# HW10

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Signals and Systems 24 October 2012 Fall 2012 Quiz: Tuesday 30 October 2012 Homework Assignment #10 1. Let x ( k + 1) = Ax ( k ) + Bu ( k ) and y ( k ) = Cx ( k ) + Du ( k ), with A = Ο Ο Ο Π Ξ Μ Μ Μ Ν Λ 1 0 0 8 . 0 2 . 0 8 . 0 75 . 0 3 . 0 25 . 0 , B = Ο Ο Ο Π Ξ Μ Μ Μ Ν Λ 1 0 0 , C = ( ) 0 0 1 , D = 0. (a) Draw the system simulation diagram. (b) Determine the poles of the system transfer function. (c) Simulate the system on a digital computer to find the response y ( k ) to a unit step input. 2. A study of student enrollment records for the Colleges of Engineering and Business at a certain university yields the following observations: Among entering students, 35% enroll in Engineering, and 65% enroll in Business. Among Engineering students at the end of each year, 65% will re-enroll for the following year in Engineering, 8% will enroll in Business, and 20% will graduate. Among Business students at the end of each year, 78% will re-enroll for the following year in Business, and 20% will graduate.
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