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Unformatted text preview: ECE 301, final exam of the session of Prof. ChihChun Wang Saturday 10:20am–12:20pm , December 20, 2008, STEW 130, 1. Enter your name, student ID number, email address, and signature in the space provided on this page, NOW! 2. This is a closed book exam. 3. This exam contains both multiplechoice and workout questions. The students are suggested not spending too much time on a single question, and working on those that you know how to solve. 4. There are 24 pages in the exam booklet. Use the back of each page for rough work. The last pages are all the Tables. You may rip the last pages for easier reference. Do not use your own copy of the Tables. Using your own copy of Tables will be considered as cheating. 5. Neither calculators nor help sheets are allowed. Name: Student ID: Email: Signature: Question 1: [30%] No need to write down justifications. 1. [10%] Let x ( t ) = cos( πt 2 ) + sin( t 3 ) (1) Is x ( t ) periodic? (If Yes, what is the period?) Is x ( t ) an odd signal? Is x ( t ) of infinite or finite power? Is x ( t ) of infinite or finite energy? 2. [10%] Let y [ n ] = ∞ X k =∞ cos(0 . 5 πn ) δ [ n 2 k ] (2) Is y [ n ] periodic? (If Yes, what is the period?) Is y [ n ] an even signal? Is y [ n ] of infinite or finite power? Is y [ n ] of infinite or finite energy? 3. [5%] Plot y [ n ] for the range between n = 2 to 6. 4. [5%] Let z [ n ] = y [ n ] 2 . (3) Plot z [ n ] for the range between n = 2 to 6. Question 2: [35%] 1. [3%] Use one or two sentences to describe what is a timeinvariant system. 2. [3%] Use one or two sentences to describe what is a linear system. 3. [8%] Consider a discretetime linear timeinvariant system with impulse response h [ n ] = 1 4 ( U [ n + 3] U [ n 1]). Let x [ n ] = 2 n U [ n ]. Find out the corresponding output y [ n ] of the given system....
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 Fall '06
 V."Ragu"Balakrishnan
 Fourier Series, Signal Processing, LTI system theory

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