Electrical Engineering 120 - Fall 1998 - Kahn - Final Exam

Electrical - University of California at Berkeley Department of Electrical Engineering and Computer Sciences Professor J M Kahn EECS 120 Fall 1998

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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: 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. ht (29 FT H j ϖ BW 1 2 π ------ Hj ϖ 2 0 2 --------------------- ϖ d = t 2 1 - 1 0123456 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 xt (29 yt Σ + + gain K delay delay ht K 1 = ut 2 =
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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. yn [] 1 2 2 + xn 1 + = Hz (29 Re z {} Im z
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4 (e) (5 pts.) Find the impulse response . (f) (5 pts.) Let the input be , . Find , . (g) (10 pts.) Let the input be , . (If you are interested in the initial conditions, they are fully specified by our specification of the input signal.) Find , . Explain why, as , doesn’t agree with the result found in part (f).
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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 University of California, Berkeley.

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Electrical - University of California at Berkeley Department of Electrical Engineering and Computer Sciences Professor J M Kahn EECS 120 Fall 1998

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