In
mathematics and, in particular,
functional analysis,
convolution is a
mathematical operation on two
functions
f and
g, producing a third function that is typically viewed as a modified version of one of the original functions, giving the integral of the
pointwise multiplication of the two functions as a function of the amount that one of the original functions is
translated. Convolution is similar to
cross-correlation. It has applications that include
probability,
statistics,
computer vision,
natural language processing,
image and
signal processing,
engineering, and
differential equations.