Skip to content Skip to navigation

Connexions

You are here: Home » Content » Desplazamientos Circulares

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.
 

Desplazamientos Circulares

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

Based on: Circular Shifts by Justin Romberg

Summary: Este modulo ve el desplazamiento circular y como se puede usar para representar el desplazamiento de secuencias periodicas.

Las muchas propiedades de la DFTS se convierten sencillas (muy similares a las de las Series de Fourier) cuando entendemos el concepto de: desplazamientos circulares.

Desplazamientos Circulares

Podemos describir las secuencias periódicas teniendo puntos discretos en un círculo como su dominio.

Figura 1
Figura 1 (fig01.png)

Desplazar mm, f⁢n+m f n m , corresponde a rotar el cilindro mm puntos ACW (en contra del reloj). Para m=-2 m -2 , obtenemos un desplazamiento igual al que se ve en la siguiente ilustración:

Figura 2: para m=-2 m -2
Figura 2 (fig2.png)
Figura 3
Figura 3 (fig03.png)

Para ciclar los desplazamientos seguiremos los siguientes pasos:

1) Escriba f⁢n f n en el cilindro, ACW

Figura 4: N=8 N 8
Figura 4 (fig4.png)

2) Para ciclar por mm, gire el cilindro m lugares ACW f⁢n→f⁢ (( n + m )) N → f n f (( n + m )) N

Figura 5: m=-3 m -3
Figura 5 (fig5.png)

Ejemplo 1

Si f⁢n=01234567 f n 0 1 2 3 4 5 6 7 , entonces f⁢ (( n - 3 )) N =34567012 f (( n - 3 )) N 3 4 5 6 7 0 1 2

Es llamado desplazamiento circular, ya que nos estamos moviendo alrededor del círculo. El desplazamiento común es conocido como “desplazamiento linear” (un movimiento en una línea).

Notas para el desplazamiento circular

f⁢ (( n + N )) N =f⁢n f (( n + N )) N f n Girar por NN lugares es lo mismo que girar por una vuelta completa, o no moverse del mismo lugar.

f⁢ (( n + N )) N =f⁢ (( n - ( N - m ) )) N f (( n + N )) N f (( n - ( N - m ) )) N Desplazar ACW mm es equivalente a desplazar CW N−m N m

Figura 6
Figura 6 (fig6.png)

f⁢ (( - n )) N f (( - n )) N La expresión anterior, escribe los valores de f⁢n f n para el lado del reloj.

Figura 7
(a) f⁢n f n (b) f⁢ (( - n )) N f (( - n )) N
Figura 7(a) (fig7a.png)Figura 7(b) (fig7b.png)

Desplazamientos Circulares y el DFT

Theorem 1: Desplazamiento Circular y el DFT

Si f⁢n ↔ DFT F⁢k f n ↔ DFT F k entonces f⁢ (( n - m )) N ↔ DFT e−(i⁢2⁢πN⁢k⁢m)⁢F⁢k f (( n - m )) N ↔ DFT 2 N k m F k (Por ejemplo. Desplazamiento circular en el dominio del tiempo= desplazamiento del ángulo en el DFT)

Proof

f⁢n=1N⁢∑k=0N−1F⁢k⁢ei⁢2⁢πN⁢k⁢n f n 1 N k 0 N 1 F k 2 N k n
(1)
así que el desplazar el ángulo en el DFT
f⁢n=1N⁢∑k=0N−1F⁢k⁢e−(i⁢2⁢πN⁢k⁢n)⁢ei⁢2⁢πN⁢k⁢n=1N⁢∑k=0N−1F⁢k⁢ei⁢2⁢πN⁢k⁢(n−m)=f⁢ (( n - m )) N f n 1 N k 0 N 1 F k 2 N k n 2 N k n 1 N k 0 N 1 F k 2 N k n m f (( n - m )) N
(2)

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