Convolution

There are several possible notations to indicate the convolution of two (multi-dimensional) signals to produce an output signal. The most common are:

We shall use the first form

In 2D continuous space:

In 2D discrete space:

Properties of Convolution

There are a number of important mathematical properties associated with convolution.

Convolution is commutative.

Convolution is associative.

Convolution is distributive.

where a, b, c, and d are all images, either continuous or discrete.