions f and g in place of Plus and Times with maximal overhangs and zero padding:
Use functions f and g in place of Plus and Times with maximal overhangs and empty padding:
 Applications   (6)
Smooth data with a weighted running average:
Normalized Gaussian profile for averaging weights:
Gaussian smoothing of an image:
Gaussian kernel with a 5×5 pixel stencil:
Smooth the image:
Edge detection in an image:
Correlate with a Laplacian filter kernel:
Use a Laplacian of a Gaussian filter kernel:
Generate Pascal's triangle: