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Este modulo introduce el Teorema de Nyquist.


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 T igual a nuestro período de muestreo (distancia entre las muestras). Después sea Ω s 2 T (frecuencia de muestreo radianes/seg). Hemos visto que si f t es limitado en banda en Ω B Ω B y muestreamos con período T Ω b 2 Ω s Ω B Ω s 2 Ω B entonces podemos reconstruir f t de sus muestras.

Teorema de nyquist ("teorema fundamental de procesamiento digital de señales dsp")

Si f t es limitado en banda a Ω B Ω B , podemos reconstruirlo perfectamente de sus muestras f s n f n T para Ω s 2 T 2 Ω B

Ω N 2 Ω B es llamada la " frecuencia Nyquist " para f t . Para la reconstrucción perfecta de ser posible Ω s 2 Ω B donde Ω s es la frecuancia de muestreo y Ω B es la frecuencia más alta en la señal.

Illustración de la Frecuencia Nyquist


  • 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.

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La formula de la reconstrucción en el dominio del tiempo se ve como f t n f s n T t n T T t n T Podemos concluir, desde antes que n n T t n T T t n T es una base para el espacio de Ω B Ω B funciones limitadas en banda, Ω B T . Los coeficientes de expansión para esta base son calculados muestreando f t en el valor 2 T 2 Ω B .

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

La gran pregunta

¿Que pasa si Ω s 2 Ω B ? ¿Qué sucede cuando muestreamos abajo del valor de Nyquist?

Vayase a través de los pasos: (véase la )

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

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Questions & Answers

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Introduction about quantum dots in nanotechnology
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Mostly, they use nano carbon for electronics and for materials to be strengthened.
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s. Reply
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Source:  OpenStax, Señales y sistemas. OpenStax CNX. Sep 28, 2006 Download for free at http://cnx.org/content/col10373/1.2
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