Quiz_2_sol

# Quiz_2_sol - ECE 483 Quiz 2 Solution Problem 1(10 points...

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ECE 483 Quiz # 2 Solution Problem 1. (10 points) For a discrete-time system with the transfer function Y ( z ) E ( z ) = z +1 ( z - 1)( z - 0 . 5) , (a) (4 pts) Find an equivalent linear di±erence equation model for the input e ( k ) and the output y ( k ), k = 0 , 1 ,... . Solution: Write Y ( z ) E ( z ) = z + 1 ( z - 1)( z - 0 . 5) = z - 1 + z - 2 1 - 1 . 5 z - 1 + 0 . 5 z - 2 (1 - 1 . 5 z - 1 + 0 . 5 z - 2 ) Y ( z ) = ( z - 1 + z - 2 ) E ( z ) y ( k ) - 1 . 5 y ( k - 1) + 0 . 5 y ( k - 2) = e ( k - 1) + e ( k - 2) . (b) (4 pts) Plot a simulation diagram that implements the above linear di±erence equation. (c) (3 pts) Write a state variable representation corresponding to the simulation diagram in (b), and identify the matrices A , B , C , and D . Solution: Part (b) and (c) have multiple answers; hence omitted. Problem 2. Suppose a discrete-time system with input r ( k ) and output y ( k ) is given by the simulation diagram above.
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