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Propiedades de la Transformada de Laplace

Module by: Melissa Selik, Richard Baraniuk Translated by: Fara Meza, Erika JacksonBased on: Properties of the Laplace Transform por Melissa Selik, Richard Baraniuk

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

Propiedad Señal Transformada de Laplace Región de Convergencia (ROC)
Linealidad αx1t+βx2t α x1 t β x2 t αX1s+βX2s α X1 s β X2 s Al menos una ROC1⋂ROC2 ROC1 ROC2
Desplazamiento en el Tiempo xt-τ x t τ ⅇ-sτXs s τ X s ROCROC
Desplazamiento de Frecuencia (modulación) ⅇηtxt η t x t Xs-η X s η Desplazado una ROCROC ( s-η s η debe de estar en la región de convergencia)
Escalamiento en el Tiempo xαt x α t 1-|α|Xs-α 1 α X s α Escalado una ROCROC ( s-α s α debe de estar en la región de convergencia)
Conjugación xt¯ x t Xs¯¯ X s ROC ROC
Convolución x1t*x2t x1 t x2 t X1tX2t X1 t X2 t Al menos una ROC1⋂ROC2 ROC1 ROC2
Diferenciación en el Tiempo ddtxt t x t sXs s X s Al menos una ROCROC
Diferenciación de la Frecuencia -txt t x t ddsXs s X s ROC ROC
Integración en el Tiempo ∫-∞txτdτ τ t x τ 1-sXs 1 s X s Al menos una ROC⋂ℜs>0 ROC s 0

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