Multidimensional discrete convolution

Visualization of Convolution between two Simple Two-Dimensional Signals

Both figures represent cascaded systems. Note that the order of the filters does not effect the output.

A system with a set of parallel filters.

Original image (left) and image after passing through edge-detecting filter (right)

In signal processing, multidimensional discrete convolution refers to the mathematical operation between two functions f and g on an n-dimensional lattice that produces a third function, also of n-dimensions. Multidimensional discrete convolution is the discrete analog of the multidimensional convolution of functions on Euclidean space. It is also a special case of convolution on groups when the group is the group of n-tuples of integers.

单词	Multidimensional Convolution
释义	Multidimensional Convolution 英语百科 Multidimensional discrete convolution In signal processing, multidimensional discrete convolution refers to the mathematical operation between two functions f and g on an n-dimensional lattice that produces a third function, also of n-dimensions. Multidimensional discrete convolution is the discrete analog of the multidimensional convolution of functions on Euclidean space. It is also a special case of convolution on groups when the group is the group of n-tuples of integers.
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Multidimensional Convolution

Multidimensional discrete convolution