HW_5_ECSE_304

# HW_5_ECSE_304 - McGill University ECSE 304B Winter 2009 Prof Jan Bajcsy Assignment 5 Due date April 14 at 16:00 TAs Mr Daniel Kim Sami el-Baddagh

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McGill University Winter 2009 ECSE 304B Prof. Jan Bajcsy Assignment 5 Due date: April 14 at 16:00 TAs: Mr. Daniel Kim, Sami el-Baddagh, Yi Feng 1. Discrete-Time Transforms (a) Find the z -transform X(z) and sketch the region of convergence for signal x[n] that is shown the figure below: -6 -4 -2 0 2 4 6 8 -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 n x[n] -(1/3) n (1/2) n (b) Does the discrete-time Fourier transform ( ) j X e w exist for the signal from part (a)? If yes, determine ( ) j X e explicitly, if not, explain why. (c) Repeat part (a) for signal 2 [ ] ( 1) [ ] y n n n u n = - + - , where u[.] is the unit step function. (d) Repeat part (b) for the above signal y[n] . 2. Discrete-Time Systems Consider a system that has its input-output relationship described by [ ] 0.7 [ 1] 0.3 [ ] y n y n x n = - + and is initially at rest, i.e., y[n]=0 for very negative values of n, n<<0. (a) Depict a schematic block diagram of this discrete-time system using delay blocks, interconnects, adders, multipliers, etc.

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## This note was uploaded on 07/09/2011 for the course ECSE 304 taught by Professor Chenandbacsy during the Spring '11 term at McGill.

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HW_5_ECSE_304 - McGill University ECSE 304B Winter 2009 Prof Jan Bajcsy Assignment 5 Due date April 14 at 16:00 TAs Mr Daniel Kim Sami el-Baddagh

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