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Filtros Anti-Aliasing

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

Based on: Anti-Aliasing Filters by Justin Romberg

Summary: Este modulo discute sobre Anti-Aliasing y da ejemplos de filtros que pueden ser usados para evitar el aliasing.

Introduction

La idea de aliasing fue descrita como el problema que ocurre si una señal es no muestreada en un valor suficientemente grande (por ejemplo, debajo de la Frecuencia de Nyquist ). Pero exactamente ¿qué tipo de distorción produce el aliasing?

Figura 1
(a)
Figura 1(a) (anti1.png)
(b)
Figura 1(b) (anti2.png)

Frecuencias altas en la señal original "se dobla" en frecuencias bajas.

Frecuencias altas disfrazadas como frecuencias bajas producen artefactos altamente indeseables en la señal reconstruida.

Cuidado:

Debemos de evitar el aliasing de la forma que podamos.

Evitando el Aliasing

¿Cómo si esto es impracticamente/imposible para muestras como Ω s >2⁢ Ω B Ω s 2 Ω B ?

Filtre hacia afuera las frecuencias anteriores Ω s 2 Ω s 2 antes de que muestree, la mejor forma de visualizarlo es imaginar los siguientes pasos:

  1. Tomar la CTFT (Transformada de Fourier de Tiempo-Continuo) de la señal, f⁢t f t .
  2. Pasar la señal a través de un filtro pasa bajas con las siguiente especificación, ω c = Ω s 2 ω c Ω s 2 .
  3. Ahora tenemos una gráfica de nuestra señal en el dominio de frecuencia con todos los valores de |ω|> Ω s 2 ω Ω s 2 igual a cero. Ahora tomamos la inversa de la CTFT para regresar a nuestra señal de tiempo continuo, f a ⁢t f a t .
  4. Y finalmente estamos listos para muestrear nuestra señal.

Ejemplo 1

Valor de muestra para CD=44.1⁢KHz CD 44.1 KHz .

Muchos instrumentos musicales, contienen las frecuencias arriba de 22⁢KHz 22 KHz (aun cucando no los podemos escuchar).

Debido a esto, podemos filtrar la señal de salida del instrumento antes de que la muestremos usando el siguiente filtro:

Figura 2: Este filtro cortara la frecuencia alta inecesaria, donde | ω c |>2⁢π⁢22⁢kHz ω c 2 22 kHz
Figura 2 (anti3.png)

Ahora la señal esta lista para ser muestreada.

Ejemplo 2: Otro Ejemplo

El discurso del ancho de banda es ±⁢20⁢kHz ± 20 kHz , pero es perfectamente inteligible cuando el filtrado pasa baja a un rango ±⁢4⁢kHz ± 4 kHz . Debido a esto podemos tomar una señal de discurso normal y pasarla a través del filtro como la mostrada en la figura 2, donde ahora ponemos | ω c |>2⁢π⁢4⁢kHz ω c 2 4 kHz . La señal que recibimos de este filtro solamente contiene valores donde |ω|>8⁢π⁢k ω 8 k .

Ahora podemos muestrear en 16⁢π⁢k=8⁢kHz 16 k 8 kHz -- rango de la telefonía estandard.

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