Solution4

Solution4 - EE 200 Fall 2008 (Weber) Homework 4 Solutions...

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EE 200 – Fall 2008 (Weber) Homework 4 Solutions 1. Problem 8 x ( t ) = 1 + cos( πt ) + cos(2 πt ) = e i 0 t + 0 . 5 e iπt + 0 . 5 e iπt + 0 . 5 e i 2 πt + 0 . 5 e i 2 πt y ( t ) = H (0) e i 0 t + 0 . 5 H ( π ) e iπt + 0 . 5 H ( - π ) e iπt + 0 . 5 H (2 π ) e i 2 πt + 0 . 5 H ( - 2 π ) e i 2 πt = (1) e i 0 t + 0 . 5( - 1) e iπt + 0 . 5( - 1) e iπt + 0 . 5(0) e i 2 πt + 0 . 5(0) e i 2 πt = 1 - cos( πt ) 2. Problem 10 a. Linear time invariant b. Linear time invariant c. Linear (not time invariant) d. Linear (not time invariant) e. Time invariant (not linear) f. Time invariant (not linear) 3. Problem 14 Since the only thing you know about the response of the system is what the output is for the x ( t ) described in the problem, you have to come up expressions for x ( t ) that are linear, time-shifted combinations of x ( t ). This will result in the output being linear, time-shifted combinations of y ( t ). a.
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Solution4 - EE 200 Fall 2008 (Weber) Homework 4 Solutions...

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