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    This module is included in aLens by: Digital Scholarship at Rice UniversityAs a part of collection: "Señales y Sistemas"

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    By: ConnexionsAs a part of collection: "Señales y Sistemas"

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    "Señales y Sistemas is a Spanish translation of Dr. Rich Baraniuk's collection Signals and Systems (col10064). The translation was coordinated by an an assistant electrical engineering professor […]"

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Procesamiento de Tiempo Discreto de Señales de Tiempo Continuo

Module by: Justin Romberg. E-mail the authorTranslated By: Fara Meza, Erika Jackson

Based on: Discrete Time Processing of Continuous Time Signals by Justin Romberg

Summary: Este modulo se enfoca en el precesamiento de tiempo discreto de las señales de tiempo continuo.

Figura 1:
 (fig1.png)

¿Cómo esta relacionada la CTFT de y(t) con la CTFT de F(t)?

Sea Giω G ω = respuesta de la frecuencia del filtro de reconstrucción Yiω=Giω Yimp iω Y ω G ω Yimp ω donde Yimp iω Yimp ω es secuencia de impulso creada de ys n ys n . Así que, Yiω=Giω Ys eiωT=GiωHeiωT Fs eiωT Y ω G ω Ys ω T G ω H ω T Fs ω T Yiω=GiωHeiωT(1Tr=FiωF2πrT) Y ω G ω H ω T 1 T r F ω F 2 r T Yiω=1TGiωHeiωTr=FiωF2πrT Y ω 1 T G ω H ω T r F ω F 2 r T Ahora asumiremos que f(t) es limitado en banda a πT πT = Ωs 2 Ωs 2 T T Ωs 2 Ωs 2 y Giω G ω es un filtro perfecto de recontrucción. Entonces Yiω={FiωHeiωT  if  |ω|πT0  otherwise   Y ω F ω H ω T ω T 0

nota:

Yiω Y ω tiene le mismo "limite en banda" como Fiω F ω .
Entonces, para señales limitadas en banda, y con un valor de muestra suficientemente alto y un filtro de reconstrucción perfecto

Figura 2:
 (fig2.png)

es equivalente a usar un filtro análogo LTI

Figura 3:
 (fig3.png)

donde Ha iω={HeiωT  if  |ω|πT0  otherwise   Ha ω H ω T ω T 0 Siendo cuidadosos podemos implementar el sistema LTI para señales limitadas en banda en nuestra propia computadora.

Figura 4:
 (fig4.png)

Nota importante:

Ha iω Ha ω = filtro inducido por nuestro sistema.

Figura 5:
 (fig5.png)

Ha iω Ha ω es LTI si y solo si

  • hh, es sistema DT es LTI
  • Fiω F ω , la entrada, es limitada en bada y el valor de la muestra es suficientemente grande.

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Lenses

A lens is a custom view of the content in the repository. You can think of it as a fancy kind of list that will let you see content through the eyes of organizations and people you trust.

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