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Introduciendo las series de fourier a los sistemas lti

Antes de ver este modulo, usted debería familiarizarse con los conceptos de Eigenfunciones de los sistemas LTI . Recuerde, para sistema LTI tenemos la siguiente relación

Señales de entrada y salida para nuestro sitema LTI.

donde s t es una eigenfunción de . Su eigenvalor correspondiente H s pueden ser calculado usando la respuesta de impulso h t H s τ h τ s τ

Así, usando la expansión de las series de Fourier para f t periódica donde usamos la entrada f t n c n ω 0 n t en el sistema,

Sistema LTI

nuestra salida y t será y t n H ω 0 n c n ω 0 n t Podemos ver que al aplicar las ecuaciones de expansión de series de fourier, podemos ir de f t a c n y viceversa, y es lo mismo para la salida, y t

Efectos de las series de fourier

Podemos pensar de un sistema LTI como el ir moldeando el contenido de la frecuencia de la entrada. Mantenga en mente el sistema básico LTI que presentamos en . El sistema LTI, , multiplica todos los coeficientes de Fourier y los escala.

Dado los coeficientes de Fourier de la entrada c n y los eigen valores del sistema H w 0 n , las series de Fourier de la salida, es H w 0 n c n (una simple multiplicación de termino por termino).

los eigenvalores, H w 0 n describen completamente lo que un sistema LTI le hace a una señal periódica con periodo T 2 w 0

¿Quéhace este sistema?

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El circuito rc

h t 1 R C t R C u t

¿Quées lo que este sistema hace a las series de fourier de la f t ?

Calcula los eigenvalores de este sistema

H s τ h τ s τ τ 0 1 R C τ R C s τ 1 R C τ 0 τ 1 R C s 1 R C 1 1 R C s τ 0 τ 1 R C s 1 1 R C s

Ahora, decimos que a este circuito RC lo alimentamos con una entrada f t periódica (con periodo T 2 w 0 ).

Vea los eigen valores para s w 0 n H w 0 n 1 1 R C w 0 n 1 1 R 2 C 2 w 0 2 n 2

El circuito RC es un sistema pasa bajas : pasa frecuencias bajas n alrededor de 0 ) atenúa frecuencias altas ( n grandes).

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PulsÓCuadrado a travÉS del circuito rc

  • Señal de entrada : tomando las series de Fourier f t c n 1 2 2 n 2 n 1 t en n 0
  • Sistema : Eigenvalores H w 0 n 1 1 R C w 0 n
  • Señal de salida: tomando las series de Fourier de y t d n H w 0 n c n 1 1 R C w 0 n 1 2 2 n 2 n

d n 1 1 R C w 0 n 1 2 2 n 2 n y t n d n w 0 n t

¿Quépodemos decir sobre y t de d n ?

  • ¿Es y t real?
  • ¿Es y t simétrico par?¿simétrico impar?
  • ¿Comóse y t ¿es mas“suave”que f t ? (el radio de descomposición de d n vs. c n )

d n 1 1 R C w 0 n 1 2 2 n 2 n d n 1 1 R C w 0 2 n 2 1 2 2 n 2 n

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Questions & Answers

how to know photocatalytic properties of tio2 nanoparticles...what to do now
Akash Reply
it is a goid question and i want to know the answer as well
Do somebody tell me a best nano engineering book for beginners?
s. Reply
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Devang Reply
are you nano engineer ?
fullerene is a bucky ball aka Carbon 60 molecule. It was name by the architect Fuller. He design the geodesic dome. it resembles a soccer ball.
what is the actual application of fullerenes nowadays?
That is a great question Damian. best way to answer that question is to Google it. there are hundreds of applications for buck minister fullerenes, from medical to aerospace. you can also find plenty of research papers that will give you great detail on the potential applications of fullerenes.
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Abhijith Reply
Mostly, they use nano carbon for electronics and for materials to be strengthened.
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s. Reply
Yeah, it is a pain to say the least. You basically have to heat the substarte up to around 1000 degrees celcius then pass phosphene gas over top of it, which is explosive and toxic by the way, under very low pressure.
Do you know which machine is used to that process?
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s. Reply
of graphene you mean?
or in general
in general
Graphene has a hexagonal structure
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Sanket Reply
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Damian Reply
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abeetha Reply
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Sravani Reply
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Victor Reply
Yes, Nanotechnology has a very fast field of applications and their is always something new to do with it...
Himanshu Reply
good afternoon madam
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what is the application of nanotechnology?
In this morden time nanotechnology used in many field . 1-Electronics-manufacturad IC ,RAM,MRAM,solar panel etc 2-Helth and Medical-Nanomedicine,Drug Dilivery for cancer treatment etc 3- Atomobile -MEMS, Coating on car etc. and may other field for details you can check at Google
anybody can imagine what will be happen after 100 years from now in nano tech world
after 100 year this will be not nanotechnology maybe this technology name will be change . maybe aftet 100 year . we work on electron lable practically about its properties and behaviour by the different instruments
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silver nanoparticles could handle the job?
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this technology will not going on for the long time , so I'm thinking about femtotechnology 10^-15
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Prasenjit Reply
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Source:  OpenStax, Señales y sistemas. OpenStax CNX. Sep 28, 2006 Download for free at http://cnx.org/content/col10373/1.2
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