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Convolution Integral Properties 
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#1
Sep3011, 09:55 PM

P: 2

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? 


#2
Oct111, 05:35 PM

P: 1,666

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] 


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