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Homework 4 - University of Southern California Ming-Hsieh...

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University of Southern California Ming-Hsieh Department of Electrical Engineering Homework 4, EE 200L, Fall 2008, Ali Zadeh ____________________________________________________________________________________ (1) Consider the following Discrete-Time Linear-Time Invariant (DT-LTI) system with impulse response h(n) x(n) y(n) h(n)=½ [ δ( n 29 δ n -1 29] (a) Using Convolution sum, find the output response y(n) when the input signal x(n) is a unit step function. < = = 0 0 0 1 n , n , ) n ( u ) n (x (b) Using Convolution sum, find the output response y(n) when the input signal x(n) is : ) n (u ) n ( Cos ) n (u ) ( ) n (x n π = - = 1 (c) Find the output response y(n) when the input signal x(n) is : ) n (u ) ( e e e ) n (u ) n (x n n ) (i n ) (i n ) (i 1 4 3 3 3 2 4 3 2 4 - + + + + = π π π (d) Find the frequency response of the system H( ϖ ) using complex exponential input signal. (e) Find the frequency response of the system using impulse response h(n). Does this match the answer in part (c)?
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