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Unformatted text preview: ECE 538 Digital Signal Processing I Exam 2 Fall 2006 Session 18, Live: 24 Oct. 2006 Cover Sheet Test Duration: 75 minutes. Open Book but Closed Notes. Calculators NOT allowed. This test contains TWO problems. All work should be done in the blue books provided. Do not return this test sheet, just return the blue books. Prob. No. Topic of Problem Points 1. Digital Subbanding 60 2. Multi-Stage Upsampling/Interpolation 40 1 EE538 Digital Signal Processing I Exam 2 Fall 2006 Problem 1. [60 points] W W F a X (F) 1/F W 3 W 3 s Consider the analog signal x a ( t ) whose Continuous Time Fourier Transform (CTFT), X a ( F ), is plotted above. x a ( t ), which is both real-valued and even-symmetric, is sampled at a rate of F s = 16 7 W to create the discrete-time signal x [ n ] = x a ( n/F s ). (a) Plot the magnitude and phase of the DTFT of x [ n ], X ( ), over- < < . That is, plot both | X ( ) | and negationslash X ( ) (separate plots) over- < < ....
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