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 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.

What is in a lens?

Lens makers point to 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 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.
  • Rice Digital Scholarship

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

    Click the "Rice Digital Scholarship" link to see all content affiliated with them.

  • 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.

Also in these lenses

  • Lens for Engineering

    This module is included inLens: Lens for Engineering
    By: Sidney Burrus

    Click the "Lens for Engineering" link to see all content selected in this lens.

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

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

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:

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

Formulas de la Derivada de Reconstrucción

¿Que es

〈sinπ⁢(t−n)π⁢(t−n),sinπ⁢(t−k)π⁢(t−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
〈·,·〉=12⁢π⁢∫−ππe−(i⁢ω⁢n)⁢ei⁢ω⁢kdω · · 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 〉=12⁢π⁢∫−ππe−(i⁢ω⁢n)⁢ei⁢ω⁢kdω=1 sinc n sinc k 1 2 ω ω n ω k 1
(4)
si n≠k n k
〈 sinc n , sinc k 〉=12⁢π⁢∫−ππe−(i⁢ω⁢n)⁢ei⁢ω⁢ndω=12⁢π⁢∫−ππei⁢ω⁢(k−n)dω=12⁢π⁢sinπ⁢(k−n)i⁢(k−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,
〈sinπ⁢(t−n)π⁢(t−n),sinπ⁢(t−k)π⁢(t−k)〉={1  if  n=k0  if  n≠k t n t n t k t k 1 n k 0 n k
(6)
Por lo tanto sinπ⁢(t−n)π⁢(t−n) n∈Z t n t n n es una base ortonormal (ONB) para el espacio de funciones limitadas de banda de −π π .

muestreo:

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

Resumen

Una última vez para f⁢t f t −π π limitado en banda

Síntesis

f⁢t=∑n=−∞∞ f s ⁢n⁢sinπ⁢(t−n)π⁢(t−n) f t n f s n t n t n
(7)

Análisis

f s ⁢n=f⁢t| 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

Download module as:

PDF | EPUB (?)

What is an EPUB file?

EPUB is an electronic book format that can be read on a variety of mobile devices.

Downloading to a reading device

For detailed instructions on how to download this content's EPUB to your specific device, click the "(?)" link.

| More downloads ...

Add module to:

My Favorites (?)

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

| A lens I own (?)

Definition of a lens

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.

What is in a lens?

Lens makers point to 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 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