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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 ROC1ROC2 ROC1 ROC2
Desplazamiento en el Tiempo xtτ x t τ e(sτ)Xs s τ X s ROCROC
Desplazamiento de Frecuencia (modulación) eηtxt η t x t Xsη X s η Desplazado una ROCROC ( sη s η debe de estar en la región de convergencia)
Escalamiento en el Tiempo xαt x α t (1|α|)Xsα 1 α X s α Escalado una ROCROC ( sα s α debe de estar en la región de convergencia)
Conjugación xt* x t Xs** X s ROC ROC
Convolución x1 t* x2 t x1 t x2 t X1 t X2 t X1 t X2 t Al menos una ROC1ROC2 ROC1 ROC2
Diferenciación en el Tiempo dd t xt t x t sXs s X s Al menos una ROCROC
Diferenciación de la Frecuencia (t)xt t x t dd s Xs s X s ROC ROC
Integración en el Tiempo txτd τ τ t x τ (1s)Xs 1 s X s Al menos una ROC(Res>0) ROC s 0

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