solutions for z-transform

solutions for z-transform - Problem (1) (a) ) ( 3 ) ( ) ( )...

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Unformatted text preview: Problem (1) (a) ) ( 3 ) ( ) ( ) ( 2 ) ( 3 2 1 z X z z X z Y z z Y z z Y--- + = +- 2 1 3 2 1 3 1 ) ( ) ( ) (--- +- + = = z z z z X z Y z H (b) ] 1 [ ) 6 . )( 6 . ( ] [ ) 4 . ( ] [ 1--- + =- n u n u n x n n According to the time shit property, the z-transform is 1 1 1 6 . 1 6 . 4 . 1 1 ) (--- +- +- = z z z z X Problem (2) (a) 1 1 1 1 1 3 . 1 6 . 1 2 ) 3 . 1 )( 6 . 1 ( 7 . 2 3 2 ) (------ + + +- =- +- +- = z B z A z z z z H { } ] [ ) 3 . ( 2 ] [ ) 6 . ( 5 ] [ 2 ) ( ] [ 2 6 . 1 7 . 2 3 5 3 . 1 7 . 2 3 1 3 . 1 1 1 6 . 1 1 1 1 1 n u n u n z H Z n h z z B z z A n n z z-- +- = = - = +- = =-- =- =--- =---- (b) 1 1 3 . 1 3 . 4 . 1 1 . 2 ) (-- + +- = z z z X ) 3 . 1 )( 4 . 1 )( 3 . 1 )( 6 . 1 ( 1836 . 819 . 41 . 7 4 . 2 ) ( ) ( ) ( 1 1 1 1 3 2 1------- +-- + +-- = = z z z z z z z z X z H z Y 1 1 1 1 3 . 1 4 . 2 4 . 1 8 . 16 3 . 1 3 . 12 6 . 1 3 . 9---- +- +-- +- + + = z z z z ] [ ) 3 . ( 4 . 2 ] [ ) 4 . ( 8 . 16 ] [ ) 3 . ( 3 . 12 ] [ ) 6 . ( 3 . 9 ] [ n u n u n u n u n y n n n n--- +- =...
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This note was uploaded on 01/11/2011 for the course EE 4015 taught by Professor Shuhungleung during the Fall '10 term at City University of Hong Kong.

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solutions for z-transform - Problem (1) (a) ) ( 3 ) ( ) ( )...

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