MAS160: Signals, Systems & Information for Media TechnologyProblem Set 7DUE: November 19, 2003Instructors: V. Michael Bove, Jr. and Rosalind Picard T.A. Jim McBrideProblem 1: z-Transforms, Poles, and ZerosDetermine the z-transforms of the following signals. Sketch the corresponding pole-zeropatterns.(a) x[n] = δ[n − 5](b) x[n] = nu[n](c) x[n] =−13nu[n](d) x[n] = (an+ a−n)u[n], a real(e) x[n] = (nancos ω0n)u[n], a real(f) x[n] =12n(u[n − 1] − u[n − 10])Problem 2: z-Transform PropertiesGiven x[n] below, use the properties of the z-transform to derive the transform of thefollowing signals.x[n] → X(z) =z−1(1 − z−1)2(a) x[n − 3](b) x[n] ∗ δ[n − 3](c) x[n] − x[n − 1](d) x[n] ∗ (δ[n] − δ[n − 1])(e) 5x[n − 1] + 4−13nu[n]PS 7-1Problem 3: Relating pole-zero plots to frequency- and impulse-response(a) DSP First 8.16(b) DSP First 8.17Problem 4: DSP First Lab 10Items to be turned in:(a) Answers to questions from C.10.4.(b) Answers to questions from C.10.5.(c) Plots and answers to questions from C.10.6.PS
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