lecture17

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

This preview shows pages 1–5. Sign up to view the full content.

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

View Full Document

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.

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 ( 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 ?...
View Full Document

{[ snackBarMessage ]}

### Page1 / 14

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

This preview shows document pages 1 - 5. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online