Question

With an example explain the Graphical representation of convolution.

Answer 1

In mathematics (and, in particular, functional analysis) convolution is a mathematical operation on two functions (f and g) to produce a third function that expresses how the shape of one is modified by the other. The term convolution refers to both the result function and to the process of computing it. Convolution is similar to cross-correlation. For discrete, real-valued functions, they differ only in a time reversal in one of the functions. For continuous functions, the cross-correlation operator is the adjoint of the convolution operator.
It has applications that include probability, statistics, computer vision, natural language processing, image and signal processing, engineering, and differential equations.[citation needed]
The convolution can be defined for functions on Euclidean space, and other groups.[citation needed] For example, periodic functions, such as the discrete-time Fourier transform, can be defined on a circle and convolved by periodic convolution. (See row 13 at DTFT § Properties.) A discrete convolution can be defined for functions on the set of integers.
Generalizations of convolution have applications in the field of numerical analysisand numerical linear algebra, and in the design and implementation of finite impulse response filters in signal processing.[citation needed]
Computing the inverse of the convolution operation is known as deconvolution