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Exam3F11

# Exam3F11 - NAME Digital Signal Processing I Session 40 Exam...

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NAME: 30 Nov. 2011 Digital Signal Processing I Exam 3 Fall 2011 Session 40 30 Nov. 2011 Cover Sheet WRITE YOUR NAME ON EACH EXAM SHEET Test Duration: 60 minutes. Open Book but Closed Notes. Calculators NOT allowed. This test contains two problems. All work should be done in the space provided. Do not just write answers; provide concise reasoning for each answer. 1

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Problem 1. 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] (a) With X N ( k ) computed as the 5-pt DFT of x [ n ] = u [ n ] - u [ n - 5] and H N ( k ) computed as the 5-pt DFT of h [ n ] = u [ n ] - u [ n - 3]. The 5-point sequence y 5 [ n ] is computed as the 5-pt inverse DFT of the product Y N ( k ) = X N ( k ) H N ( k ). Write out the 5 numerical values of y 5 [ n ] in sequence form as { y 5 [0] ,y 5 [1] ,y 5 [2] ,y 5 [3] ,y 5 [4] } . 2
(b) With X N ( k ) computed as the 8-pt DFT of x [ n ] = u [ n ] - u [ n - 5] and H N ( k ) computed as the 8-pt DFT of h [ n ] = u [ n ] - u [ n - 3]. The 8-point sequence y 8 [ n ] is computed as the 8-pt inverse DFT of the product Y

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