Challenge_24

# Challenge_24 - EEL 3135 Dr Fred J Taylor Professor Lesson...

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Unformatted text preview: EEL 3135: Dr. Fred J. Taylor, Professor Lesson Title: Inverse z-transform Lesson Number: 24 (Section 8-7 to 8-8) Challenge You are going to have to perform a little math to complete this Challenge. What is x[k] if ) 5 . ( ) 1 ( 3 5 3 ) ( 2 2 3-- +- = z z z z z z X ? Response The partial fraction expansion of X ( z ) is given by ( 29 ( 29 ( 29 2 2 , 2 1 , 2 1 1 1 5 . ) (- +- +- + = z z z z z z z X α α α α , and ( 29 ( 29 ] [ 5 . ] [ ] [ 2 , 2 1 , 2 1 k u k k k x k α α α δ α + + + = , where α corresponds to the weight applied to a Kronecker delta function (i.e., δ [ k ]), α 1 weights z /( z –0 . 5) which corresponds to an exponential (0 . 5) k u [ k ] , α 2,1 scales z /( z –1) , corresponding to a step function u [ k ] , and α 2,2 is applied to z / ( z –1) 2 , corresponding to a ramp, ku [ k ] . The partial fraction expansion of X’ ( z ) =X ( z )/ z is given by ( 29 ( 29 ( 29 2 2 , 2 1 , 2 1 1 1 1 1 5 ....
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Challenge_24 - EEL 3135 Dr Fred J Taylor Professor Lesson...

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