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Unformatted text preview: ECE 538 Digital Signal Processing I Exam 2 Fall 2009 16 Nov. 2009 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 loose blank 8.5 x 11 sheets (not provided.) You do not have to return this test sheet. Prob. No. Topic of Problem Points 1. Efficient Upsampling 60 2. Perfect Reconstruction Filter Bank 40 1 EE538 Digital Signal Processing I Exam 2 Fall 2009 Problem 1. [60 points] Consider the upsampler system below in Figure 1. h[n] 3 x[n] y[n] Figure 1. (a) Draw a block diagram of an efficient implementation of the upsampler system in Figure 1. (b) Your answer to part (a) should involve the polyphase components of h [ n ]: h [ n ] = h [3 n ], h 1 [ n ] = h [3 n + 1], and h 2 [ n ] = h [3 n + 2]. (i) For the ideal case where h [ n ] = 3 sin( 3 n ) n , plot the magnitude of the DTFT of h [ n ] = h [3 n ], H ( ), over- &lt; &lt; ....
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