# A8

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Signals and Systems Issued: 8 October 2014 Fall 2014 Due: Friday , 17 October 2014 Homework Assignment #8 1. Use z transforms to find the ZIR y ZI ( k ), the ZSR y ZS ( k ), and the complete response y ( k ) for each system. (a) (E + 0.5){ y ( k )} = 0, y (0) = 0. (b) (E 2 3E + 2){ y ( k )} = u s ( k ), y (0) = 2, y (1) = 0. ( u s ( k ) = unit step sequence.) (c) (E 2 2E + 2){ y ( k )} = (2) k u s ( k ), y (0) = y (1) = 0. (d) (E 2 3E + 2){ y ( k )} = (E-2) x ( k ), y (0) = 2, y (1) = 0, x ( k ) = (0.8) k u s ( k ). 2. Use a digital computer to plot the frequency response of the system H ( z ) = a z a 1 for the cases a = 0.95, a = 0.85, and a = 0.75. 3. The transfer function 4 2 3 125 . 0 25 . 0 5 . 0 ) ( z z z z z G + + + = is an FIR approximation to the transfer function 5 . 0 1 ) ( = z z H . (a) Plot the impulse response of each system. (b) Plot the step response of each system. Determine the d.c. gain of each system from its
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