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 list[[1]]ker[[kL]] and whose last element contains list[[-1]]ker[[kR]].
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 pi.
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.
Details
- With kernel Kr and list as, 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 kL and kR are negated in ListConvolve relative to ListCorrelate.
- Common settings for {kL,kR} 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
Examples
open allclose allBasic Examples (4)
Scope (5)
Generalizations & Extensions (4)
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:
ListCorrelate works with TimeSeries:
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:
Correlate with a Laplacian filter kernel:
Use a Laplacian of a Gaussian filter kernel:
Apply a finite difference formula to a uniformly sampled function:
Show the error for different numbers of grid points:
Show the error for different numbers of grid points for a second derivative approximation:
Properties & Relations (3)
ListCorrelate is equivalent to ListConvolve with the kernel reversed:
A function for constructing a circulant matrix from a vector:
Cyclic correlation is equivalent to multiplication with a circulant matrix:
Cyclic correlation is also equivalent to multiplication in the discrete Fourier transform domain:
A function for constructing an upper triangular Toeplitz matrix from a vector:
Cyclic correlation with zero-padding is equivalent to multiplication with an upper triangular Toeplitz matrix:
Text
Wolfram Research (1999), ListCorrelate, Wolfram Language function, https://reference.wolfram.com/language/ref/ListCorrelate.html.
CMS
Wolfram Language. 1999. "ListCorrelate." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/ListCorrelate.html.
APA
Wolfram Language. (1999). ListCorrelate. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/ListCorrelate.html