Overlap–add method

In signal processing, the overlap–add method is an efficient way to evaluate the discrete convolution of a very long signal ${\displaystyle x[n]}$ with a finite impulse response (FIR) filter ${\displaystyle h[n]}$:

where ${\displaystyle h[m]=0}$ for ${\displaystyle m}$ outside the region ${\displaystyle [1,M].}$ 

This article uses common abstract notations, such as ${\textstyle y(t)=x(t)*h(t),}$ or ${\textstyle y(t)={\mathcal {H}}\{x(t)\},}$ in which it is understood that the functions should be thought of in their totality, rather than at specific instants ${\textstyle t}$ (see Convolution#Notation).