2008%20ECE%20700%20Final%20Solution - Department of...

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1 Department of Electrical and Computer Engineering The Ohio State University WINTER 2008 ECE 700 Digital Signal Processing 11:30 AM-1:18 PM 3/11/08 Final Examination Directions You are allowed to have two sheets of paper with anything you want on it. No other books or notes are allowed in the examination. The examination has 6 questions and 14 pages. Each question is worth 20 points. Please make sure that you answer all questions. Write clearly and show all work for full credit. If you are making any assumptions in solving any of the problems, please state these clearly at the beginning of your solution. The ECE Honor System applies to this examination. At the end of the examination, if the pledge below applies, please sign your name in the line below the pledge. “No aid given, received or observed during the course of this examination.” Signature Your name:
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2 1. (20 points) a. Show that the two systems shown below are equivalent. b. Consider the system shown below. Express y [ n ] in terms of x [ n ]. Simplify your expression as much as possible. c. For the system above, express Y ( z ) in terms of X ( z )? a. For the LHS system, y 1 [ n ]= s 1 [3 n ], s 1 [ n ] = x [2 n ], so y 1 [ n ] = x [6 n ] For the RHS system, y 2 [ n ]= s 2 [2 n ], s 2 [ n ] = x [3 n ], so y 2 [ n ] = x [6 n ] So LHS is same as RHS b. Using result of part a, exchange middle two blocks. Then 3 and 3 cancel leaving 2 and 2. [ ], even Output of 2 is [ ] [2 ], and output of 2 is [ ] 2 0, otherwise [ ], even So [ ] . 0, otherwise
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This note was uploaded on 04/21/2009 for the course ECE 700 taught by Professor Un during the Winter '09 term at Ohio State.

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2008%20ECE%20700%20Final%20Solution - Department of...

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