Convolutions

$$(f\ast g)(t)={\int }_0^{t}f(t-v)g(v)dv$$

Properties

• $f\ast g=g\ast f$
• $f\ast (g+h)=(f\ast g)+(f\ast h)$
• $(f\ast g)\ast h=f\ast (g\ast h)$
• $f\ast 0=0$

Convolution Theorem

$$\mathcal{L}\{f\ast g\}=F(s)G(s)$$