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Homework4 - EE 200 Fall 2009(Weber Homework 4 At the upper...

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EE 200 – Fall 2009 (Weber) Homework 4 At the upper right corner on page 1 of all homeworks, show: Last name, First name Date EE 200, Homework # Show intermediate steps whenever possible. 1. Three systems are connected in cascade: the output of S 1 goes to the input of S 2 , the output of S 2 is the input to S 3 . The systems are specified as follows. S 1 : y 1 [ n ] = x 1 [ n ] - x 1 [ n - 1] S 2 : y 2 [ n ] = x 2 [ n ] + x 2 [ n - 2] S 3 : y 3 [ n ] = x 3 [ n - 1] + x 3 [ n - 2] a. What is the frequency response of the overall system, S , with input x [ n ] = x 1 [ n ] and output y [ n ] = y 3 [ n ]? b. Based on your result in part a, Write a difference equation similar to the ones above that describes the system S in terms of x [ n ] and y [ n ]. 2. A system has an impulse response of h [ n ] = δ [ n ] - δ [ n - 3]. a. What is the frequency response of the system? b. Determine the output of the system when the input is x [ n ] = cos(2 πn/ 3) c. Determine the output of the system when the input is x [ n ] = cos( πn/ 3 + π/ 2). d. Determine the output of the system when the input is x [ n ] = cos( πn/ 6 + π/ 2). 3. For each of the following frequency responses, determine the impulse response h [ n ]. a. H ( e j ˆ ω ) = 3 + 4 e - j ω b. H ( e j ˆ ω ) = 5 e - j ω cos(ˆ ω ) c. H ( e j ˆ ω ) =
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