Generic Definition

convolution is a mathematical operator which takes two functions f and g and produces a third function that, in a sense, represents the amount of overlap between f and a reversed and translated version of g

Mathematical Definition

$ f \ast g = \int_{-\infty}^{\infty}f(\tau)g(t-\tau)dt $

Descriptive Definition

The convolution of two functions results in a new function that is a product of the overlap of the two functions when one is flipped across the x-axis and then shifted from $ {-\infty} $ to $ \infty $. It is easily demonstrated visually and can be used to find the output of an LTI system. The output is simply the convolution of the input and the system's impulse response.