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Exam2F10 - EE538 Digital Signal Processing I Session 27...

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EE538 Digital Signal Processing I Session 27 Exam 2 Live: Friday, Oct. 29, 2010 Cover Sheet Test Duration: 55 minutes. Open Book but Closed Notes. Calculators NOT allowed. This test contains two problems and four pages including this cover page. All work should be done on loose blank sheets of 8 1/2 x 11 paper which will NOT be provided. Write on only one side of each sheet and then staple together. You must show all work for each problem to receive full credit. Do not return this test sheet, just return the exam sheets. No. Topic(s) of Problem Points 1. Perfect Reconstruction Filter Bank - Two Channel 45 2. Vestigial Sideband Modulation 55 1
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Digital Signal Processing I Exam 2 Fall 2010 Problem 1. [45 points] In the system below, the two analysis filters, h 0 [ n ] and h 1 [ n ], and the two synthesis filters, f 0 [ n ] and f 1 [ n ], form a Quadrature Mirror Filter (QMF). Specifically, h 0 [ n ] = 2 β cos[(1 + β ) π ( n + . 5) / 2] π [1 - 4 β 2 ( n + . 5) 2 ] + sin[(1 - β ) π ( n + . 5) / 2] π [( n + . 5) - 4 β 2 ( n + . 5) 3 ] , -∞ < n < with β = 0 . 5 (1) h 1 [ n ] = ( - 1) n h 0 [ n ] f 0 [ n ] = h 0 [ n ] f 1 [ n ] = - h 1 [ n ] The DTFT of the halfband filter h 0 [ n
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