Skip to content Skip to navigation

Connexions

You are here: Home » Content » Teorema de Nyquist

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.

Teorema de Nyquist

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

Based on: Nyquist Theorem by 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 introduce el Teorema de Nyquist.

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

Anteriormente habia estado expuesto a los conceptos detras del muestreo y el teorema de muestreo. Mientras aprendía estas ideas, debio haber empezado a notar que si muestreamos a muy bajo valor, hay una oportunidad que nuestra señal original no sea únicamente definida por nuestra señal muestreada. Si esto sucede, entonces no es garantia de que recontruyamos correctamente la señal. Como resultado de esto, el Teorema de Nyquist ha sido creado. A continuación veremos exactamente lo que este torema nos dice.

Teorema de Nyquist

Sea TT igual a nuestro período de muestreo (distancia entre las muestras). Después sea Ωs=2πT Ωs 2 T (frecuencia de muestreo radianes/seg). Hemos visto que si ft f t es limitado en banda en -ΩBΩB ΩB ΩB y muestreamos con período T<πΩb⇒(2πΩs<πΩB⇒Ωs>2ΩB) T Ωb 2 Ωs ΩB Ωs 2 ΩB entonces podemos reconstruir ft f t de sus muestras.

Theorem 1: Teorema de Nyquist ("Teorema Fundamental de Procesamiento Digital de Señales DSP")

Si ft f t es limitado en banda a -ΩBΩB ΩB ΩB , podemos reconstruirlo perfectamente de sus muestras fsn=fnT fs n f n T para Ωs=2πT>2ΩB Ωs 2 T 2 ΩB

ΩN=2ΩB ΩN 2 ΩB es llamada la "frecuencia Nyquist " para ft f t . Para la reconstrucción perfecta de ser posible Ωs≥2ΩB Ωs 2 ΩB donde Ωs Ωs es la frecuancia de muestreo y ΩB ΩB es la frecuencia más alta en la señal.

Figura 1: Illustración de la Frecuencia Nyquist
Figura 1 (nyq_f1a.png)

Ejemplo 1: Ejemplos:

  • El oído humano oye frecuencias hasta 20 kHz → CD el valor de la muestra es 44.1 kHz.
  • La linea telefónica pasa frecuencias de hasta 4 kHz → la muestra de la compañia de telefonos es de 8 kHz.

Reconstrucción

La formula de la reconstrucción en el dominio del tiempo se ve como ft=∑n=-∞∞fsnsinπTt−nTπTt−nT f t n fs n T t n T T t n T Podemos concluir, desde antes que ∀n,n∈ℤ:sinπTt−nTπTt−nT n n T t n T T t n T es una base para el espacio de -ΩBΩB ΩB ΩB funciones limitadas en banda, ΩB=πT ΩB T . Los coeficientes de expansión para esta base son calculados muestreando ft f t en el valor 2πT=2ΩB 2 T 2 ΩB .

nota:

La base también es ortogonal. Para hacerla ortonormal, necesitamos un factor de normalización de T T .

La gran Pregunta

Exercise 1

¿Que pasa si Ωs<2ΩB Ωs 2 ΩB ? ¿Qué sucede cuando muestreamos abajo del valor de Nyquist?

Solution

Vayase a través de los pasos: (véase la figura 2)

Figura 2:
Figura 2 (nyq_f2a.png)

Finalmente, ¿Qué le pasara ahora a F s ⅇⅈω F s ω ? Para contestar esta última pregunta, necesitamos ver el concepto de aliasing.

Content actions

Give Feedback:

E-mail the module author | 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