Sample Test 2 - Name Signals and Systems 31 October 2012...

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Name: Signals and Systems 31 October 2012 Fall 2012 Test #2 Closed-book, closed-notes. Do all work in the space provided. Clearly indicate the answer to each part. 1. A discrete-time system is described by q ( k + 1) = Aq ( k ) + Bx ( k ) y ( k ) = Cq ( k ), with A = 0 3 0 0 0 1 0 0 2 ! " # # # $ % & & & , B = 0 0 4 ! " # # # $ % & & & , C = (5 0 0). (a) Draw a simulation diagram of the system, with the state variables appearing as the outputs of the delay blocks. (b) Find the system transfer function H ( z ) = Y ( z )/ X ( z ). (c) Determine the zero-input response y ZI ( k ) for k 0 if the initial state is q (0) = Ο Ο Ο Π Ξ Μ Μ Μ Ν Λ 0 1 0 . (d) Is the system BIBO stable? Justify your answer. (25 points)
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2. Four different LTI discrete-time systems have the step responses shown at the left. Mark the approximate z -plane locations of the poles of the corresponding system transfer functions H ( z ). 1 z 1 z 1 z 1 z (20 points) -5 0 5 10 15 20 -5 0 5 10 15 20 -5 0 5 10 15 20 -5 0 5 10 15 20
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3. A certain LTI discrete-time system has the z -domain transfer function ) 5 . 0 ( ) 5 . 0 ( 3 ) ( + = z z z z H .
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