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Exam2F05 - ECE 538 Digital Signal Processing I Exam 2 Fall...

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ECE 538 Digital Signal Processing I Exam 2 Fall 2005 26 Oct. 2005 Cover Sheet Test Duration: 50 minutes. Open Book but Closed Notes. Calculators NOT allowed. This test contains three 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 50 2. Multi-Stage Upsampling/Interpolation 20 3. IIR Filter Design 30 1
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EE538 Digital Signal Processing I Exam 2 Fall 2003 Problem 1. [50 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 = 8 3 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 ( ω ), over - π < ω < π . That is, plot both | X ( ω ) | and negationslash X ( ω ) (separate plots) over - π < ω < π . Ideal A/D F = W s x [n] x (t) a x [n] ^ h [n] 1 8 3 Figure 1. As shown in Figure 1, x [ n ] is input to a discrete-time LTI system with impulse response h 1 [ n ] = 16 sin parenleftBig 3 π 8 n parenrightBig πn sin parenleftBig π 8 n
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