Convolution

A binary operation that combines two functions (or sequences) into a third by integrating (or summing) the product of one function with a shifted copy of the other: (f * g)(t) = ∫ f(τ) g(t−τ) dτ (or discrete analogue).

A binary operation on functions, measures, or distributions defined (in the classical case) by (f * g)(x) = ∫ f(y) g(x − y) dy (or an analogous formula on groups) that produces a combined function used for smoothing, filtering, and representing translation-invariant linear operators.