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MIT OpenCourseWare http://ocw.mit.edu MAS.160 / MAS.510 / MAS.511 Signals, Systems and Information for Media Technology Fall 2007 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms.DUE: November 19, 2003s and Rosalind Picard T.A. Jim McBrideMAS160: Signals, Systems & Information for Media Technology Problem Set 7 Instructor : V. Michael Bove, Jr. Problem 1: z-Transforms, Poles, and Zeros Determine the z-transforms of the following signals. Sketch the corresponding pole-zero patterns. (a) x[n] = δ[n − 5] (b) x[n] = nu[n] (c) x[n] = �−1 �n u[n]3 (d) x[n] = (an + a−n)u[n], a real (e) x[n] = (nan cos ω0n)u[n], a real (f) x[n] = �1 �n (u[n − 1] − u[n − 10])2 Problem 2: z-Transform Properties Given x[n] below, use the properties of the z-transform to derive the transform of the following 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 �−31 �n u[n] PS 7-1Problem 3: Relating pole-zero plots to frequency- and impulse-response (a) DSP First 8.16 (b) DSP First 8.17 Problem 4: DSP First Lab 10 Items 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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