HW#8

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Signals and Systems 6 October 2010 Fall 2010 Quiz: Wednesday 13 October 2010 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. 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. Comment on the effect of the pole location on the magnitude and phase of the frequency response. 3. The transfer function 3 2 3 125 . 0 25 . 0 5 . 0 ) ( z z z z z G is an FIR approximation to the transfer function 5 . 0 ) ( z z z H . (a) Plot the impulse response of each system. (b) Plot the step response of each system.
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