# HW05

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Signals and Systems 19 September 2012 Fall 2012 Quiz: Tuesday 25 September 2012 Homework Assignment #5 1. Are the following systems BIBO stable? Justify your answer. (a) (E 2 + 3E + 2) y ( k ) = x ( k ) (b) (10E 2 + 3E + 2) y ( k ) = (E 2){ x ( k )} (c) (E 2 + 1.2E + 0.2) y ( k ) = x ( k ) (d) (E 3 + 3E 2 + 3E + 1) y ( k ) = (E 2 0.1E){ x ( k )} 2. (a) Plot the impulse response and the step response of the discrete-time system whose operational transfer function is H 1 (E) = 5 . 0 E E . (b) Plot the impulse response and the step response of the discrete-time system whose operational transfer function is H 2 (E) = 4 2 3 4 0625 . 0 125 . 0 25 . 0 5 . 0 E E E E E + + + + . 3. Find the simulation diagrams and transfer functions of the systems having the following impulse responses: (a) h ( k ) = Ω Ψ Χ = 2 , 0 2 , 1 k k (b) h (
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