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Unformatted text preview: Lectures 31+32 LaPlace Transform The basic transform • LaPlace transform converts functions from time domain to “s” (s is a sort of generalized frequency) – Formally an integral: – Also an inverse form • But rarely use it • Big benefit of LaPlace transform: it works on both functions and operations ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 t f ds st s F j s F L s F dt st t f t f L jT jT T = = = = ∫ ∫ ∞ → ∞ exp lim 2 1 exp 1 π Some functions: • Step Function: • Decaying exponential: • Decaying sinusoid: ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 2 2 1 1 2 1 2 exp exp exp exp 2 exp exp sin exp 1 exp exp exp exp 1 exp ϖ ϖ ϖ ϖ ϖ ϖ ϖ ϖ ϖ + + = + + + = + + + = = + = + = = = = ∫ ∫ ∫ ∫ ∫ ∞ ∞ ∞ ∞ ∞ a s j s a j s a j dt j j s a t j s a t dt st at j t j t j t at L a s dt a s t dt st at at L s dt st t u t u L Table of functional transforms:...
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This note was uploaded on 11/21/2011 for the course ECE 2100 taught by Professor Kelley/seyler during the Spring '05 term at Cornell University (Engineering School).
 Spring '05
 KELLEY/SEYLER
 Sort, Frequency

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