Ve451Su2010C3 - Ve451 Lecture Notes Dianguang Ma Summer...

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Ve451 Lecture Notes Dianguang Ma Summer 2010
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Chapter 3 The z-Transform and Its Application to the Analysis of LTI Systems
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Properties of the z-Transform { } { } 1 2 1 2 1 2 1 2 1 1 1 2 2 2 1 1 2 1 2 1 2 1 1 2 1 2 1 2 Correlation of two sequence. If ( ) ( ), ; ( ) ( ), then ( ) ( ) ( ) ( ) ( ) ( ) Proof. ( ) ( )* ( ) 1 ( ) ( ) ( ) ( ) ( ), at least z z z x x x x n x x x x x n X z R x n X z R r l x n x n l R z X z X z r l x l x l R z Z x l Z x l X z X z R R - =-∞ - = - = = - = - = I
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Cauchy’s Integral Theorem 0 0 Let ( ) be a function of the complex variable and be a closed path in the -plane. If the derivative ( ) / exists on and inside the counter and if ( ) has no poles at , then 1 ( ) 2 f z z C z df z dz C f z z f z d j z z π - 0 0 0 0 0 0 0 ( ), if is inside 0, if is outside The values on the right-hand side are called the residues ( ) ( ) of at the pole and denoted by Res , . C f z z C z z C f z f z z z z z z z z = = - - Ñ
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0 0 1 0 1 0 0 More generally, if the (
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This note was uploaded on 10/14/2011 for the course EE 451 taught by Professor Dianguangma during the Summer '10 term at Shanghai Jiao Tong University.

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Ve451Su2010C3 - Ve451 Lecture Notes Dianguang Ma Summer...

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