CÁLCULO GRACELI SINTÉTICO [41]

$f(x)=\int _{-\infty }^{\infty }{\hat {f}}(\xi )e^{2i\pi x\xi }\,d\xi$ ${$ $\mathrm {\omega _{n}\ {\overset {\underset {\mathrm {def} }{}}{=}}\ n{\frac {2\pi }{T}}}$ $sin$ $\mathrm {e^{i2\pi \phi }}$ $T^{\nu }{}_{\alpha }$ $\lambda$ ω ${\mathcal {T}}$ , $\sigma$ , $\psi$

${\overline {f(t)}}={\frac {1}{2\pi }}\int _{-\infty }^{\infty }{\overline {F(\omega )}}e^{-i\omega t}\,d\omega$ ${$ $\mathrm {\omega _{n}\ {\overset {\underset {\mathrm {def} }{}}{=}}\ n{\frac {2\pi }{T}}}$ $sin$ $\mathrm {e^{i2\pi \phi }}$ $T^{\nu }{}_{\alpha }$ $\lambda$ ω ${\mathcal {T}}$ , $\sigma$ , $\psi$

$\int \limits _{-\infty }^{\infty }\left\vert tf(t)\right\vert ^{2}dt\cdot \int \limits _{-\infty }^{\infty }\left\vert \omega F(\omega )\right\vert ^{2}d\omega \geq {\pi \over 2}\left\vert \int \limits _{-\infty }^{\infty }\left\vert f(t)\right\vert ^{2}dt\right\vert ^{2}$ . ${$ $\mathrm {\omega _{n}\ {\overset {\underset {\mathrm {def} }{}}{=}}\ n{\frac {2\pi }{T}}}$ $sin$ $\mathrm {e^{i2\pi \phi }}$ $T^{\nu }{}_{\alpha }$ $\lambda$ ω ${\mathcal {T}}$ , $\sigma$ , $\psi$

${\mathcal {F}}\{f'(t)\}=\int _{-\infty }^{\infty }f'(t)e^{-i\omega t}dt$ ${$ $\mathrm {\omega _{n}\ {\overset {\underset {\mathrm {def} }{}}{=}}\ n{\frac {2\pi }{T}}}$ $sin$ $\mathrm {e^{i2\pi \phi }}$ $T^{\nu }{}_{\alpha }$ $\lambda$ ω ${\mathcal {T}}$ , $\sigma$ , $\psi$

$\mathrm {f(t)=g(t)*h(t)=\int _{-\infty }^{\infty }g(\nu )h(t-\nu )d\nu }$ ${$ $\mathrm {\omega _{n}\ {\overset {\underset {\mathrm {def} }{}}{=}}\ n{\frac {2\pi }{T}}}$ $sin$ $\mathrm {e^{i2\pi \phi }}$ $T^{\nu }{}_{\alpha }$ $\lambda$ ω ${\mathcal {T}}$ , $\sigma$ , $\psi$

$\mathrm {f_{N}(t)={\frac {a_{0}}{2}}+\sum _{n=1}^{N}a_{n}\ cos(\omega _{n}t)+\sum _{n=1}^{N}b_{n}\ sen(\omega _{n}t)\ .}$ ${$ $\mathrm {\omega _{n}\ {\overset {\underset {\mathrm {def} }{}}{=}}\ n{\frac {2\pi }{T}}}$ $sin$ $\mathrm {e^{i2\pi \phi }}$ $T^{\nu }{}_{\alpha }$ $\lambda$ ω ${\mathcal {T}}$ , $\sigma$ , $\psi$

${\mathcal {F}}\{h(t)\}=H{\bigl (}\omega {\bigr )}=-i\omega {\frac {\sqrt {\pi }}{2}}e^{-{\tfrac {\omega ^{2}}{4}}}$ ${$ $\mathrm {\omega _{n}\ {\overset {\underset {\mathrm {def} }{}}{=}}\ n{\frac {2\pi }{T}}}$ $sin$ $\mathrm {e^{i2\pi \phi }}$ $T^{\nu }{}_{\alpha }$ $\lambda$ ω ${\mathcal {T}}$ , $\sigma$ , $\psi$

$F(w)={\mathcal {F}}\left\{f(t)\right\}=\int \limits _{-\infty }^{\infty }f(t)e^{-iwt}dt$ ${$ $\mathrm {\omega _{n}\ {\overset {\underset {\mathrm {def} }{}}{=}}\ n{\frac {2\pi }{T}}}$ $sin$ $\mathrm {e^{i2\pi \phi }}$ $T^{\nu }{}_{\alpha }$ $\lambda$ ω ${\mathcal {T}}$ , $\sigma$ , $\psi$

$f(t)={\frac {1}{\pi }}\int \limits _{0}^{\infty }(A(w)cos(wt)+B(w)sen(wt))dw$ $\mathrm {\omega _{n}\ {\overset {\underset {\mathrm {def} }{}}{=}}\ n{\frac {2\pi }{T}}}$ $sin$ $\mathrm {e^{i2\pi \phi }}$ $T^{\nu }{}_{\alpha }$ $\lambda$ ω ${\mathcal {T}}$ , $\sigma$ , $\psi$

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CÁLCULO GRACELI SINTÉTICO [41]

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