Introduction
We call the convolution product between two functions x(t) and h(t), the operation * defined by :
\(\left(x\ast h\right)(t)=\int_{-\infty}^{+\infty}x\left(\tau\right)h\left(t-\tau\right)d\tau\)
If the impulse response of a linear system (like a filter, for example) is represented by the function h(t), the signal output y(t) is obtained as the convolution product of the input x(t) with the impulse response h(t).
The convolution product quantifies the extent of overlap between a function x(t) when shifted across another function ℎ(t); it serves as a function mixer.