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Unformatted text preview: ECE 301, Final 3:20-5:20pm Monday Dec. 11, PHYS 112, 1. Enter your name, student ID number, e-mail address, and signature in the space provided on this page, NOW! 2. This is a closed book exam. 3. This exam contains 7 questions. For multiple-choice and short-answer questions, there is no need to justify your answers. You have one hour to complete it. I will suggest not spending too much time on a single question, and work on those you know how to solve. 4. The sub-questions of a given question are listed from the easiest to the hardest. The best strategy may be to finish only the sub-questions you know exactly how to solve. 5. There are a total of 17 pages in the exam booklet. Use the back of each page for rough work. 6. Neither calculator nor crib sheet is allowed. 7. You are NOT allowed to turn in your exam booklet in the last 5 minutes of the exam. 8. Read through all of the problems first, and consult with the TA during the first 15 minutes. After that, no questions should be asked unless under special circum- stances, which is at TA’s discretion. You can also get a feel for how long each question might take after browsing through the entire question set. Good luck! Name: Student ID: E-mail: Signature: Provided | r | < 1. The infinite geometric sum formula: ∞ X n =0 ar n = a 1- r (1) The finite geometric sum formula: K X n =0 ar n = a (1- r K +1 ) 1- r (2) The continuous Fourier series pair: x ( t ) = ∞ X k =-∞ a k e jkω t (3) a k = 1 T Z T x ( t ) e- jkω t dt (4) The continuous Fourier transform pair: x ( t ) = 1 2 π Z ∞ ω =-∞ X ( ω ) e jωt dω (5) X ( ω ) = Z ∞ t =-∞ x ( t ) e- jωt dt (6) The discrete Fourier transform pair: x [ n ] = 1 2 π Z 2 π X ( ω ) e jωn dω (7) X ( ω ) = ∞ X n =-∞ x [ n ] e- jωn (8) Question 1:...
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This note was uploaded on 02/07/2011 for the course ECE 301 taught by Professor V."ragu"balakrishnan during the Fall '06 term at Purdue University.
- Fall '06