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Cuando usamos la transformada-z

X z n x n z n
Es de gran ayuda el poder encontrar x n dado X z . Existen al menos 4 métodos diferentes para hacer esto:
  • Inspección
  • Expansion de fracciones parciales
  • Expansión de series de potencia
  • Integración del contorno

El método de inspección

Este "método" es el familiarizarse con la tabla para los pares de la transformada-z y el usar “ingeniería inversa”.

Dado X z z z α Con un ROC de z α Al “inspeccionar” podemos determinar que x n α n u n

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Método de expansión de fracciones parciales

Cuando tratamos con sistemas lineares de tiempo invariante la transformada-z tiene la forma

X z B z A z k 0 M b k z k k 0 N a k z k
Que también se puede expresar como
X z a 0 b 0 k 1 M 1 c k z k 1 N 1 d k z
donde c k representa los ceros con valor no ceros de X z y d k representa los polos con valores no cero

Si M N entonces X z se puede representar por

X z k 1 N A k 1 d k z
Esta forma ayuda el invertir cada termino de la suma usando el método de inspección y la tabla de transformadas . Por lo tanto el numerador es un polinomio se vuelve necesario usar la expansión de fracciones parciales para poder poner X z en la forma descrita arriba. Si M N entonces X z se puede expresar como
X z r 0 M N B r z r k 0 N 1 b k ' z k k 0 N a k z k

Encuentre la transformada inversa-z de X z 1 2 z z -2 1 -3 z 2 z -2 Donde el ROC es z 2 . En este caso M N 2 , así que tenemos que la división larga para obtener X z 1 2 1 2 7 2 z 1 -3 z 2 z -2 Tenemos que factorizar el denominador. X z 2 -1 5 z 1 2 z 1 z Ahora utilizamos la expansión de fracciones parciales. X z 1 2 A 1 1 2 z A 2 1 z 1 2 9 2 1 2 z -4 1 z Ahora cada término se puede invertir usando el método de inspección y la tabla de transformada-z. ya que la ROC es z 2 , x n 1 2 δ n 9 2 2 n u n -4 u n

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Método de expansión de series de potencia

Cuando la transformada-z es definida con una serie de potencia en la forma de

X z n x n z n
entonces cada termino de la secuencia x n se puede terminar al ver los coeficientes del respectivo poder z n .

Ve la siguiente transformada -z de la secuencia de tamaño finito .

X z z 2 1 2 z 1 1 2 z 1 z z 2 5 2 z 1 2 z
En este caso, ya que no hay polos, multiplicamos los factores de X z . Al inspecciónala, se vuele claro que x n δ n 2 5 2 δ n 1 1 2 δ n δ n 1 .

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Una de las ventajas de las series de potencia es que muchas funciones usadas en funciones de ingeniería tienen tabuladas sus series de potencia. Por lo tanto funciones como el Log, seno, exponencial, seno h, etc., se pueden invertir fácilmente.

Suponga X z n logbase --> 1 α z Al notar que n logbase --> 1 x n 1 -1 n 1 x n n Entonces X z n 1 -1 n 1 α n z n n Por lo tanto X z -1 n 1 α n n n 1 0 n 0

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Método de integración del contorno

Sin entrar en detalles

x n 1 2 z r X z z n 1
donde r es el contorno del lado contrario del reloj en la ROC de X z circulando el origen del plano-z. Para expandir este método para encontrar la inversa se necesita conocimiento de teoría de variables complejas y esto no se vera en este modulo.

Questions & Answers

where we get a research paper on Nano chemistry....?
Maira Reply
nanopartical of organic/inorganic / physical chemistry , pdf / thesis / review
Ali
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..
learn
Even nanotechnology is pretty much all about chemistry... Its the chemistry on quantum or atomic level
learn
Google
da
no nanotechnology is also a part of physics and maths it requires angle formulas and some pressure regarding concepts
Bhagvanji
hey
Giriraj
Preparation and Applications of Nanomaterial for Drug Delivery
Hafiz Reply
revolt
da
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.
Damian
yes that's correct
Professor
I think
Professor
Nasa has use it in the 60's, copper as water purification in the moon travel.
Alexandre
nanocopper obvius
Alexandre
what is the stm
Brian Reply
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
Rafiq
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
Damian
How we are making nano material?
LITNING Reply
what is a peer
LITNING Reply
What is meant by 'nano scale'?
LITNING Reply
What is STMs full form?
LITNING
scanning tunneling microscope
Sahil
how nano science is used for hydrophobicity
Santosh
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
Rafiq
what is differents between GO and RGO?
Mahi
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
Rafiq
if virus is killing to make ARTIFICIAL DNA OF GRAPHENE FOR KILLED THE VIRUS .THIS IS OUR ASSUMPTION
Anam
analytical skills graphene is prepared to kill any type viruses .
Anam
Any one who tell me about Preparation and application of Nanomaterial for drug Delivery
Hafiz
what is Nano technology ?
Bob Reply
write examples of Nano molecule?
Bob
The nanotechnology is as new science, to scale nanometric
brayan
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Damian
Is there any normative that regulates the use of silver nanoparticles?
Damian Reply
what king of growth are you checking .?
Renato
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
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
Adin
why?
Adin
what school?
Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
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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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