The *convolution operation* is a mathematical operation which
takes two functions *f*(*x*) and *g*(*x*) and produces a third function
*h*(*x*). Mathematically, convolution is defined as:

In spatial domain image processing, you discretize the
operation. *f*(*x*) becomes an array of pixels *F*[*x*]. The kernel
*g*(*x*) is an array of values
*G*[0...(*width*-1)] (assume finite
support). Equation 13 becomes: