Use this result to find the convolution of ht with xt where

Question

1. The response of a system to the complex exponentlal e^j5t is te^j5t,

e^j5t → te^j5t

Which of the followiug statements is sive, led given an explanation for why smu choite your answer:

(a) This system is definitely LTI (linear and time-invariant).

(b) This system could be linear and time-freesia. but there not enough informetion to tell.

(c) This system is definitely not LTI.

2.

(a) Prove that

y(t)= x(t) * h(t) = {dx(t)/dt}*{h(t)*u(t)}

(b) Use this result to find the convolution of h(t) with x(t) where

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

and x(t) as Wore below, by fire performing the convolution h(t)*u(t) and then cenvolving this with x'(t).