lecture18

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

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Unformatted text preview: 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 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 1 : numerators two the Equating : (poles) r denominato in Roots 2 2 2 2 ϖ ϖ ϖ ϖ ϖ ϖ ϖ ϖ ϖ ϖ ϖ ϖ = + = + +- = = = ⇒ =- = + +- + + = + +- = ± = + =- 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 2 2 3 : division polynomial Perform...
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lecture18 - EE313 Linear Systems and Signals Fall 2010...

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