it.wikipedia.org website review
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SEO Keyword summary for it.wikipedia.org/wiki/trasformata_di_fourier
Keywords are extracted from the main content of your website and are the primary indicator of the words this page could rank for. By frequenty count we expect your focus keyword to be displaystyle
Focus keyword
Short and long tail
Short Tail Keywords displaystyle trasformata fourier |
long Tail Keywords (2 words) di fourier trasformata di teorema di una funzione fdisplaystyle f |
long Tail Keywords (3 words) trasformata di fourier il teorema di 1sqrt 2pi int della trasformata di trasformata di laplace di una funzione serie di fourier |
it.wikipedia.org On-Page SEO Scan
Descriptive Elements
The <head> element of a it.wikipedia.org/wiki/trasformata_di_fourier page is used to inform the browser and visitors of the page about the general meta information. The head section of the page is where we place the page title, the definition of the HTML version used, the language of in which the page is written. In the head section we can also include JavaScript and CSS (markup) files for the page.
Page title
Title length
trasformata fourier wikipedia
Meta description
Meta description legth
Meta description SEO
No meta relevance in the description detected !
Content SEO
Number of Words
Spam detected?
Headings
Heading distribution
Heading normalisation
Heading SEO impact
Emphasis (bold and italic)
Emphasis SEO impact
Images
Number of images
Images dimensions
Image alt descriptions
Images SEO impact
displaystyle hat mathcal fleftxtrightomega siomega cdot icdot fomega uneintnin mathbb fin sum ninfty infty fnunsum fneint fnfrac funun funfrac int fxeinxdx fxei leftfrac ntrightxdx ffleftn over tright ffthat ftfrac sqrt fxeixtdxqquad forall tin ffmapsto fmathbf ffmathbf frac neimathbf mathbf dmathbf qquad xin fxfrac fteixtdt phi fgphi fphi gqquad fgin beta linfty ffrac fxbeta xdx fgfrac gyphi fxydy gphi gybeta ydy fbeta yphi fxy fyx fzbeta xyphi fzxyphi fzxbeta xbeta xybeta xebeta xeitx fex sneq fhat falpha galpha ffbeta alpha gtftalpha gomega eialpha omega gtfteialpha gtft gtftlambda lambda flambda quad fgtfrac isqrt nftiomega giomega mathrm ffgmathcal ffcdot gmathcal ffmathcal fgmathcal big fgbig hxfstar gxint overline fygxydy fhxi ffxi fgxi fxint fyfxydy gtitft ftext widehat tithat cap fto atfrac aafxeixtdx psi axfrac aahat lim ato ahat axsum aneinxqquad bxsum bneinx anoverline bnfrac axoverline bxdx axbx dtint aomega domega fat fleftxtrightxomega leftxomega rightxt leftxtrightxomega fcolon fxeizxdxrightarrow text per zrightarrow fleftftrightomega fleftftrightmathcal lleftftrightsiomega eiomega tftmathrm utchi uomega tchi tdtfrac tiomega right iomega sin utfrac tutdtfrac geq gamma oint dzrightarrow dtqquad textper rrightarrow zpm operatorname res zilim ieiomega zfrac ziz eomega ibig collabora wikimedia commons modifica wikidata foundation powered mediawiki
Mobile SEO it.wikipedia.org/wiki/trasformata_di_fourier
Mobile rendering
Mobile optimizations
Responsive design detected (mobile css)
No flash detected !
Mobile improvement
Marketing / lead generation for it.wikipedia.org/wiki/trasformata_di_fourier
Social Media
Facebook shares | Facebook likes | ||
Facebook comments | Tweets | ||
Google +1 |
Conversion form
Search form
Analytics
Online presence
SERP Preview
SERP Title
SERP Link
SERP Description
Domain Level SEO
Domain name
16 characters long
Domain name SEO Impact
Path name
fourier found in path !
trasformata found in path !
Structured data
Publisher Markup
Other Structured data
Website configuration
Correct processing of non-existing pages?
Favicon icon found?
Robots.txt found?
Sitemap found?
Navigation and internal links
Navigation
Url seperator
Human readable urls
Number of links
Link SEO Impact
statistiche
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versione stampabile
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wiki jean baptiste joseph fourier
analisi matematica
trasformata integrale
1822
fisica
ingegneria
scienze pure
applicate
esponenziali
dominio delle frequenze
spettro di un operatore
segnale periodico
serie di fourier
campionamento
contenuto informativo
teoria dellinformazione
sua variante discreta
teorema di inversione di fourier
trasformata di laplace
se e solo se
discreto
valor medio
analisi di fourier
analisi armonica
eulero
teoria dei segnali
unit immaginaria
combinazione lineare
sistemi dinamici
equazioni differenziali
ingegneria dei sistemi
risposta impulsiva
risposta in frequenza
frequenze
ampiezze
fasi
sistema ortonormale
quadrato sommabile
proiezioni ortogonali
supporto
trasformata inversa di fourier
funzione
spazio di schwartz
numero reale
teorema di plancherel
spazio di hilbert
quasi ovunque
operatore
prodotto scalare
endomorfismo
onde
omomorfismo
convoluzione
funzione continua
complesso coniugato
cambio di variabile
teorema di convoluzione
teorema di fubini
correlazione incrociata
autocorrelazione
integrazione per parti
derivata
funzioni integrabili
lebesgue
sommabile
isometria
isomorfismo
denso
teorema di parseval
riemannintegrabili
dominio del tempo
formula di sommazione di poisson
teorema del campionamento
delta di dirac
lemma di riemannlebesgue
funzione misurabile
funzione rettangolare
teorema dei residui
lemma di jordan
walter rudin
isbn
barry simon
teorema di wienerchinin
trasformata di fourier a tempo discreto
trasformata di fourier veloce
trasformata discreta di fourier
trasformata di fourier quantistica
istituto dellenciclopedia italiana
enciclopedia britannica
open library
internet archive
mathworld
encyclopaedia of mathematics
thesaurus bncf
leggi
pagina principale
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SEO Advice for it.wikipedia.org
In this section we provide pointers on how you can to optimize your web page so it can be found more easily by search engines and how to make it rank higher by optimizing the content of the page itself. For each of the individual criteria the maximum score is 100%. A score below 70% is considered to be indication that the page is not complying with general SEO standards and should be evaluated and/or fixed. Not every factor is weighted the same and some are not as important as others. Relatively unimportant factors like meta keywords are not included in the overall score.
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Title relevance | 87% | A title should reflect the contents of a site. This site has a 67 % match | |
Title Length | 80% | Limit your title to anywhere between 40 and 70 characters. Your title was 35 characters long | |
Meta Description | 0% | A meta description is the second element that shows in the search results so always use the meta description. | |
Meta description length | 0% | The meta description should be between 145 and 160 characters. This meta description is 1 characters long. | |
Meta description relevance | 0% | Meta Description should reflect the contents of a site. This site has a 0 % match | |
Number of internal links | 50% | Linking to internal pages makes pages easier to find for search engines. Try to keep the number of links on your page roughly below 100. There are 181 internal links on this page. | |
Folder structure | 100% | We found a folder structure in the links on your page. A good folder structure makes a site easier to navigate. We found 3 level 1 folders and 5 folders above or in the first level of navigation. | |
Headings | 37% | Headers should reflect the contents of a site. This site has a 16 % match | |
Links | 14% | Link anchors should to some degree reflect the contents of a site. This site has a 7 % match | |
Image alt tags | 22% | Image alt tags should to some degree reflect the contents of a site. This site has a 8 % match | |
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WordCount | 20% | An ideal page contains between 400 and 600 words.This page contains 5002 words | |
Server response time | 100% | A fast server speeds up a website. This server responds 93.41% faster then average | |
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Keywords in Domainname | 30% | There are no important keywords in your domain name | |
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Structured Data | 100% | Structured data makes it easier for search engines to index your website | |
Inline css | 0% | Do not use inline css declarations. Inline css will slow down the rendering of the website. We detected 516 inline style declarations ( <a style="color:green">) with a size of 17242 bytes | |
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Mobile Website | 100% | Perfect, we found a responsive design for mobile users | |
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Normalized headings | 100% | Perfect, we found a correct use of normalized headings ! |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/e4dd1394b366c601c7735f53839bc54eed51f284 height: height attribute not set width: width attribute not set description: {\displaystyle f(y-x)} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/c9e5a36747c5373be60c26bcee2ea34188d2f510 height: height attribute not set width: width attribute not set description: {\displaystyle \phi (f(z))\beta (x+y)=\phi (f(z-(x+y)))=\phi (f(z-x))\beta (y)=\phi (f(z))\beta (x)\beta (y),} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/41603f3c9acead5a1fa829e9757c1e1e39346b93 height: height attribute not set width: width attribute not set description: {\displaystyle \beta (x+y)=\beta (x)\beta (y),} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/e556678a0ec1c8716944a85aed96d9bf074239c0 height: height attribute not set width: width attribute not set description: {\displaystyle \beta (0)=1} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/094f824655138f6b11d96a0da32e7f0716ba6959 height: height attribute not set width: width attribute not set description: {\displaystyle y=0} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/b7f803e59d696fb17dfcd7e9861b967ab86a9248 height: height attribute not set width: width attribute not set description: {\displaystyle \beta '(x)=\beta '(0)\beta (x),} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/d860d4134dab37b6bdd9375575386be5993e763c height: height attribute not set width: width attribute not set description: {\displaystyle \beta '(0)} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/f4265d36706424814d8c112fe50fa2427b9c5639 height: height attribute not set width: width attribute not set description: {\displaystyle \beta (x)=e^{\beta '(0)x}.} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/b5c72cc0af1a07a2543699571d03848c79fe37c5 height: height attribute not set width: width attribute not set description: {\displaystyle \beta '(x)=e^{-itx}.} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/038a8057bb51eafa885c9dadb0fcff14aa0fd9e4 height: height attribute not set width: width attribute not set description: {\displaystyle f=e^{-|x|}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/24358444e0dfe86484eba840a5f5362597b26ac5 height: height attribute not set width: width attribute not set description: {\displaystyle s\neq t} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/14ce989fd75da938ec6f95a0cdb71037b23a11cb height: height attribute not set width: width attribute not set description: {\displaystyle {\hat {f}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/01d131dfd7673938b947072a13a9744fe997e632 height: height attribute not set width: width attribute not set description: {\displaystyle s} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/02800e6580f30f876b4bc0c7de3f9d6b0eb73d4d height: height attribute not set width: width attribute not set description: {\displaystyle \phi (f)={\hat {f}}(t).} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/005abdc04f9ec7a034ebc56f8aee247e5cb4fb30 height: height attribute not set width: width attribute not set description: {\displaystyle {\mathcal {f}}(\alpha f+\beta g)=\alpha {\mathcal {f}}(f)+\beta {\mathcal {f}}(g),} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/3b80f9acc3deaf03a4fa2fca88f56a44ec5aeedc height: height attribute not set width: width attribute not set description: {\displaystyle f,g\in l^{1}(\mathbb {r} )} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/94d6f18f24f5aae87ddd480dcc73f73d4cf31631 height: height attribute not set width: width attribute not set description: {\displaystyle \alpha ,\beta \in \mathbb {c} } |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/8b74a27234b1df8cb0ef6c17fd8062ac0ceef576 height: height attribute not set width: width attribute not set description: {\displaystyle f\in l^{1}(\mathbb {r} )} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/7988141e89a37e7f4deb883dbd74d9bbd6d11317 height: height attribute not set width: width attribute not set description: {\displaystyle \alpha \in \mathbb {r} } |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/4494315cabe637dca41a2fcd8c5f59a168f498b1 height: height attribute not set width: width attribute not set description: {\displaystyle g(t)=f(t-\alpha )} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/d59ee2ba48c7d5c49c883838b6ebd2a8834da1d1 height: height attribute not set width: width attribute not set description: {\displaystyle {\hat {g}}(\omega )={\hat {f}}(\omega )e^{-i\alpha \omega }} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/4d7bb847aadb244a51129f686de359ade0a6c176 height: height attribute not set width: width attribute not set description: {\displaystyle g(t)=f(t)e^{i\alpha t}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/08c411d15541e5f579aa7d1e76c6690007721457 height: height attribute not set width: width attribute not set description: {\displaystyle {\hat {g}}(\omega )={\hat {f}}(\omega -\alpha )} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/b87d4fad16756ec052cba6231782d877b8db3892 height: height attribute not set width: width attribute not set description: {\displaystyle g(t)=f(-t)} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/bb58bb97498940ae5cffa87e38832eb15bab71fd height: height attribute not set width: width attribute not set description: {\displaystyle {\hat {g}}(\omega )={\hat {f}}(-\omega )} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/f5ab61f770d324f313a0911c209a8c75e5bbdce8 height: height attribute not set width: width attribute not set description: {\displaystyle g(t)=f(-t)^{*}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/25bb94c68136c8bdfa2534f42290139781c362e5 height: height attribute not set width: width attribute not set description: {\displaystyle {\hat {g}}(\omega )={\hat {f}}(\omega )^{*}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/831d02e1a3c6b8eccfccaf405bbcd52d123adf97 height: height attribute not set width: width attribute not set description: {\displaystyle g(t)=f(t/\lambda ),} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/bed6c5db0b6df2bf3ec1182eb89433a799bf5507 height: height attribute not set width: width attribute not set description: {\displaystyle {\hat {g}}(\omega )=\lambda {\hat {f}}(\lambda \omega ),\quad \lambda >0.} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/d3556280e66fe2c0d0140df20935a6f057381d77 height: height attribute not set width: width attribute not set description: {\displaystyle g} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/c510b63578322050121fe966f2e5770bea43308d height: height attribute not set width: width attribute not set description: {\displaystyle \mathbb {r} ^{n}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/2e12710d7dddcf0a2981dfef6d0711eece1f3aa8 height: height attribute not set width: width attribute not set description: {\displaystyle (f*g)(t)={\frac {i}{\sqrt {2\pi }}}\int _{\mathbb {r} ^{n}}f(t-i\omega )g(i\omega )\mathrm {d} \omega .} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/87e923cd67cb395ed1d0c857b96f9f51bc889c59 height: height attribute not set width: width attribute not set description: {\displaystyle \ {\mathcal {f}}\{g\}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/9e7578e947673cc9eadf52f3bd9d020202ba458d height: height attribute not set width: width attribute not set description: {\displaystyle {\mathcal {f}}\{f*g\}={\mathcal {f}}\{f\}\cdot {\mathcal {f}}\{g\},} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/ba2c023bad1bd39ed49080f729cbf26bc448c9ba height: height attribute not set width: width attribute not set description: {\displaystyle \cdot } |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/91096ea81c470995816fbbf389a25f46049cd506 height: height attribute not set width: width attribute not set description: {\displaystyle {\mathcal {f}}\{f\cdot g\}={\mathcal {f}}\{f\}*{\mathcal {f}}\{g\}.} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/798153399d91ed4f7c88fa012bd0fabe708c4de2 height: height attribute not set width: width attribute not set description: {\displaystyle {\mathcal {f}}^{-1}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/9f6953f02bdfa644f48789cbd7966fc5efcfa503 height: height attribute not set width: width attribute not set description: {\displaystyle f*g={\mathcal {f}}^{-1}{\big \{}{\mathcal {f}}\{f\}\cdot {\mathcal {f}}\{g\}{\big \}}.} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/02c07825dae28705df03d15daeb8844d49c4dbd4 height: height attribute not set width: width attribute not set description: {\displaystyle h(x)} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/c6ca91363022bd5e4dcb17e5ef29f78b8ef00b59 height: height attribute not set width: width attribute not set description: {\displaystyle g(x)} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/0639a063304bc080f54f3e4f61505c8ac1f9f91a height: height attribute not set width: width attribute not set description: {\displaystyle h(x)=(f\star g)(x)=\int _{-\infty }^{+\infty }{\overline {f(y)}}\,g(x+y)\,dy,} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/54a1214b144f5e2f38f09ca99c1ee91c7ec363be height: height attribute not set width: width attribute not set description: {\displaystyle {\mathcal {f}}\{h\}(\xi )={\overline {{\mathcal {f}}\{f\}(\xi )}}\,{\mathcal {f}}\{g\}(\xi ).} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/1a2dd8403e66efe049e053b067f1e2efe3344021 height: height attribute not set width: width attribute not set description: {\displaystyle h(x)=(f\star f)(x)=\int _{-\infty }^{+\infty }{\overline {f(y)}}f(x+y)\,dy,} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/09705258e509aa948444c3c7abeefdc3ac214d85 height: height attribute not set width: width attribute not set description: {\displaystyle {\mathcal {f}}\{h\}(\xi )={\overline {{\mathcal {f}}\{f\}(\xi )}}\,{\mathcal {f}}\{f\}(\xi )=|{\mathcal {f}}\{f\}(\xi )|^{2}.} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/49dbf1b277c0480cd65e6a8ceb00539361f5c3e0 height: height attribute not set width: width attribute not set description: {\displaystyle g(t)=-itf(t),} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/dedd79bc52b0c4b1e83b8122066fe544b5e39d9e height: height attribute not set width: width attribute not set description: {\displaystyle {\hat {f}}{\text{ }}'(t)={\hat {g}}(t).} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/f7e721f4035d028a233bb65ed21658b2f3c68a8f height: height attribute not set width: width attribute not set description: {\displaystyle f'\in l^{1}(\mathbb {r} )} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/318b3c3b78d0ae485d795671a64ab2c878a15987 height: height attribute not set width: width attribute not set description: {\displaystyle {\widehat {f'{\text{ }}}}(t)=it{\hat {f}}(t).} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/c699871018692725caf7d2ea3cb7208b2b388075 height: height attribute not set width: width attribute not set description: {\displaystyle l^{1}\cap l^{2}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/8fac0e644d17b43fce6bb695d2632de685353d66 height: height attribute not set width: width attribute not set description: {\displaystyle f\in l^{1}\cap l^{2}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/9e23ddbe604686bcd44efe74987ff95dd78e2333 height: height attribute not set width: width attribute not set description: {\displaystyle f\in l^{2}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/4c4684ab1ba09fafebe194e370d1ff0935b00886 height: height attribute not set width: width attribute not set description: {\displaystyle \|{\hat {f}}\|_{2}=\|f\|_{2}.} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/a5aba08df5b5cedb8393afe83de5039b932b5a3e height: height attribute not set width: width attribute not set description: {\displaystyle f\to {\hat {f}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/20f303eeaf97f2c664dc3995b3924e293718a28a height: height attribute not set width: width attribute not set description: {\displaystyle \phi _{a}(t)={\frac {1}{\sqrt {2\pi }}}\int _{-a}^{a}f(x)e^{-ixt}\,dx,} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/021f88bb92e6ac7069d99d7d0d378df66c910623 height: height attribute not set width: width attribute not set description: {\displaystyle \psi _{a}(x)={\frac {1}{\sqrt {2\pi }}}\int _{-a}^{a}{\hat {f}}(t)e^{ixt}\,dt,} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/125032a1428f49fae512492eda608a63543852f8 height: height attribute not set width: width attribute not set description: {\displaystyle \lim _{a\to \infty }\|\phi _{a}-{\hat {f}}\|_{2}=0,\qquad \lim _{a\to \infty }\|\psi _{a}-f\|_{2}=0.} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/b078651e6d1a522e8955b73059fbd63e13aec616 height: height attribute not set width: width attribute not set description: {\displaystyle a(x)} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/b5dfb5ce580fb90ec93f88f878c55ea000650826 height: height attribute not set width: width attribute not set description: {\displaystyle b(x)} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/786849c765da7a84dbc3cce43e96aad58a5868dc height: height attribute not set width: width attribute not set description: {\displaystyle \mathbb {r} } |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/73efd1f6493490b058097060a572606d2c550a06 height: height attribute not set width: width attribute not set description: {\displaystyle 2\pi } |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/76e735b1cecde948a5bb2e7d2b9afb5913a0ce1d height: height attribute not set width: width attribute not set description: {\displaystyle a(x)=\sum _{n=-\infty }^{+\infty }a_{n}e^{inx},\qquad b(x)=\sum _{n=-\infty }^{+\infty }b_{n}e^{inx}.} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/eddbac98dabf21905e644938d82d27f3a85a153b height: height attribute not set width: width attribute not set description: {\displaystyle \sum _{n=-\infty }^{+\infty }a_{n}{\overline {b_{n}}}={\frac {1}{2\pi }}\int _{-\pi }^{\pi }a(x){\overline {b(x)}}dx.} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/8a45a168acfae09fb985806ddfb9d98ab3dc2d3d height: height attribute not set width: width attribute not set description: {\displaystyle a(x)=b(x)} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/4fd6a5946b7e916352b0afc557f992328bac85e8 height: height attribute not set width: width attribute not set description: {\displaystyle c^{2}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/ee7937f28572acf490efd1a642dcd05b3a0f099b height: height attribute not set width: width attribute not set description: {\displaystyle \sum _{n=-\infty }^{+\infty }|a_{n}|^{2}={\frac {1}{2\pi }}\int _{-\pi }^{\pi }|a(x)|^{2}dx.} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/a06a4409cbb9cb22d727c01396a50f60cbd9b9e2 height: height attribute not set width: width attribute not set description: {\displaystyle \int _{-\infty }^{+\infty }|a(t)|^{2}dt=\int _{-\infty }^{+\infty }|{\hat {a}}(\omega )|^{2}d\omega ,} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/e41f0a352a364d656811ae5a27b6faab7395fa08 height: height attribute not set width: width attribute not set description: {\displaystyle {\hat {a}}(\omega )={\mathcal {f}}\{a(t)\}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/48eff443f9de7a985bb94ca3bde20813ea737be8 height: height attribute not set width: width attribute not set description: {\displaystyle \omega } |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/7daff47fa58cdfd29dc333def748ff5fa4c923e3 height: height attribute not set width: width attribute not set description: {\displaystyle a} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/cf6126dbac18200926b49cbd29c792dccf899e76 height: height attribute not set width: width attribute not set description: {\displaystyle {\mathcal {f}}\left\{x(t)\right\}=x(\omega )} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/cd6513f286ed47b255391063aa1725461f377fa4 height: height attribute not set width: width attribute not set description: {\displaystyle {\mathcal {f}}\left\{x(t)\right\}=x(-\omega )} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/955a2345f1dfef09f754a00c4240af17f4fe9050 height: height attribute not set width: width attribute not set description: {\displaystyle {\mathcal {f}}^{-1}\left\{x(\omega )\right\}=x(t)} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/4555035b9f784ff6a356abd9d9f4b37e4e81b9ba height: height attribute not set width: width attribute not set description: {\displaystyle {\mathcal {f}}^{-1}\left\{x(t)\right\}=x(-\omega )} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/61eea3e1ffb71496a64f0494395a0dcb7bed87d1 height: height attribute not set width: width attribute not set description: {\displaystyle f\colon \mathbb {r} \to \mathbb {c} } |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/48c3f292d8e54b220c70dbf48b029debcda4e9dc height: height attribute not set width: width attribute not set description: {\displaystyle \int _{-\infty }^{+\infty }f(x)e^{-izx}\,dx\rightarrow 0{\text{ per }}z\rightarrow \pm \infty .} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/2aae8864a3c1fec9585261791a809ddec1489950 height: height attribute not set width: width attribute not set description: {\displaystyle 0} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/bf368e72c009decd9b6686ee84a375632e11de98 height: height attribute not set width: width attribute not set description: {\displaystyle z} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/7c8c67ebee34f2824006b42f74a52e0bc8997f79 height: height attribute not set width: width attribute not set description: {\displaystyle {\mathcal {f}}\left\{f(t)\right\}(\omega )} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/5bf044fe2fbfc4bd8d6d7230f4108430263f9fd6 height: height attribute not set width: width attribute not set description: {\displaystyle f(t)} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/21514243af8b990f14aa1f23da14ecbef91f5301 height: height attribute not set width: width attribute not set description: {\displaystyle {\mathcal {f}}\left\{f(t)\right\}={\mathcal {l}}\left\{f(t)\right\}|_{s=i\omega }=\int _{-\infty }^{+\infty }e^{-i\omega t}f(t)\,\mathrm {d} t.} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/4eb3ca0fcf557f7997bb0197d69be973bbdbf601 height: height attribute not set width: width attribute not set description: {\displaystyle u(t)=\chi _{[-1,+1]}(t)} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/18d9e39cdc2bd2af871aece13215fd1da1472ab7 height: height attribute not set width: width attribute not set description: {\displaystyle {\hat {u}}(\omega )={\frac {1}{\sqrt {2\pi }}}\int _{\mathbb {r} }e^{-i\omega t}\chi _{[-1,+1]}(t)\,dt={\frac {1}{\sqrt {2\pi }}}\int _{-1}^{+1}e^{-i\omega t}\,dt={\frac {1}{\sqrt {2\pi }}}{\left[{\frac {e^{-i\omega t}}{-i\omega }}\right]}_{-1}^{+1}={\frac {1}{\sqrt {2\pi }}}{\frac {e^{i\omega }-e^{-i\omega }}{i\omega }}={\sqrt {\frac {2}{\pi }}}{\frac {\sin \omega }{\omega }}.} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/2f61e907d2f39461ac2ab39dfa8cb195c36f87f1 height: height attribute not set width: width attribute not set description: {\displaystyle u(t)={\frac {1}{1+t^{2}}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/c92eb92d6443b8644f6806dd06c4fd26771a67a3 height: height attribute not set width: width attribute not set description: {\displaystyle {\hat {u}}(\omega )={\frac {1}{\sqrt {2\pi }}}\int _{\mathbb {r} }e^{-i\omega t}u(t)\,dt={\frac {1}{\sqrt {2\pi }}}\int _{-\infty }^{+\infty }{\frac {e^{-i\omega t}}{1+t^{2}}}dt.} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/9b1dda7010fa2f7d9fb8a8f4251b3b5ebe8c554f height: height attribute not set width: width attribute not set description: {\displaystyle \omega \geq 0} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/4cfde86a3f7ec967af9955d0988592f0693d2b19 height: height attribute not set width: width attribute not set description: {\displaystyle \gamma } |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/4b0bfb3769bf24d80e15374dc37b0441e2616e33 height: height attribute not set width: width attribute not set description: {\displaystyle r} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/b92bfc06485cc90286474b14a516a68d8bfdd7b3 height: height attribute not set width: width attribute not set description: {\displaystyle z=0} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/f03571bb2543323094f0f400fed086ddbab0335d height: height attribute not set width: width attribute not set description: {\displaystyle {\frac {1}{\sqrt {2\pi }}}\oint _{\gamma }{\frac {e^{-i\omega z}}{1+z^{2}}}\,dz\rightarrow -{\frac {1}{\sqrt {2\pi }}}\int _{\mathbb {r} }{\frac {e^{-i\omega t}}{1+t^{2}}}\,dt,\qquad {\text{per }}r\rightarrow +\infty .} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/04a7db2fc5df56d3b59b42ee625bb6f0009b0d23 height: height attribute not set width: width attribute not set description: {\displaystyle z=\pm i} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/c2f82b13f7a46e0e7a098e79fde8f53828833d5d height: height attribute not set width: width attribute not set description: {\displaystyle z=-i} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/1e95931f55dd9ae812f65c38ea083705d19a2b3a height: height attribute not set width: width attribute not set description: {\displaystyle \operatorname {res} _{z=-i}=\lim _{z\rightarrow -i}e^{-i\omega z}{\frac {z+i}{z^{2}+1}}=-{\frac {e^{-\omega }}{2i}}.} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/b3df896602d29ffa92623b6c9f1162c6cc7a5065 height: height attribute not set width: width attribute not set description: {\displaystyle {\hat {u}}(\omega )=-{\frac {2\pi i}{\sqrt {2\pi }}}{\big (}-{\frac {e^{-\omega }}{2i}}{\big )}={\sqrt {\frac {\pi }{2}}}e^{-\omega }.} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/97c76d875ea6d73f6dbbab165cfa2ece32ef1b89 height: height attribute not set width: width attribute not set description: {\displaystyle \omega <0} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/5ddcadd85d9141e2af0c4522bd661701732f0f19 height: height attribute not set width: width attribute not set description: {\displaystyle z=+i} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/bcbaefeac2c525136f1f78d3305bb48ce29c06ef height: height attribute not set width: width attribute not set description: {\displaystyle \operatorname {res} _{z=+i}=\lim _{z\rightarrow +i}e^{-i\omega z}{\frac {z-i}{z^{2}+1}}=+{\frac {e^{+\omega }}{2i}}.} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/ed9d237d6b0ea9cc79678d386061e91a90f0b243 height: height attribute not set width: width attribute not set description: {\displaystyle {\hat {u}}(\omega )={\sqrt {\frac {\pi }{2}}}e^{-|\omega |}.} |
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