EE20-2005-12-13-Final

EE20-2005-12-13-Final - EECS 20N Structure and...

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EECS 20N: Structure and Interpretation of Signals and Systems Department of Electrical Engineering and Computer Sciences U NIVERSITY OF C ALIFORNIA B ERKELEY Final Exam 13 December 2005 LAST Name FIRST Name Lab Time (10 Points) Please print your name and lab time in legible, block lettering above, and on the back of the last page. This exam should take you about two hours to complete. However, you will be given up to about three hours to work on it. We recommend that you budget your time as a function of the point allocation and difficulty level (for you) of each problem or modular portion thereof. This exam printout consists of pages numbered 1 through 14. Also in- cluded is a double-sided appendix sheet containing transform properties. When you are prompted by the teaching staff to begin work, verify that your copy of the exam is free of printing anomalies and contains all of the fourteen numbered pages and the appendix. If you find a defect in your copy, notify the staff immediately. This exam is closed book. Collaboration is not permitted. You may not use or access, or cause to be used or accessed, any reference in print or elec- tronic form at any time during the quiz. Computing, communication, and other electronic devices (except dedicated timekeepers) must be turned off. Noncompliance with these or other instructions from the teaching staff— including, for example, commencing work prematurely or continuing beyond the announced stop time —is a serious violation of the Code of Student Conduct. Please write neatly and legibly, because if we can’t read it, we can’t grade it. For each problem, limit your work to the space provided specifically for that problem. No other work will be considered in grading your exam. No exceptions. Unless explicitly waived by the specific wording of a problem, to receive full credit, you must explain your responses succinctly, but clearly and convinc- ingly. We hope you do a fantastic job on this exam. It has been a pleasure having you in EECS 20N. Happy holidays! 1
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Complex exponential Fourier series synthesis and analysis equations for a periodic discrete-time signal having period p : x ( n ) = X k = h p i X k e ikω 0 n ←→ X k = 1 p X n = h p i x ( n ) e - ikω 0 n , where p = 2 π ω 0 and h p i denotes a suitable contiguous discrete interval of length p (for example, X k = h p i can denote p - 1 X k =0 ).
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