Electrical Engineering 120 - Fall 1997 - Kahn - Final Exam

# Electrical Engineering 120 - Fall 1997 - Kahn - Final Exam...

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University of California at Berkeley Department of Electrical Engineering and Computer Sciences Professor J.M. Kahn, EECS 120, Fall, 1997 Final Examination, Wednesday, December 17, 1997, 5-8 pm NAME: 1. The exam is closed-book. You are permitted to use three, two-sided pages of notes. No calculators are permitted. 2. Do all work in the space provided. If you need more room, use the back of previous page. 3. Indicate your answer clearly by circling it or drawing a box around it. Problem 1 (75 pts.) A LTI discrete-time system with input x [ n ] and output y [ n ] has an impulse response: . A sketch of h [ n ] is shown here. (a) (5 pts.) Give a closed-form expression for the system transfer function H ( z ). P r o b l e m 123456 T O T A L Points 75 30 30 25 30 10 200 Score hn [] 12 1 3 --   n 1 2 n un = 0 2 4 6 8 10 -2 -1 0 1 2 n h [ ]

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2 (b) (5 pts.) Find the poles and zeros of H ( z ),andsketchthemonthe z -plane below. (c) (5 pts.) Find the output y [ n ] when input is . (d) (5 pts.) Clearly the frequency response exists. Sketch the magnitude response , labeling the vertical and horizontal axes of your plot. Re( z ) Im( z ) 1 xn [] 3 n n 2200 , = He j (29 j j
3 (e) (10 pts.) Evaluate without explicitly using the expression for . (f) (10 pts.) Evaluate without explicitly using the expression for .

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## This note was uploaded on 05/17/2009 for the course EE 120 taught by Professor Ayazifar during the Spring '09 term at Berkeley.

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Electrical Engineering 120 - Fall 1997 - Kahn - Final Exam...

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