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Electrical Engineering 120 - Fall 1998 - Kahn - Final Exam

# Electrical Engineering 120 - Fall 1998 - 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 1998 Final Examination, Wednesday, December 16, 1998, 5-8 pm NAME: 1. The exam is closed-book. You are permitted to use three, two-sided pages of notes. No Problem 1 (15 pts.) The equivalent noise bandwidth of a CT LTI system is defined as: . Find the value of BW for the system having the following impulse response. h t ( 29 FT H j ϖ ( 29 BW 1 2 π ------ H j ϖ ( 29 2 H j 0 ( 29 2 --------------------- ϖ d = h t ( 29 t 2 1 - 1 0 1 2 3 4 5 6 h t ( 29 0 for t 0 and t 6 < = Note to students in Fall 99: Only problems 1, 2, 5, 6 would be appropriate for your Midterm 2.

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2 Problem 2 (25 pts.) The CT LTI system shown here can model many simple situations that produce echoes. Here, K and are real constants, and . (a) (10 pts.) Find an expression for the impulse response . (b) (10 pts.) For what values of K is the system stable? Justify your answer. (c) (5 pts.) Let , and assume . Sketch . 0 x t ( 29 y t ( 29 Σ + + gain K delay delay h t ( 29 K 1 = x t ( 29 u t ( 29 u t 2 ( 29 = y t ( 29
3 Problem 3 (40 pts.) Consider a DT system described by the difference equation: . (a) (5 pts.) Sketch a realization of this system using only two delay elements. (b) (5 pts.) Find the transfer function . (c) (5 pts.) Plot the poles and zeros and indicate the region of convergence of . (d) (5 pts.) Is the system BIBO stable? Justify your answer. y n [ ] y n 1 [ ] 2 y n 2 [ ] + x n [ ] x n 1 [ ] + = H z ( 29 H z ( 29 Re z { } Im z { }

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4 (e) (5 pts.) Find the impulse response .
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