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11.2 Properties of the laplace transform

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A table of Laplace Transform properties.
Table of Laplace Transform properties.
Table of laplace transform properties
Property Signal Laplace Transform Region of Convergence
Linearity α x 1 t β x 2 t α X 1 s β X 2 s At least ROC 1 ROC 2
Time Shifting x t τ s τ X s ROC
Frequency Shifting (modulation) η t x t X s η Shifted ROC ( s η must be in the region of convergence)
Time Scaling x α t 1 α X s α Scaled ROC ( s α must be in the region of convergence)
Conjugation x t X s ROC
Convolution x 1 t x 2 t X 1 t X 2 t At least ROC 1 ROC 2
Time Differentiation t x t s X s At least ROC
Frequency Differentiation t x t s X s ROC
Integration in Time τ ∞ t x τ 1 s X s At least ROC s 0

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Source:  OpenStax, Signals and systems. OpenStax CNX. Aug 14, 2014 Download for free at http://legacy.cnx.org/content/col10064/1.15
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