# ELEC 242 - Midterm 1.2 Solution (2016-W).doc - ELEC242-W...

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ELEC242-W Continuous-Time Signals and Systems Question 1: Consider a continuous-time system which has input of ) ( t x and the output of dt t x t x e t y jt t ) ( ) ( ) ( 2 . Evaluate the output signal ) ( t y , if the input is ) ( ) ( t t x . Solution 1: dt t e dt t e dt t t e dt t x t x e t y jt t jt t jt t jt t ) ( ) ( ) ( ) ( ) ( ) ( ) ( 2 2 2 2 j j j e dt t e dt t e dt t e dt t e t y 2 2 0 2 0 1 ) ( ) ( ) ( ) ( ) ( 2 2 2 2 2 1 0 1 1 sin cos 1 1 1 ) ( e e j e e e e t y j j 2 1 ) ( e t y Question 2: Consider a continuous-time system which has input of ) ( t x and output of ) 2 3 ( ) ( t x t y . If the input signal is ) 1 ( ) ( ) ( t u t u t t x , draw the input signal ) ( t x and output signal ) ( t y with respect to time.

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