HW#4

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Signals and Systems 8 September 2010 Fall 2010 Quiz: Wednesday 15 September 2010 Homework Assignment #4 1. (a) For the given simulation diagram, find the operational transfer function relating y ( k ) and x ( k ); (b) Write a computer program to simulate the system and plot its output. Make your program correspond to the given simulation diagram; that is, program coupled difference equations in variables that correspond to the outputs of the delay blocks. (c) Run the program to determine the zero-input response of y 1 ( k ), y 2 ( k ), y 3 ( k ), and y ( k ) if the initial conditions are y 1 (0) y 2 (0) 1, y 3 (0) 1. (d) Run the program to determine the zero-state response of y 1 ( k ), y 2 ( k ), y 3 ( k ), and y ( k ) if the input x ( k ) is the unit step sequence. x ( k ) y ( k ) 0.45 E 1 1.05 E 1 1.4 E 1 2 y 1 ( k ) y 2 ( k ) y 3 ( k ) 2. Find the complete closed-form solution of the following difference equations: (a) (E 0.5){ y ( k )} 0, y (0) 7. (b) (E 1){ y ( k )} 3 (0.5) k , y (0) 0. (c) (E 2 3E 2){ y ( k )} 0, y (0) 1, y (1) 0. (d) (E 2 1){ y ( k )} 3

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