<< Chapter < Page Chapter >> Page >
Este modulo introdice las funciones racionales y describe algunas de sus propiedades. En particular, explica como se relacionan con la trasformada-z y los sistemas LTI.


Cuando usamos operaciones con polinomios, el término de funciones racionales es una manera simple de describir una relación particular entre dos polinomios.

Función Racional
Para dos polinomios cualquiera, A y B, su fracción es conocida cono una función racional.

Si usted ha empezado a usar la transformada-z , usted debió notar que todas las transformadas son funciones racionales. En seguida veremos algunas de las propiedades de las funciones racionales y como se pude usar para reveler características importantes de la transformada-z, y por lo tanto revelar una señal o un sistema LTI.

Propiedades de las funciones racionales

Para poder entender lo que hace que las funciones racionales sean tan especiales, tenemos que observar algunas de sus propiedades y características. Si usted esta familiarizado con las funciones racionales y que las funciones básicas de algebra, podrá ir directamente a la siguiente seccion y ver como las funciones racionales nos ayudan a entender la transformada-z.


Para entender muchas de las características de las funciones racionales, tenemos que empezar por encontrar las raíces de la función racional. Para ser esto, factoricemos los dos polinomios para poder observar las raíces fácilmente. Como todos los polinomios, las raíces nos darán información sobre muchas de sus propiedades. Esta función nos muestra el resultado que da el factorizar la función racional anterior, .

f x x 2 x 2 2 x 3 x 1

Así, las raíces para esta función son las siguientes:

Las raíces del numerador son: -2 2

Las raíces del denominador son: -3 1

Para entender las funciones racionales, es esencial el saber y entender las raíces que forman parte de esta función.


Ya que estamos viendo la división de dos polinomios, tenemos que ver los valores de la variable que darán que el denominador de nuestra fracción sea cero. Cuando esto pasa, la función racional se vuelve indefinida, por lo tanto, tenemos una discontinuidad en la función. Ya que sabemos nuestras raíces, es muy fácil saber cuando ocurre esto. Cuando tenemos una variable en el denominador igual a cualquier raíz en el denominador, la función se vuelve indefinida.

Usando la función racional anterior, , podemos observar que función tendrá discontinuidades en los siguientes puntos: x -3 1

Got questions? Get instant answers now!

Con respecto al plano cartesiano podemos decir que las discontinuidades ocurren con respecto al eje de las x . Esta discontinuidades serán asintoticamente vertical en la grafica y representara los valores donde la función esta indefinida.


Usando las raíces anteriores, el dominio de la función racional se puede definir.

El grupo, o conjunto, de valores que son definidos por una función.


La intercesión en la x es definida como el punto (s) donde f x ,en otras palabras la salida de la función racional iguala a cero. Ya que hemos encontrado las raíces de la función este proceso es muy simple. Usando algebra, sabemos que la salida será cero cuando el numerador de la función igual a cero. Por lo tanto, la función tendrá una intercepciones en x cuando sea igual a una de las raíces del numerador.

La intercepción y ocurre cuando x es igual a cero. Se puede encontrar al tener todos los valores de x igual a cero y resolver la función racional.

Las funciones racionales y la transformada-z

Como ya lo hemos mencionado todas las transformadas-z se pueden escribir como función racional, lo cual es la manera mas común de representar la transformada-z. Por esto, podemos usar las transformadas anteriores especialmente las de la raíces, para reveler algunas de las características de la señal o sistema LTI descritos por la transformada-z.

La siguiente ecuación muestra la forma general de escribir la transformada-z como una función racional:

X z b 0 b 1 z -1 b M z M a 0 a 1 z -1 a N z N
Si usted ya vio el modulo titulado el entender graficas de polos y ceros y la transformada-z , usted sabrá como las raíces de las funciones racionales forman un papel importante para entender la transformada-z. La ecuación anterior, , se puede expresar en una forma factorizada similar la función racional vista anterior menta, vea . Por lo tanto podemos encontrar las raíces del numerador y denominador de la transformada-z. Las siguientes dos relaciones se vuelven obvias:

    Relación de raíces en polos y ceros

  • Las raíces del numerado en la función racional son lo ceros en la transformada-z
  • Las raíces en el nominador de la función racional son los polos de la transformada-z


Una vez que usemos nuestro conocimiento de funciones razónales para encontrar sus raíces, podemos manipular una transformada-z en varias maneras útiles. Podemos usar este conocimiento para representar un sistema LTI gráficamente usando una grafica de polos y ceros , o para analizar o diseñar un filtro digital a través de la transformada-z .

Questions & Answers

which comes first emotion or thinking
hamed Reply
either could come first. arguing for the supremacy of one over the other may not hold, ceteris paribus.
Depends on which part of brain is dominated in individual.
thinking. it's a thought that provokes an emotion
I often saw cat in my dreams nd thats why i m afraid of cats.. wherever i see cat i just escape from that place what is this nd why this happens
Tasneem Reply
usually whatever you see during the day or what impacted you in the slightest, will appear in your dream.
What kind of dream? Why you afraid of cat because you dream about it? Bad dream?
i saw cat nd lizard nd oftenly they attack me nd i could not save my self nd then i wakeup nd feels fear
from childhood i like cata nd play with it but now because of that dreams i dont like cats nd lizards
some times you feels uncomfortable to cat have around you ,but still you should take out from fear..
yes i want to take out this fear but i cannot face cat wherever i see cat i feel fear
you know your weakness, that is it..you should see the videos on cats ..it will be enough for you.. after that you see the variation in your mind illusions
if it is more fear, you take Consultancy from psychiatrist..
thats the problem i can't see cats videos i dont wanna see cats or lizards
what you think? that cat attack on you..😅
is there any past memory relate with this?
yes i think that cat will attack me but i just saw cats in dreams attacking me
can you understand hindi?
اچھا ہے..آپ نے کبھی علم نفسیات اور خواب کی تعبیرات کی کتابیں پڑی ہے..اپنے آپ کو درست کرنے کے لیے یہ سب سے بہترین نسخہ ہے..
the cat is your mind reflecting your Self. you are not afraid of cats, the cat is just a symbol for the fear you have of life and death. Cat is life, cat eats lizard, cat brings death. You are either the cat or the lizard, in your subconscious mind.
next time you dream, ask your mind to become the cat
it may have bitten in your childhood stage,and you still remember it
Where is semantic memory u mentioned the name but didn't disscuss the topic..?
Iqra Reply
If u have want to make happy ur babby not by blood but by heart by giving all ur time to them but ur mother wants u to gave that time on urself and ur studies and that makes her happy and mom doesnot know that i accept her as my babby she thought she is just my friend
Actually she is 4 years younger than me but i love her and said my baabby to her what should i do now?
If anyone can help me plz do it i am super depressed
Hlo Iqra...
If u r in real conjunction wd him say ur mom fluently that I wana make him mine I feel depressed
Mom has best hearing power as to understood her/his baby
But my mom dont accept that she think i am just runing my life
U have to b very clear wd ur mom
Where from u
Well i didn't tell about that but i said i love her she is like my soul sister and i love to gave her time but she said if u want to meat her itsok but dont talk on phone because u consume alot time on her and thats not fair
Bhai i am from earth
How can I suggest u it WL take alot time
Actually she dont like her because i gave 3 to 4 hours on phone to her
Where frm u r?
Okay thank u so much bhai i think i got my answer
whats your relation with her ? where you meet her nd why your mom forbid you from talking with her
Ur most welcome sister
She live in my neighborhood we are frnds from childhood but she is 4 yeras younger than me thats why i called her my bachaa and i gave alot of time to her because she have no sister brother and also no frnd and my mom dont like that
Because 3 to 4 hours on phone she dont like usage of phone so much no one did accept me infront her thats why she is against her she dont hate her she just said meet her face to face not on phone
Okay thank u so much all of u now i am feeling good and got my answe also
yeah your mom said right but dont talk too face to face sometimes things that are above limits leads to problems
Yeah u are right inshallah everything will be alright soon
Thank u
inshaa allah..
i have a question?
Yes u can ask
what is one strategy that would promote positive risk taking behavior?
I dont know
Why do I get upset when my girlfriend doesn't tell me she loves me back in front of her friends?
Apollo Reply
Do not depend on her, or don't hope just take care of her ..it doesn't matter that how much she love you..matter that how much you love her..
Because you're insecure, read "The Rational Male" by Rollo Tomassi if you want to make sure that you and your girlfriend are/remain satisfied in your relationship
and don't listen to Kanzul, don't be a pushover
may be you are suspicios if she stay around her male friends
Thank you both, yeah umm it makes sense that I'm insecure and yeah I mean I do love her alot the thing is it's not with her Male friends it's in general.
But also what is considered a pushover so I can avoid that Leon
what is this that a persom constantly saw dream from very early age till now nd saw same dream what is this
Tasneem Reply
Your soul
it is your inner being,it knows, your heart,inner spirit
thank you
samething keeps happening,repeat
why do I have dreams of my boyfriend boss
Nicole Reply
Because you love him and his memories. Or that you are reminded of him very often.
There are some explanation why we have dream. It can be just your brain picking random memory in your brain when you sleep (eventhough we sleep our brain still working) and this random memory your brain pick out become your dream
or this boss left an impression in you, but it doesn't necessarily mean you have a romantic feelings towards this person. Maybe this boss just do some random thing and it left an impression in your memory and you still think about it subconsciously when you sleep and it manifested itself in ur dream
That is perfectly normal and no cause for worry. You might not want to tell your boyfriend though ;)
What do you think is the reason for your friends or the family members coming into the dreams especially wet dreams? And after that what's the feeling of the person?
how to get rid of fearful avoidant issues
Alexsus Reply
Do you think that seminary student needs psychological studies?
Jobin Reply
I think it's best for high schoolers.. we all should be aware of what we are
Yes definitely, especially in an age like this were more and more I've observed students not knowing what they truly are and not knowing how to deal with psychological issues. Plus, it gives them the advantage of knowing how to deal with other people with different ideas and issues.
Absolutely. How would you be able to make any serious decisions in your life, when you are a mess and don't understand your feelings, motivation and reasoning behind this or that issue. Moreover, I think whether you are a seminary student or not, you should also be taught critical thinking skills.
Thank you all
whats is schizophrenia
mobile Reply
long-term mental disorder of a type involving a breakdown in the relation between thought, emotion, and behavior, leading to faulty perception, inappropriate actions and feelings, withdrawal from reality and personal relationships into fantasy and delusion, and a sense of mental fragmentation.
What is burn out syndrome?
Emotional and physical exhaustion which appears after a long period of stress.
what is social conflict
deen Reply
a conversation with someone & having conflict with .
Soory Guys hope you ar doing well Im in strong desire to get this kind of book INTRODUCTORY PSYCHOLOGY but ther cost is too and I'm not able to buy it If you see this announcement please I need soft copy even few please
Anybody who is able to access this book just help even soft copy to saves me Im so soory
Deen social conflict means misunderstand occurred among the people in a certain social context can be caused by poor governance
what is top-notch?
Vi Reply
excellent? the best?
the very best.
best of something. above the expectation
something like expert level
Hi! what is introspection?
the ultimate best.. of excellent quality
honor and respect
Hi! This book INTRODUCTORY PSYCHOLOGY I'm not able to buy anybody can help me even soft copy
i want some pdf books who can help me
Google "libgen", you can download almost any book there. I can't send the link as links are blocked by the app
is there any website where I can get a true diagnosis of a personality disorder I think I may possess? I can't seek therapy due to insurance complications
Bailey Reply
Well most websites that offer actual medical diagnoses cost money or they will connect you to a doctor for some sort of meeting.
yeah I've been looking for a decent site for around a year now and that's all Ive found thank you
Yeah it is quite hard to find a reliable site.
diagnosis couldn't get from a websites. you have to refer a doctors for a consultation.
please which site can I download child psychology textbook?
Compare and contrast situational influences and dispositional influences and give an example of each. Explain how situational influences and dispositional influences might explain inappropriate behavior.
Babafemi Reply
please tell me about ethical consideration and research method
Its Reply
what is an ethical consideration that is what a search for my research is seeking out the truth what lies in the darkness and it's hidden by the light
Ethical consideration includes the risk of doing your research
as well as the research can not have lasting affects on the subjects.
Is this live
We as researchers should not harm the subjects of our research, be it the population under study or the selected sample. I think ethical consideration requires that we disclose as much as is practically possible about the requirements of the research to all concerned.
It is ethically sound also to to acknowledge others' findings wherever we reference them in our research because we are to build and grow the body of knowledge by building on the research others have done. This is my contribution.
What is CBT?
cognitive behavioral therapy
When they use this CBT?
what is cbt
mostly used to help treat anxiety and depression related diagnosis. But it's used in other types of mental health issues.
cognitive behavioral therapy. As stated earlier in this discussion.
Thank yoi
Got questions? Join the online conversation and get instant answers!
QuizOver.com Reply

Get the best Algebra and trigonometry course in your pocket!

Source:  OpenStax, Señales y sistemas. OpenStax CNX. Sep 28, 2006 Download for free at http://cnx.org/content/col10373/1.2
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'Señales y sistemas' conversation and receive update notifications?

Start Quiz