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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^(th) 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.
  • 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 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
EXAMPLESCLOSE ALL
Basic Examples   (4)
Correlate a kernel {x, y} 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:
Pad with zzz instead of using the data cyclically:
Two-dimensional correlation:
Correlate a kernel {x, y} with a list of data:
In[1]:=
Click for copyable input
Out[1]=
 
Make a cyclic correlation the same length as the original data:
In[1]:=
Click for copyable input
Out[1]=
Align element 2 in the kernel with successive elements in the data:
In[2]:=
Click for copyable input
Out[2]=
 
Pad with zzz instead of using the data cyclically:
In[1]:=
Click for copyable input
Out[1]=
 
Two-dimensional correlation:
In[1]:=
Click for copyable input
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:
Generalizations & Extensions   (3)
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:
Additive cellular automata:
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   (2)
ListCorrelate is equivalent to ListConvolve with the kernel reversed:
Cyclic correlation is equivalent to multiplication in the discrete Fourier transform domain:
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