Exam3F10

# Exam3F10 - Digital Signal Processing I Session 41 Exam 3...

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Digital Signal Processing I Exam 3 Fall 2010 Session 41 3 Dec. 2010 Cover Sheet Test Duration: 60 minutes. Open Book but Closed Notes. Calculators NOT allowed. This test contains two problems. All work should be done on blank 8.5” x 11” white sheets of paper. Do not return this test sheet, just return your answer sheets. 1

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Digital Signal Processing I Exam 3 Fall 2010 Problem 1. [65 pts] For all parts of this problem, the reconstructed spectrum is computed according to Equa- tion 1 below: Y r ( ω ) = N - 1 X k =0 Y N ( k ) sin h N 2 ± ω - 2 πk N ²i N sin h 1 2 ± ω - 2 πk N ²i e - j N - 1 2 ( ω - 2 πk N ) (1) (a) Let x [ n ] be a discrete-time rectangular pulse of length L = 5 and h [ n ] be a discrete-time rectangular pulse of length M = 3 as deﬁned below: x [ n ] = u [ n ] - u [ n - 5] h [ n ] = u [ n ] - u [ n - 3] (i) With X N ( k ) computed as the 12-pt DFT of x [ n ] and H N ( k ) computed as the 12-pt DFT of h [ n ], the product Y N ( k ) = X N ( k ) H N ( k ) is used in Eqn (1) with N
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## This note was uploaded on 02/19/2012 for the course ECE 538 taught by Professor Zoltolski during the Fall '08 term at Purdue.

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Exam3F10 - Digital Signal Processing I Session 41 Exam 3...

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