CÁLCULO GRACELI SINTÉTICO.

$\mathrm {e^{i2\pi \phi }}$ e $\mathrm {e^{-i2\pi \phi }}$ cos $\mathrm {e^{i2\pi \phi }}$ $[+/ -] sin$ $\mathrm {e^{i2\pi \phi }}$ $T^{\nu }{}_{\alpha }$ $\lambda$ ω ${\mathcal {T}}$ , $\sigma$ , $\psi$

\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)}}

\mathrm {C_{n}={\frac {1}{T}}\int _{-{\frac {T}{2}}}^{\frac {T}{2}}f(t)\ e^{-i\omega _{n}t}\operatorname {d} \!t\ \ \ \ \ \ \ \omega _{n}\equiv n{\frac {2\pi }{T}}}

\mathrm {f(t)=\sum _{n=-\infty }^{\infty }C_{n}\ e^{i\omega _{n}t}\equiv \sum _{n=-\infty }^{\infty }{\hat {f}}{\Bigl (}{\frac {\omega _{n}}{2\pi }}{\Bigr )}\ e^{i\omega _{n}t}{\frac {\Delta \omega _{n}}{2\pi }}}

Pesquisar este blog

CÁLCULO GRACELI SINTÉTICO.

Comentários

Postar um comentário

Postagens mais visitadas deste blog