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Este modulo describe la Transformada rápida de Fourier (FFT).


La Transformada Rápida de Fourier (Fast Fourier Transform) (FFT) es un algoritmo eficiente O(NlogN) para calcular la DFT

  • orignalmente descubierta por Gauss a primcipios de 1800
  • redescubierta por Cooley y Tukey en IBM durante 1960
  • C.S. Burrus, de la Universidad de Rice University siendo jefe del departamento de Ingenieria, literalmente "escribio el libro" de los algoritmos de la rápida Transformada Discreta de Fourier DFT.
La FFT explota las simetrias en la matriz W para aproximarse "divide y conquistaras". No hablaremos del actual algoritmo de la FFT aqui, veamos estas notas si usted esta interesado en leer mas a cerca de la idea detras de la FFT.

ComparaciÓN de la velocidad

¿En cuánto es mejor O(NlogN) que O( N 2 )?

Esta figura muestra que tan lento crece el tiempo de solución de un proceso de O(NlogN).
N 10 100 1000 10 6 10 9
N 2 100 10 4 10 6 10 12 10 18
N N 1 200 3000 6 10 6 9 10 9

Digamos que tiene una maquina de 1 MFLOP (un millión de "puntos flotantes" de operacione spor segundo). Sea N 1 millión 10 6 .

Un algoritmo de O( N 2 ) toma 10 12 procesos→ 10 6 segundos≃11.5 días.

Un algoritmo de O( N N ) toma 6 10 6 procesos→6 segundos.

N 1 millión es razonable.

Una camara digital de 3 megapixeles arroja 3 10 6 números por cada foto. Asíque para dos N secuencias de punto f n y h n . Si resolvemos directamente f n h n : O( N 2 ) operaciones.

Tomando la FFTs -- O(NlogN)

multiplicando la FFTs -- O(N)

la inversa de FFTs -- O(NlogN).

el total de complejidad es O(NlogN).

FFT + computación didigital fue completamente responsable de la "explosión" del Procesamiento Digital de Señales DSP en los años 60's.

Got questions? Get instant answers now!

La Universidad de Rice fue (y sigue siendo) uno de los lugares de hacer investigación en DSP.

Questions & Answers

what does nano mean?
Anassong Reply
nano basically means 10^(-9). nanometer is a unit to measure length.
do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
Damian Reply
absolutely yes
how to know photocatalytic properties of tio2 nanoparticles...what to do now
Akash Reply
it is a goid question and i want to know the answer as well
characteristics of micro business
for teaching engĺish at school how nano technology help us
Do somebody tell me a best nano engineering book for beginners?
s. Reply
what is fullerene does it is used to make bukky balls
Devang Reply
are you nano engineer ?
fullerene is a bucky ball aka Carbon 60 molecule. It was name by the architect Fuller. He design the geodesic dome. it resembles a soccer ball.
what is the actual application of fullerenes nowadays?
That is a great question Damian. best way to answer that question is to Google it. there are hundreds of applications for buck minister fullerenes, from medical to aerospace. you can also find plenty of research papers that will give you great detail on the potential applications of fullerenes.
what is the Synthesis, properties,and applications of carbon nano chemistry
Abhijith Reply
Mostly, they use nano carbon for electronics and for materials to be strengthened.
is Bucky paper clear?
so some one know about replacing silicon atom with phosphorous in semiconductors device?
s. Reply
Yeah, it is a pain to say the least. You basically have to heat the substarte up to around 1000 degrees celcius then pass phosphene gas over top of it, which is explosive and toxic by the way, under very low pressure.
Do you know which machine is used to that process?
how to fabricate graphene ink ?
for screen printed electrodes ?
What is lattice structure?
s. Reply
of graphene you mean?
or in general
in general
Graphene has a hexagonal structure
On having this app for quite a bit time, Haven't realised there's a chat room in it.
what is biological synthesis of nanoparticles
Sanket Reply
what's the easiest and fastest way to the synthesize AgNP?
Damian Reply
types of nano material
abeetha Reply
I start with an easy one. carbon nanotubes woven into a long filament like a string
many many of nanotubes
what is the k.e before it land
what is the function of carbon nanotubes?
I'm interested in nanotube
what is nanomaterials​ and their applications of sensors.
Ramkumar Reply
what is nano technology
Sravani Reply
what is system testing?
preparation of nanomaterial
Victor Reply
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit 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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