Convolution Integral Properties

benfrankballi

how would I show that y'(t) = x(t) * h'(t) and y'(t) = x'(t) * h(t)

I know that in an LTI system y(t) = x(t) * h(t) = [itex]\int[/itex] x([itex]\tau[/itex]) * h(t-[itex]\tau[/itex]) from [itex]\infty[/itex] to -[itex]\infty[/itex]

But how would I go about trying to prove the first two equations?

jackmell

Why not just differentiate the convolution integral:

[tex]\frac{d}{dt}\int_{-\infty}^{\infty} x(\tau) h(t-\tau)d\tau=\int_{-\infty}^{\infty} x(\tau)h'(t-\tau)d\tau=x(t)*h'(t)[/tex]