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Unformatted text preview: Digital Signal Processing I Exam 3 Fall 2009 Session 41 4 Dec. 2009 Cover Sheet Test Duration: 50 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 (NOT provided). Do not return this test sheet, just return your answer sheets. 1 Digital Signal Processing I Exam 3 Fall 2009 Problem 1. [65 pts] For all parts of this problem, the reconstructed spectrum is computed according to Equa- tion 1 below: X r ( ) = N- 1 summationdisplay k =0 X N ( k ) sin bracketleftBig N 2 parenleftBig - 2 k N parenrightBigbracketrightBig N sin bracketleftBig 1 2 parenleftBig - 2 k N parenrightBigbracketrightBig e- j N- 1 2 ( - 2 k N ) (1) (a) Let x [ n ] be a discrete-time rectangular pulse of length L = 12 as defined below: x [ n ] = u [ n ]- u [ n- 12] (i) X N ( k ) is computed as a 16-point DFT of x [ n ] and used in Eqn (1) with N = 16....
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