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Este modulo define la desigualdad de Cauchy-Schwarz y discute algunos de sus usos prácticos, especialmente en el detector de filtro acoplado. También, provaremos la desigualdad de CS para espacios vectoriales reales.


Recordando que en 2 , x y x y θ

x y x y
La misma relación se mantiene para espacios de producto interno .

Desigualdad de cauchy-schwarz

Desigualdad de Cauchy-Schwarz
Para x , y en un espacio de producto interno x y x y que mantiene la igualdad si y solo si x y y son linealmente dependientes , es decir x α y para un escalar α .

Detector de filtro acoplado

También conocido como una de las aplicaciones de Cauchy-Schwarz.

Conceptos detrás de los filtros acoplados

Dados dos vectores, f y g , entonces la desigualdad de Cauchy-Schwarz CSI (Cauchy-Schwarz Inequality) es maximizada cuando f α g . Esto nos dice que:

  • f es en la misma "dirección" como g .
  • Si f y g son funciones, f α g significa que f y g tienen la misma forma.
Por ejemplo, suponiendo que tenemos un conjunto de señales, definidas como g 1 t g 2 t g k t , y que queremos ser capaces de decir cual, y si alguna de estas señales se asemeja a otra señal dada f t .
Para poder encontrar las señal(es) que se asemeja a f t tomamos el producto interno. Si g i t se asemeja a f t , entonces el valor absoluto del producto interno, f t g i t , será largo .
Esta idea de ser capaz de medir el rango de dos señales “semejantes” nos da un Detector de Filtro Acoplado .

Comparando señales

El simple uso de Filtro Acoplado será tomar un conjunto de “candidatos” de señales, digamos que nuestro conjunto de g 1 t g 2 t g k t , y tratar de acoplarla a nuestra “plantilla” de señal, f t . Por ejemplo digamos que tenemos las siguientes plantillas ( ) y señales de candidatos ( ):

Señal platilla

Nuestra señal de la queremos encontrar una semejante a esta.

Señales candidatas

Claramente podemos ver cual de las señales nos dará una mejor semejanza a nuestra señal de platilla.

Ahora si nuestra única pregunta fuera cual de estas funciones se acerca mas f t entonces fácilmente tenemos la respuesta basada en la inspección g 2 t . Sin embargo, este no siempre será el caso. También querremos obtener un método o algoritmo que pueda automatizar estas comparaciones. O tal vez queramos tener un valor cuantitativo expresando que tan similares son las señales. Para tratar estas especificaciones, presentaremos un método mas formal para comparar señales, el cual, tal como se menciono anteriormente, esta basado en el producto interno.

Para poder ver cuales de las señales candidatas, g 1 t ó g 2 t , mejor se asemeja a f t % necesitamos realizar los siguientes pasos:

  • Normalice g i t
  • Tome el producto interno con f t
  • Encuentre el más grande
O ponerlo matemáticamente
Mejor candidato i f g i g i

Encontrando un patrón

Extendiendo estos pensamientos del Filtro Acoplado para encontrar semejanzas entre señales, podemos usar la idea de buscar un patrón en una señal larga. La idea es simplemente realizar en varias ocasiones el mismo cálculo como lo hicimos anteriormente; sin embargo, ahora en lugar de calcular en diferentes señales, simplemente realizamos el producto interno con una versión diferente cambiada por nuestra señal patrón. Por ejemplo, digamos que tenemos las siguientes dos señales: una señal patrón ( ) y una señal larga ( ).

Questions & Answers

how did psychology begin?
Valerie Reply
of psychologys commencement, the traces can be seen in the work of Aristotle, where he talk about soul and body, likewise work in durrant, de anima, all these were somewhere supporting dualism, in which soul could exist separately from body
but if you talk about the moder psychology, Gustav fechner, is credited with performing scientific experiments, basis of his experiments in psychology with his studies perception.
does psychology deal with love?
Mohammed Reply
Maybe, i think
I definitely would say yes
how so
there are so many different reasons why you can fall in love with someone, many of them develope subconsciously -> psychology
love messes with the brain, a lot, ergo I believe that Psychology does indeed deal with love
what is synapse
Katie Reply
In the central nervous system, a synapse is a small gap at the end of a neuron that allows a signal to pass from one neuron to the next. synapse are found where nerve cells connect with other nerve cells
can you do auto book auto
Mariah Reply
WHT u mean?
heyy, may i join the conversation please?
edem Reply
who is the father of psychology
Richy Reply
and please, how would you guys, describe the study of psychology at college ?
psychologist student?
i mean not yet but am about to start college so wanna know how is it(college in general and psychology course) please
Psychology is the study of mind and behaviour. So if you will take psychology as a subject so you will get to know how your everything (physical, mental, social, spiritual aspects) effects your behaviour
With this brief knowledge you can help people to cope up with their problems and only you can guide them correctly
And if you go for further specialisations you can study hypnosis, face reading, body language etc
Thanks a lot🙏🏾 And ik some of the stuffs u said but i am also going to write thesis, right ?
ok no prob, thanks a lot🙏🏾✨
hae everyone, hope you are well this evning my question is what is the difference between drive and motivation
good question
drive is more like an impulse or urge and i think they both go together (drive and motivation) even if there is a slight difference
@ Michael Drive is delivered to be innate without the use of an external stimuli, motivation normally evolves an outside stimuli which may include praise, appreciate, or reward.
*believed...sorry for typo
@Reginald, can't the motivation come from the inner self?
Good question, please give an example.
can we say desire of success for example
Wilhelm Wundt is the father of psychology
Wilhem Wundt thank you for the road that you opened.
You mean who is the father of having a great educated argumentative guess? nothing is more wrong than this question. The question is you should ask yourselfs is, how sure are you abour their scientific studying? one's percieved assimilated approach to judging another person and saying they are
the biggest problem with scientific research and data is that ya you could get the same result 1000 times then it could go the other way 1000 times, but we would never know that and we did, we would still say ya but the proof is there. The only thing science proves is that humanity has
no facts about human behavior in the scientific context, but more in the trial and error.. sorry to tell you, but so far no one has proven Father of anything, thats up to you and i, judgement is bias, science is good enough lazy
cognitive development is the growing and development of the brain.
Jessy Reply
Anyone knows about Techno-fascism?
Hussein Reply
Ecofascism is a theoretical political model in which an authoritarian government would require individuals to sacrifice their own interests to the "organic whole of nature". The term is also used as a rhetorical pejorative to undermine the environmental movement.
what's the big difference between prejudice and discrimination?
Danice Reply
A prejudiced person may not act on their attitude.  Therefore, someone can be prejudiced towards a certain group but not discriminate against them.  Also, prejudice includes all three components of an attitude (affective, behavioral and cognitive), whereas discrimination just involves behavior
Nancy Lee
what is all about cognitive development?
cognitive development is the growing and development of the brain
how do you control a variable when using spss whilst running a pearsons correlation analysis?
Jessie Reply
it dependa on your study. according to what you want to say and explain your result
why does it say her and she
Jayla Reply
stages of cognitive development
brivia Reply
sensory preoperatinal concrete formal
what is psychology
Chethani Reply
the study of insecurities and the effect on the host .
Psychology is the scientific study of behavior & mental processes
psychology is science about learning human behaviour
In thinking about the case of Candace described earlier, do you think that Candace benefitted or suffered as a result of consistently being passed on to the next grade?
Nene Reply
what is reward
Angeles Reply
reward is a technique to change behaviour
Reward is a way to promote a specific behaviour or to teach someone/ something to behave a specific way or perform a specific task.
a reward is something that is usually associated with desirable behavior. The child got a reward for winning the game. A reinforcer is different in that a reinforcer is anything that increases behavior, even if it is increasing an undesirable behavior.
reward is earned effort realized
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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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