A5

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Signals and Systems Issued: 18 September 2013 Fall 2013 Due: 24 September 2013 Homework Assignment #5 1. For each of the following systems, find an expression for the impulse response h ( k ) by iterating until you see a pattern. (a) y ( k ) 25 . 0 1 E { x ( k )} [Ans: h ( k ) (0.25) k 1 u s ( k 1).] (b) y ( k ) ) 25 . 0 ( 1 E E { x ( k )} (c) y ( k ) 1 2 1 2 E E { x ( k )} 2. Find the simulation diagrams and transfer functions of the systems having the following impulse responses: (a) h ( k ) 2 , 0 2 , 1 k k (b) h ( k ) 0 , 0 0 , 1 k k (c) h ( k ) 1 , 0 1 , 1 k k (d) h ( k ) 2 , 0 2 , 1 k k (e) h ( k ) otherwise 0 2 , 1 1 , 2 0 , 3 k k k 3. Use a convolutional sum to find the zero-state response of an LTI system to a unit step sequence if the system impulse response is (a) h ( k ) 0 , 0 0 , 1 k k , (b) h ( k )
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