7.11 Teoremas de plancharel y parseval

 Page 1 / 1
Este modulo contiene la definición del teorema de Plancharel y del teorema de Parseval con sus demostraciones y ejemplos.

Teorema de plancharel

El producto interno de dos vectores/señales es el mismo que en $\ell ^{2}$ el producto interno de su expansión de coeficientes.

Sea $\{{b}_{i}\}$ una base ortonormal para un Espacio de Hilbert $H$ . $x\in H$ , $y\in H$ $x=\sum {\alpha }_{i}{b}_{i}$ $y=\sum {\beta }_{i}{b}_{i}$ entonces ${x\dot y}_{H}=\sum {\alpha }_{i}\overline{{\beta }_{i}}$

Aplicando las Series de Fourier, podemos ir de $f(t)$ a $\{{c}_{n}\}$ y de $g(t)$ a $\{{d}_{n}\}$ $\int_{0}^{T} f(t)\overline{g(t)}\,d t=\sum_{n=()}$ c n d n el producto interno en el dominio-tiempo = producto interno de los coefientes de Fourier.

$x=\sum {\alpha }_{i}{b}_{i}$ $y=\sum {\beta }_{j}{b}_{j}$ ${x\dot y}_{H}=\sum {\alpha }_{i}{b}_{i}\dot \sum {\beta }_{j}{b}_{j}=\sum {\alpha }_{i}({b}_{i}\dot \sum {\beta }_{j}{b}_{j})=\sum {\alpha }_{i}\sum \overline{{\beta }_{j}}({b}_{i}\dot {b}_{j})=\sum {\alpha }_{i}\overline{{\beta }_{i}}$ usando las reglas del producto interno .

${b}_{i}\dot {b}_{j}=0$ cuando $i\neq j$ y ${b}_{i}\dot {b}_{j}=1$ cuando $i=j$

Si el espacio de Hillbert H tiene un ONB, los productos internos son equivalentes a los productos internos en $\ell ^{2}$ .

Todo H con ONB son de alguna manera equivalente a $\ell ^{2}$ .

Teorema de parseval

La energía de una señal = suma de los cuadrados de su expansión de coeficientes.

Sea $x\in H$ , $\{{b}_{i}\}$ ONB

$x=\sum {\alpha }_{i}{b}_{i}$ Entonces $(, x)^{2}=\sum \left|{\alpha }_{i}\right|^{2}$

Directamente de Plancharel $(, x)^{2}={x\dot x}_{H}=\sum {\alpha }_{i}\overline{{\alpha }_{i}}=\sum \left|{\alpha }_{i}\right|^{2}$

Series de Fourier $\frac{1}{\sqrt{T}}e^{i{w}_{0}nt}$ $f(t)=\frac{1}{\sqrt{T}}\sum {c}_{n}\frac{1}{\sqrt{T}}e^{i{w}_{0}nt}$ $\int_{0}^{T} \left|f(t)\right|^{2}\,d t=\sum_{n=()}$ c n 2

important of enocomic
what is division of labour
division of labour can be defined as the separation of task to individuals in any economic system to specialize on it.
what is demand curve
demand curve is a downward sloping economic graph that shows the relationship between the price of product and the quantity of the product demanded.
What is demand
It refers to the quantity of a commodity purchased in the market at a price and at a point of time.
Basanta
refers to amount of commodities a consumer is willing and able to buy at particular price within a period of time
Clifford
It is the ability and willingness a customer buys a product or service at a particular price, place and time while other things remaining constant or the same
kum
In which case is opportunity cost is zero
where no alternative is available
Bhartendu
who is the father of economic
Suraj
ok
Tony
Francis
Opana
Basanta
What is monopoly
it an economic situation where one individual controls the essential commodities or value product for maximum profit
James
monopoly is a market situation in which there is only one producer of a good or service which has no close substitutes
eliano
is where only one person is solely the price taker
Francis
what is Monopoly
The word Monopoly is a Latin word. it is the combination of two words-Mono means single and Poly means seller. thus Monopoly means single seller. but this is not the full meaning of Monopoly. Monopoly must produce a product which does not have close substitute in the market.
Basanta
Monopoly is define as a firm in an industry with very high barriers to entry.
Favour
If close substitute is available, Monopoly will be a king without a crown.
Basanta
what does it array
what are the differences between monopoly and.oligopoly
what are the difference between monopoly and oligopoly
Cbdishakur
The deference between Monopoly and Oligopoly: Monopoly means:A single-firm-Industry producing and selling a product having no close business and Oligopoly means:A market structure where a few sellers compete with each other and each controls a significant portion of market .
Basanta
so that the price-output policy one affects the other.
Basanta
what are difference between physical policy and monotory policy
hon
what is economic
what is economic
Cbdishakur
the word economic was derived from the Greek word oikos (a house)and mein(to manage) which in effect meant managing a household with the limited funds available 🙂.
Basanta
hon
An Enquiry into the nature and causes of wealth Nations, this book clearly defined what economic is🙂🙂🙏🙏 thank you...
Basanta
good example about scarcity: money,time, energy, human or natural resources. Scarcity of resources implies that there supply is very much limited in relation to demand.
Basanta
equilibrium is a situation in which economic forces such as demand and supply are balanced and in the absence of external influences,the value of economic variables will not change
hmnn
Emakpor
marginal cost and marginal revenue is equilibrium .
Kho
yessss
Basanta
what is equilibrium
policy prescriptions for unemployment
Am working on it
Blacks
Study
Janelle
study
simeon
what are the factors effecting demand sedule
we should talk about more important topics, you can search it on Google n u will find your answer we should try to focus on how we can improve our society using economics
shubham
so good night
hon
Why do people buy more grapes in December than in July?
lungi
because at time know money
Researchers demonstrated that the hippocampus functions in memory processing by creating lesions in the hippocampi of rats, which resulted in ________.
The formulation of new memories is sometimes called ________, and the process of bringing up old memories is called ________.
Got questions? Join the online conversation and get instant answers!