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Propiedades de la Transformada de Laplace

Module by: Melissa Selik, Richard Baraniuk. E-mail the authorsTranslated By: Fara Meza, Erika Jackson

Based on: Properties of the Laplace Transform by Melissa Selik, Richard Baraniuk

Summary: Tabla de señales, transformada de Laplace, y región de convergencia para propiedades severas.

Tabla 1
Propiedad Señal Transformada de Laplace Región de Convergencia (ROC)
Linealidad α⁢ x1 ⁢t+β⁢ x2 ⁢t α x1 t β x2 t α⁢ X1 ⁢s+β⁢ X2 ⁢s α X1 s β X2 s Al menos una ROC1∩ROC2 ROC1 ROC2
Desplazamiento en el Tiempo x⁢t−τ x t τ e−(s⁢τ)⁢X⁢s s τ X s ROCROC
Desplazamiento de Frecuencia (modulación) eη⁢t⁢x⁢t η t x t X⁢s−η X s η Desplazado una ROCROC ( s−η s η debe de estar en la región de convergencia)
Escalamiento en el Tiempo x⁢α⁢t x α t (1−|α|)⁢X⁢s−α 1 α X s α Escalado una ROCROC ( s−α s α debe de estar en la región de convergencia)
Conjugación x⁢t* x t X⁢s** X s ROC ROC
Convolución x1 ⁢t* x2 ⁢t x1 t x2 t X1 ⁢t⁢ X2 ⁢t X1 t X2 t Al menos una ROC1∩ROC2 ROC1 ROC2
Diferenciación en el Tiempo dd t x⁢t t x t s⁢X⁢s s X s Al menos una ROCROC
Diferenciación de la Frecuencia (−t)⁢x⁢t t x t dd s X⁢s s X s ROC ROC
Integración en el Tiempo ∫−∞tx⁢τd τ τ t x τ (1−s)⁢X⁢s 1 s X s Al menos una ROC∩(Re⁢s>0) ROC s 0

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