HW9_FA08 - UNIVERSITY OF ILLINOIS AT URBANA-CHAMPAIGN...

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UNIVERSITY OF ILLINOIS AT URBANA-CHAMPAIGN Department of Electrical and Computer Engineering ECE 410 Digital Signal Processing Homework 9 Wednesday, October 22, 2008 Prof. Bresler, Prof. Jones Due by October 29, 2008 Problem 1 (30 points) (a) Given an ideal D/A with period T = 2 ms, and input sequence y [ n ] = cos( nπ/ 4) for all n , (i) Determine a closed-form expression for the output y ( t ). (ii) Sketch (by hand) the output for 0 t 20ms. (iii) Determine a closed-form expression for the Fourier Transform of the output. (iv) Sketch (by hand) the magnitude of the Fourier Transform of the output for 0 Ω 4000 π (v) Identify on your sketch from (iv) the spurious component with the largest magnitude, and determine a closed-form expression for its magnitude and frequency. (b) Repeat (ii), (iv), and (v) in (a) above, when the ideal D/A is replaced by a zero-order hold. (c) Repeat (i)-(v) in (a) above when the ideal D/A is replaced by a zero-order hold followed by an analog compensator with frequency response

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HW9_FA08 - UNIVERSITY OF ILLINOIS AT URBANA-CHAMPAIGN...

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