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:

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:

ListCorrelate works with TimeSeries:

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:

ListCorrelate is equivalent to ListConvolve with the kernel reversed:

Generate two random vectors:

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:

Generate two random vectors:

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: