{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

lecture17

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

This preview shows pages 1–5. 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 Laplace Transform

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

View Full Document
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 →

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

View Full Document
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 ? 2 2 1 1 2 2 1 1 s F a s F a t f a t f a L + → + ( 29 ( 29 { } ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 s F a s F a dt e t f a dt e t f a dt e t f a t f a t f a t f a L st st st
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}