lecture17 - 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 Laplace Transform 17 - 2 Forward Laplace Transform • Decompose a signal f ( t ) into complex sinusoids of the form e s t where s is complex: s = σ + j 2 π f • Forward (bilateral) Laplace transform f ( t ): complex-valued function of a real variable t F ( s ): complex-valued function of a complex variable s • Bilateral means that the extent of f ( t ) can be infinite in both the positive t and negative t direction (a.k.a. two-sided) ( 29 ( 29 ∫ ∞ ∞-- = dt e t f s F t s 17 - 3 Inverse (Bilateral) Transform • Inverse (Bilateral) Transform is a contour integral which represents integration over a complex region– recall that s is complex c is a real constant chosen to ensure convergence of the integral • Notation F ( s ) = L { f ( t )} variable t implied for L f ( t ) = L-1 { F ( s )} variable s implied for L-1 ( 29 ( 29 ds e s F j t f t s j c j c 2 1 ∞ + ∞- ∫ = π ( 29 ( 29 s F t f L → ← ∫ 17 - 4 ( 29 ( 29 ( 29 ( 29 s F t f s F t f L L 2 2 1 1 and → ← → ← ( 29 ( 29 ( 29 ( 29 ?...
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This note was uploaded on 01/22/2012 for the course EE 312 taught by Professor Shafer during the Spring '08 term at University of Texas.

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lecture17 - EE313 Linear Systems and Signals Fall 2010...

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