lecture18

# lecture18 - EE313 Linear Systems and Signals Fall 2010...

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

EE313 Linear Systems and Signals Fall 2010 Initial conversion of content to PowerPoint by Dr. Wade C. Schwartzkopf Prof. Brian L. Evans Dept. of Electrical and Computer Engineering The University of Texas at Austin Inverse Laplace Transform

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

View Full Document
18 - 2 Inverse Laplace Transform Definition has integration in complex plane We will use lookup tables instead Roberts, Appendix F Many Laplace transform expressions are ratios of two polynomials, a.k.a. rational functions Convert complicated rational functions into simpler forms Apply partial fractions decomposition Use lookup tables
18 - 3 Partial Fractions Example #1 ( 29 ( 29 [ ] [ ] ( 29 ( 29 ( 29 ( 29 ( 29 t u t t u e e t f j s j s s F B A B A B A s B j Bs Aj As j s B j s A s F j s s s s F t j t j cos 2 1 2 1 2 1 2 1 2 1 0 1 : numerators two the Equating : (poles) r denominato in Roots 0 0 0 2 0 2 0 0 0 0 0 2 0 2 0 0 ϖ = + = + + - = = = = - = + + - + + = + + - = ± = + = -

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

View Full Document
18 - 4 Partial Fractions Example #2 ( 29 ( 29 ( 29 ( 29 ( 29 [ ] ( 29 ( 29 ( 29 [ ] ( 29 ( 29 ( 29 ( 29 ( 29 t u e e s s L t f s s s F s F s k s F s k s k s k s s s s F t t s s 3 4 3 3 2 4 3 3 2 4 3 2 3 6 21 3 4 3 2 6 14 2 3 2 3 2 6 7 3 2 1 3 2 2 1 2 1 + = - + + = - + + = = + - = - = = - - - - = + = - + + = - + - = - - = - =
18 - 5 Partial Fractions Example #3 ( 29 ( 29 ( 29 ( 29 1 6 4 6 2 2 5 0 2 2 3 : division polynomial

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 02/16/2011 for the course ECE 313 taught by Professor Evans during the Spring '11 term at University of Texas.

### Page1 / 15

lecture18 - EE313 Linear Systems and Signals Fall 2010...

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

View Full Document
Ask a homework question - tutors are online