HW07

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Signals and Systems 3 October 2012 Fall 2012 Quiz: Wednesday 10 October 2012 Homework Assignment #7 1. Find the inverse z transform of each of the following functions. (a) F ( z ) = 2 + 3 z 1 + 6 z 3 + 4 z 7 (b) F ( z ) = ) )( 1 ( 1 2 T e z z z + , T = 2 1 (c) F ( z ) = ) 1 ( 1 6 + z z z (d) F ( z ) = 2 3 1 2 + + z z z (e) F ( z ) = ) 1 ( ) 5 . 0 ( 1 2 3 2 + + + z z z z (f) F ( z ) = 2 2 1 2 + + z z z 2. For each of the z -domain functions given in Problem 1, determine whether the Final Value Theorem is applicable. If so, use it to compute the limit of f ( k ) as k + . 3. Use the z transform to find the zero-state response of an LTI system to a unit step sequence if the system impulse response is (a) h ( k ) = Ω Ψ Χ < 0 , 0 0 , 1 k k , (b) h ( k ) = Ϊ Ϊ Ω Ϊ Ϊ Ψ Χ = = = otherwise 0 2 , 3 1 , 2 0 , 1 k k k , (c) h ( k ) = Ω Ψ Χ < 0 , 0 0 , ) 9 . 0 ( k k k . [Ans: y ( k ) = 10 9(0.9) k , k = 0,1,2, ⋅⋅⋅ .] 4. Use z transforms to find the zero-state response
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