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Stuck in convolution

Guest TaNGo
Guest TaNGo
in Analysis and Calculus

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Hello,

I'm stuck in a convolution question.

 

x(t) = u(t) - 2u(t-2) + u(t-5)

h(t) = e^(2t) u(1-t)

y(t) = x(t) * h(t)

 

(I'm using capital T as tao and Int as integral from minus infinity to plus infinity)

 

y(t) = Int ( x(t-T) h(T) ) dT

 

= Int ( u(t-T)-2u(t-T-2)+u(t-T-5)[e^(2T)u(1-T)] )dT

 

= Int ( [e^(2T)u(1-T)] u(t-T) ) - Int ....

------------------------------------------

 

I'm going to set integral limits due to the interval that the step functions are nonzero. So:

 

1-T > 0 -> T < 1

t-T > 0 -> T < t

 

But the T is smaller than both 1 and t...

 

so.. What do I have to take as integral limits? I'm stuck here.

 

Thank you for your assistance.

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