An LTI system has an impulse response h (t) = 2 e ?3t u (t) .
(a) Write an expression for h (t) ? u (t) .
(b) Let the excitation of the system be x (t) = u (t) ? u (t ? 1/3) . Write an expression for the response y (t) .
(c) Find the numerical value of y (t) at t = 1/2.
0.2556,
y (t) = (2/3) [ (1 ? e ?3t ) u (t) ? (1 ? e ?3 (t?1/3) ) u (t ? 1/3) ] ,
h (t) ? u (t) = (2/3) (1 ? e ?3t ) u (t)
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