Ve451Su2010C3

Ve451Su2010C3 - Ve451 Lecture Notes Dianguang Ma Summer...

This preview shows pages 1–6. Sign up to view the full content.

Ve451 Lecture Notes Dianguang Ma Summer 2010

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Chapter 3 The z-Transform and Its Application to the Analysis of LTI Systems
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

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
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
0 0 1 0 1 0 0 More generally, if the (

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

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.

Page1 / 8

Ve451Su2010C3 - Ve451 Lecture Notes Dianguang Ma Summer...

This preview shows document pages 1 - 6. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online