Electrical Engineering 120 - Fall 1996 - Kahn - Final Exam

Electrical Engineering 120 - Fall 1996 - 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, 1996 Final Examination, Wednesday, December 18, 1996, 5-8 pm NAME: 1. The exam is open book and open notes. 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 (35 pts.) Consider the four signals , which have Fourier trans- forms , respectively. (a) (10 pts.) Use an “X” to indicate any symmetry property that pertains. P r o b l e m 123456 T O T A L Points 35 15 25 30 35 60 200 Score Fourier Transform Property Purely Real Purely Imaginary Even function of ϖ Oddfunctionof ϖ X ( ϖ ) X 1 ( ϖ ) X 2 ( ϖ ) X 3 ( ϖ ) xt (29 x 1 t x 2 t x 3 t ,,, X ϖ X 1 ϖ X 2 ϖ X 3 ϖ -3 -2 -1 2 3 0 1 -1 1 t π 2 -- t cos , 0 t 3 ≤≤ 0, otherwise = -3 -2 -1 2 3 0 1 -1 1 t x 1 t -3 -2 -1 2 3 0 1 -1 1 t x 2 t -3 -2 -1 2 3 0 1 -1 1 t x 3 t
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2 (b) (10 pts.) Without calculating explicitly, use Fourier transform properties to express in terms of . More than one correct answer is possible in some cases. (c) (15 pts.) Give an explicit expression for X ( ϖ ).
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Electrical Engineering 120 - Fall 1996 - Kahn - Final Exam...

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