Skip to content Skip to navigation

Connexions

You are here: Home » Content » Más sobre Reconstrucción Perfecta

Navigation

Lenses

What is a lens?

Definition of a lens

Lenses

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

What is in a lens?

Lens makers point to Connexions materials (modules and collections), creating a guide that includes their own comments and descriptive tags about the content.

Who can create a lens?

Any individual Connexions member, a community, or a respected organization.

What are tags? tag icon

Tags are descriptors added by lens makers to help label content, attaching a vocabulary that is meaningful in the context of the lens.

This content is ...

Affiliated with (What does "Affiliated with" mean?)

This content is either by members of the organizations listed or about topics related to the organizations listed. Click each link to see a list of all content affiliated with the organization.
  • Featured Content display tagshide tags

    This module is included inLens: Connexions Featured Content
    By: ConnexionsAs a part of collection:"Señales y Sistemas"

    Comments:

    "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 […]"

    Click the "Featured Content" link to see all content affiliated with them.

    Click the tag icon tag icon to display tags associated with this content.

Recently Viewed

This feature requires Javascript to be enabled.

Tags

(What is a tag?)

These tags come from the endorsement, affiliation, and other lenses that include this content.

Más sobre Reconstrucción Perfecta

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

Based on: More on Perfect Reconstruction by Roy Ha, Justin Romberg

User rating (How does the rating system work?)
Ratings

Ratings allow you to judge the quality of modules. If other users have ranked the module then its average rating is displayed below. Ratings are calculated on a scale from one star (Poor) to five stars (Excellent).

How to rate a module

Hover over the star that corresponds to the rating you wish to assign. Click on the star to add your rating. Your rating should be based on the quality of the content. You must have an account and be logged in to rate content.

:
(0 ratings)

Summary: Este modulo examina la idea y detras de la formula de reconstrucción perfecta más a fondo.

Note: Your browser may not currently support MathML. See our browser support page for additional details. You can always view the correct math in the PDF version.

Introducción

En el modulo previo en reconstrucción, dimos una introducción de como trabaja la reconstrucción y temporalemte derivamos una ecuación usada para realizar una perfecta reconstrucción. Ahora tomemos un vistazo más cercano a la formula de la reconstrucción perfecta:

ft=∑n=-∞∞ f s sinπt−nπt−n f t n f s t n t n (1)
Escribiremos ft f t en términos de las funciones sinc desplazadas y escaladas sinπt−nπt−n n∈ℤ t n t n n es una base para el espacio de señales limitadas en bada -ππ . Pero espere . . . .

Formulas de la Derivada de Reconstrucción

¿Que es

<sinπt−nπt−n,sinπt−kπt−k>=? t n t n t k t k ? (2)
Este producto interno puede ser difícil de calcular en el dominio del tiempo, asi que usaremos el Teorema de Plancharel
<·,·>=12π∫-ππⅇ-ⅈωnⅇⅈωkdω · · 1 2 ω ω n ω k (3)

Figura 1
(a)
Figura 1(a) (fig1a.png)
(b)
Figura 1(b) (fig1b.png)

si n=k n k

< sinc n , sinc k >=12π∫-ππⅇ-ⅈωnⅇⅈωkdω=1 sinc n sinc k 1 2 ω ω n ω k 1 (4)
si n≠k n k
< sinc n , sinc k >=12π∫-ππⅇ-ⅈωnⅇⅈωndω=12π∫-ππⅇⅈωk−ndω=12πsinπk−nⅈk−n=0 sinc n sinc k 1 2 ω ω n ω n 1 2 ω ω k n 1 2 k n k n 0 (5)

nota:

En la ecuación 5 usamos el echo de que la integral de la senosoidal en un intervalo completo es 0 para simplificar nuestra ecuación.
Así,
<sinπt−nπt−n,sinπt−kπt−k>=1ifn=k0ifn≠k t n t n t k t k 1 n k 0 n k (6)
Por lo tanto sinπt−nπt−n n∈ℤ t n t n n es una base ortonormal (ONB) para el espacio de funciones limitadas de banda de -ππ .

muestreo:

Muestreo es lo mismo que calcular los coeficientes de ONB, que es el producto interno con sincs

Resumen

Una última vez para ft f t -ππ limitado en banda

Síntesis

ft=∑n=-∞∞ f s nsinπt−nπt−n f t n f s n t n t n (7)

Análisis

f s n=ft| t=n f s n t n f t (8)
Para poder entender un poco más sobre como podemos reconstruir una señal exacatamente, será útil examinar la relación entre las transformadas de Fourier (CTFT y DTFT) a más profundidad.

Content actions

Give Feedback:

E-mail the module authors | Rate module ( How does the rating system work?)

Rating system

Ratings

Ratings allow you to judge the quality of modules. If other users have ranked the module then its average rating is displayed below. Ratings are calculated on a scale from one star (Poor) to five stars (Excellent).

How to rate a module

Hover over the star that corresponds to the rating you wish to assign. Click on the star to add your rating. Your rating should be based on the quality of the content. You must have an account and be logged in to rate content.

(0 ratings)

Download:

Module PDF

Add module to:

My Favorites (?)

'My Favorites' is a special kind of lens which you can use to bookmark modules and collections directly in Connexions. 'My Favorites' can only be seen by you, and collections saved in 'My Favorites' can remember the last module you were on. You need a Connexions account to use 'My Favorites'.

| A lens (?)

Definition of a lens

Lenses

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

What is in a lens?

Lens makers point to Connexions materials (modules and collections), creating a guide that includes their own comments and descriptive tags about the content.

Who can create a lens?

Any individual Connexions member, a community, or a respected organization.

What are tags? tag icon

Tags are descriptors added by lens makers to help label content, attaching a vocabulary that is meaningful in the context of the lens.

| External bookmarks