Quiz_1_sol - ECE 483 Quiz # 1 Solution Problem 1. (6...

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ECE 483 Quiz # 1 Solution Problem 1. (6 points) For each of the following z -transforms, determine the ±nal value of the corresponding signal f ( k ) as k → ∞ . If the ±nal value theorem does not apply, state the reason that this is so and no further computation is needed. (a) (1.5 points) F ( z ) = z +2 ( z +1)( z - 0 . 5) . Solution: FVT does not apply as F ( z ) has a pole at - 1, which is on the unit circle but not at 1. (b) (1.5 points) F ( z ) = z ( z 2 - 0 . 25)( z - 1) . Solution: FVT applies, and f ( ) = 1 / 0 . 75 = 1 . 3333. (c) (1.5 points) F ( z ) = z - 4 + 3 z - 7 . Solution: FVT applies, and f ( ) = 0. (d) (1.5 points) F ( z ) = 2 z 2 +3 ( z - 0 . 3)( z 2 +2 z +2) . Solution: FVT does not apply as F ( z ) has poles at 1 ± j which are outside the unit circle. Problem 2. (6 points) Given F ( z ) = 2 z 2 +1 z 4 - z 3 +3 z - 1 , ±nd the corresponding f ( k ) for k = 0 , 1 , 2 , 3. Solution: Using the long division method, we have f (0) = f (1) = 0, f (2) = f (3) = 2. Problem 3. (8 points) For the following F ( z ), ±nd its inverse
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This note was uploaded on 04/15/2011 for the course ECE 483 taught by Professor Evens during the Spring '08 term at Purdue University-West Lafayette.

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