Teste das equações math

Formulas antigas

$H(j\omega )=H(s)\left|{\begin{matrix}\\s=j\omega \end{matrix}}\right.$

$H(j\omega )=\left|H(j\omega )\right|e^{j\phi (\omega )}$

$\left|H(j\omega )\right|^{2}=H(j\omega )H(-j\omega )$

$e^{j\phi (\omega )}={\frac {H(j\omega )}{H(-j\omega )}}$

Formulas Novas

Apenas acrescentei um 1 no H, H -> H1

$H1(j\omega )=H1(s)\left|{\begin{matrix}\\s=j\omega \end{matrix}}\right.$

$H1(j\omega )=\left|H1(j\omega )\right|e^{j\phi (\omega )}$

$\left|H1(j\omega )\right|^{2}=H1(j\omega )H1(-j\omega )$

$e^{j\phi (\omega )}={\frac {H1(j\omega )}{H1(-j\omega )}}$

Esta dando erro na nova wiki

A equação de análise

É uma transformação de um domínio de uma variável real $\mathrm {x(t)}$ de tempo continuo em uma variável complexa $\mathrm {X(\Omega )}$ de frequência contínua.

$DT\rightarrow DF$.

$\mathrm {x:\mathbb {R} \rightarrow \mathbb {C} }$.

$\mathrm {\ DT\rightarrow DFFx(t)}$.

$\mathrm {X(\Omega )\equiv {\mathcal {F}}\{x(t)\}}$

$\mathrm {\ DT\rightarrow DF}$.

Recomendado pela wikipedia

FONTE: https://en.wikipedia.org/wiki/Wikipedia:Manual_of_Style/Mathematics#Using_LaTeX_markup

$\int _{0}^{\pi }\sin x\,dx.$

$\sum _{n=1}^{\infty }1/n^{2}=\pi ^{2}/6$

Using LaTeX markup

Wikipedia allows editors to typeset mathematical formulae in (a subset of) LaTeX markup (see also TeX); the formulae are, for a default reader, translated into PNG images. They may also be rendered as MathML or HTML (using MathJax), depending on user preferences. For more details on this, see Help:Displaying a formula.

The LaTeX formulae can be displayed inline (like this: $\mathbf {x} \in \mathbb {R} ^{2}$), as well as on their own line:

$\int _{0}^{\pi }\sin x\,dx.$

When displaying formulae on their own line, one should indent the line with one or more colons (:). The above was typeset using

:<math>\int_0^\pi \sin x\,dx.</math>

If you find an article which indents lines with spaces in order to achieve some formula layout effect, you should convert the formula to LaTeX markup.

Having LaTeX-based formulae inline has the following drawbacks:

• The font size is larger than that of the surrounding text on some browsers, making text containing inline formulae hard to read.
• Misalignment can result. For example, instead of e^x, with "e" at the same level as the surrounding text and the x in superscript, one may see the e lowered to put the vertical center of the whole "e^x" at the same level as the center of the surrounding text.
• The download speed of a page is negatively affected if it contains many formulae.
• Copy-pasting of the inline mathematics images that are generated by LaTeX markup will not work if the application into which you are pasting only accepts text.

If an inline formula needs to be typeset in LaTeX, often better formatting can be achieved with the \textstyle LaTeX command. By default, LaTeX code is rendered as if it were a displayed equation (not inline), and this can frequently be too big. For example, the formula <math>\sum_{n=1}^\infty 1/n^2 = \pi^2/6</math>, which displays as $\sum _{n=1}^{\infty }1/n^{2}=\pi ^{2}/6$, is too large to be used inline. \textstyle generates a smaller summation sign and moves the limits on the sum to the right side of the summation sign. The code for this is <math>\textstyle\sum_{n=1}^\infty 1/n^2 = \pi^2/6</math>, and it renders as the much more aesthetic $\textstyle \sum _{n=1}^{\infty }1/n^{2}=\pi ^{2}/6$. However, the default font for \textstyle is larger than the surrounding text on many browsers.

HTML-generating formatting, as described below, is adequate for most simple inline formulae and better for text-only browsers.

Deprecated formatting

Older versions of the MediaWiki software supported displaying simple LaTeX formulae as HTML rather than as an image. Although this is no longer an option, some formulae have formatting in them intended to force them to display as an image, such as an invisible quarter space (\,) added at the end of the formula, or \displaystyle at the beginning. Such formatting can be removed if a formula is edited and need not be added to new formulae.

Alt text

Images generated from LaTeX markup have alt text, which is displayed to visually impaired readers and other readers who cannot see the images. The default alt text is the LaTeX markup that produced the image. You can override this by explicitly specifying an alt attribute for the math element. For example, <math alt="Square root of pi">\sqrt{\pi}</math> generates an image ${\sqrt {\pi }}$ whose alt text is "Square root of pi". Small and easily explained formulas used in less technical articles can benefit from explicitly specified alt text. More complicated formulas, or formulas used in more technical articles, are often better off with the default alt text.

Teste de uma fórmula da wikipedia

Diversas notações são convencionadas para denotar a transformação de Fourier de uma função $\mathrm {f:\mathbb {R} \rightarrow \mathbb {C} }$. Utilizaremos a seguinte representação:

$$\mathrm {{\hat {f}}(\omega )\equiv F(\omega )\equiv {\mathcal {F}}\{f(t)\}\ {\overset {\underset {\mathrm {def} }{}}{=}}\int _{-\infty }^{\infty }f(t)\ e^{-i\omega t}\operatorname {d} \!t} \ \ \ \ \ {\begin{aligned}&{\mathsf {Transformada\ de\ Fourier\ }}\\&{\mathsf {do\ dominio\ do\ tempo\ }}\end{aligned}}$$

$$\mathrm {f(t)\equiv {\mathcal {F}}^{-1}\{F(\omega )\}\ {\overset {\underset {\mathrm {def} }{}}{=}}\ {\frac {1}{2\pi }}\int _{-\infty }^{\infty }F(\omega )\ e^{i\omega t}\operatorname {d} \!\omega \ \ \ \ \ \ \omega \equiv 2\pi f} \ {\mathsf {(Frequ{\hat {e}}ncia\ angular)}}$$

$$\mathrm {{\hat {f}}(\kappa )\equiv F(\kappa )\equiv {\mathcal {F}}\{f(x)\}\ {\overset {\underset {\mathrm {def} }{}}{=}}\int _{-\infty }^{\infty }f(x)\ e^{-i\kappa x}\operatorname {d} \!x} \ \ \ \ \ {\begin{aligned}&{\mathsf {Transformada\ de\ Fourier\ }}\\&{\mathsf {do\ dominio\ do\ espaco\ }}\end{aligned}}$$

$$\mathrm {f(x)\equiv {\mathcal {F}}^{-1}\{F(\kappa )\}\ {\overset {\underset {\mathrm {def} }{}}{=}}\ {\frac {1}{2\pi }}\int _{-\infty }^{\infty }F(\kappa )\ e^{i\kappa x}\operatorname {d} \!\kappa \ \ \ \ \ \kappa \equiv {\frac {2\pi }{\lambda }}} \ {\mathsf {(Vetor\ de\ onda)}}$$

A afirmação de que $\mathrm {f}$ pode ser reconstruída a partir de $\mathrm {\hat {f}}$ é conhecida como o teorema da inversão de Fourier e foi introduzido no estudo Analytical Theory of Heat, de Fourier, apesar de que a definição moderna de demonstração teria sido construída muito tempo depois. As funções $\mathrm {f}$ e $\mathrm {\hat {f}}$ são conhecidas como par integral de Fourier.

FONTE: https://pt.wikipedia.org/wiki/Transformada_de_Fourier?action=edit&section=1&veswitched=1