summer2008final

# summer2008final - EE 4541 Digital Signal Processing Summer...

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EE 4541 – Digital Signal Processing – Summer Session, 2008 Final Exam (12:20 – 2:15 PM) Closed book, closed notes, no calculators, no electronic devices. Two 8.5”x11” information sheets are allowed. NOTE : Be sure to clearly show how you obtained your answer to each question! 1. Goertzel’s algorithm for computing the DFT can be written as: ) 1 ( ) ( ) ( 0 , ) 2 ( ) 1 ( 2 cos 2 ) ( ) ( = + = N v W N v k X N n n v n v N k n x n v k k N k k k e k π Consider the time-domain sequence {x[n]} = {1, 2, 3, 4, 1, 2, 3, 4}. (a) (10 points) Apply Goertzel’s algorithm to calculate the values of v 6 (n) for n = 0, 1, 2, 3, 4, 5, 6, 7 and 8 and then use this information to calculate X(6). Be sure to clearly show the values obtained at each step of the algorithm. (b) (5 points) Demonstrate that your answer is correct by calculating X(6) directly from the definition of the DFT and showing that you obtain the same result as in part (a). 2. (15 points) Apply the inverse bilinear transformation with T = 2 to the following

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## This note was uploaded on 10/09/2009 for the course ECE 4541 taught by Professor Xyz during the Summer '09 term at Minnesota.

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summer2008final - EE 4541 Digital Signal Processing Summer...

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