Test3_Falls1112 - 1 Name Signals and Systems 10 Dec 2012...

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1 Name: Signals and Systems 10 Dec. 2012 Fall 2012 Test #3 Closed-book, closed-notes. There are Five Problems. Except Problem 2, work out the problems on the separate sheets provided and turn them in with this test paper. Note The last page (page 5) contains useful formulas/operations. However, you might not need all of them 1. Consider the following simulation diagram: E 1 E 1 2 2 y ( k ) + + + + + + u ( k ) (a) Please identify matrices A , B , C , D and write the state equations in the matrix form x ( k +1) = A x ( k ) + B u ( k ), and the output equation in the form y ( k ) = C x ( k ) + D u ( k ). (b) Find the operational transfer function ( ) ( ) -1 H E = E - + C I A B D . (15 points)
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