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Este modulo ve las diferentes propiedades de simetria de las series de fourier y de sus coefficientes.

Propiedades de simetría

Señales reales

Señales reales tienen una serie de fourier con un conjugado simétrico.

Si f t es real eso implica que f t f t ( f t es el complejo conjugado de f t ), entonces c n c - n lo cual implica que c n c - n , Por ejemplo , la parte real de c n es par, y c n c - n , Por ejemplo , tla parte imaginaria de c n es impar. Vea . Lo que tambien implica que c n c - n , Por ejemplo, que la magnitud es par, y que la c n c - n , Por ejemplo , elángulo es impar.

c - n 1 T t 0 T f t ω 0 n t t f t f t 1 T t 0 T f t ω 0 n t 1 T t 0 T f t ω 0 n t c n

c n c - n , y c n c - n .
c n c - n , y c n c - n .

Señales reales y pares

Las señales reales y pares tienen series de fourier que son pares y reales.

If f t f t y f t f t , Por ejemplo , las señal es real y par, entonces entonces c n c - n y c n c n .

c n 1 T t T 2 T 2 f t ω 0 n t 1 T t T 2 0 f t ω 0 n t 1 T t 0 T 2 f t ω 0 n t 1 T t 0 T 2 f t ω 0 n t 1 T t 0 T 2 f t ω 0 n t 2 T t 0 T 2 f t ω 0 n t
f t y ω 0 n t son reales lo cual implica que c n es real. También ω 0 n t ω 0 n t entonces c n c - n . Es tán fácil demostrar que f t 2 n 0 c n ω 0 n t ya que f t , c n , y ω 0 n t son reales y pares.

Señales reales e impares

Señales reales e impares tienen series de fourier que son impares y completamente imaginarias.

Si f t f t y f t f t , Por ejemplo , la señal es real y impar, entonces c n c - n y c n c n , Por ejemplo, c n es impar y completamente imaginaria.

Hágalo usted en casa.

Si f t es impar, podemos expenderlos en términos de ω 0 n t : f t n 1 2 c n ω 0 n t


Podemos encontrar f e t , una función par, y f o t , una función impar, por que

f t f e t f o t
lo cual implica, que para cualquier f t , podemos encontrar a n y b n que da
f t n 0 a n ω 0 n t n 1 b n ω 0 n t

La función triangular

T 1 y ω 0 2 .

f t es real e impar. c n 4 A 2 n 2 n -11 -7 -3 1 5 9 4 A 2 n 2 n -9 -5 -1 3 7 11 0 n -4 -2 0 2 4 ¿Es c n c - n ?

Series de Fourier para una funcion triangular.
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Usualmente podemos juntar información sobre la suavidad de una señal al examinar los coeficientes de Fourier.
Hecha un vistazo a los ejemplos anteriores. Las funciones del pulso y sawtooth no son continuas y sus series de Fourier disminuyen como 1 n . La función triangular es continua, pero no es diferenciable, y sus series de Fourier disminuyen como 1 n 2 .

Las siguientes 3 propiedades nos darán una mejor idea de esto.

Questions & Answers

where we get a research paper on Nano chemistry....?
Maira Reply
what are the products of Nano chemistry?
Maira Reply
There are lots of products of nano chemistry... Like nano coatings.....carbon fiber.. And lots of others..
Even nanotechnology is pretty much all about chemistry... Its the chemistry on quantum or atomic level
no nanotechnology is also a part of physics and maths it requires angle formulas and some pressure regarding concepts
Preparation and Applications of Nanomaterial for Drug Delivery
Hafiz Reply
Application of nanotechnology in medicine
what is variations in raman spectra for nanomaterials
Jyoti Reply
I only see partial conversation and what's the question here!
Crow Reply
what about nanotechnology for water purification
RAW Reply
please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment.
yes that's correct
I think
Nasa has use it in the 60's, copper as water purification in the moon travel.
nanocopper obvius
what is the stm
Brian Reply
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
How we are making nano material?
what is a peer
What is meant by 'nano scale'?
What is STMs full form?
scanning tunneling microscope
how nano science is used for hydrophobicity
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
what is differents between GO and RGO?
what is simplest way to understand the applications of nano robots used to detect the cancer affected cell of human body.? How this robot is carried to required site of body cell.? what will be the carrier material and how can be detected that correct delivery of drug is done Rafiq
analytical skills graphene is prepared to kill any type viruses .
Any one who tell me about Preparation and application of Nanomaterial for drug Delivery
what is Nano technology ?
Bob Reply
write examples of Nano molecule?
The nanotechnology is as new science, to scale nanometric
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Is there any normative that regulates the use of silver nanoparticles?
Damian Reply
what king of growth are you checking .?
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
Stoney Reply
why we need to study biomolecules, molecular biology in nanotechnology?
Adin Reply
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
what school?
biomolecules are e building blocks of every organics and inorganic materials.
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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