Topics: Complex Exponentials and LTI Systems

Exercise 1. CONTINUOUS-TIME SYSTEM RESPONSE GIVEN COMPLEX EXPONENTIAL INPUT

(i) Consider an LTI system with impulse response h(t)=e5u(t). What is the output y(t) when the input

is r(t) = ³³

(ii) For the same system, find the output y(t) if the input is more generally r(t) = e. Note that this is a

function of w. Also, find the magnitude ly(t)] and sketch as a function of w.

(iii) For the same system, suppose now the input is r(t) = cos(2t) sin(t). What is the output y(t)? (Hint:

use the linearity of the system.)