Convolution
Definition
Wikipedia:
In mathematics (in particular, functional analysis), convolution is a mathematical operation on two functions ($f$ and $g$) that produces a third function $\left. (f*g) \right.$ 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. It is defined as the integral of the product of the two functions after one is reversed and shifted. And the integral is evaluated for all values of shift, producing the convolution function.
Wolfram:
A convolution is an integral that expresses the amount of overlap of one function g as it is shifted over another function $f$. It therefore “blends” one function with another.
Abstractly, a convolution is defined as a product of functions $f$ and $g$ that are objects in the algebra of Schwartz_functions in $\mathbb{R}^{n}$. Convolution of two functions $f$ and $g$ over a finite range $\left. \lbrack 0,t\rbrack \right.$ is given by
$$ \left. \lbrack f*g\rbrack \right.\left. (t) \right. = \int_{0}^{t}f\left. (\tau) \right.g\left. (t - \tau) \right.d\tau $$where $\left. \lbrack f*g\rbrack \right.$ denotes the convolution of $f$ and $g$.
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