Convolution is a fundamental operation in signal and system analysis. It combines two functions to produce a third that represents how the shape of one is modified by the other.
\[ (f * g)(x) = \int_{-\infty}^{\infty} f(u)g(x-u)du \]
\[ f * g = g * f \quad ; \quad f * (g * h) = (f * g) * h \]
\[ f(x)g(x) \iff F(s) * G(s) \]