Tabla de la transformada de Fourier

11δ(t)\delta(t)11
δ(ω)\delta(\omega)11δ(ω)\delta(\omega)
2aa2+4π2ω2\dfrac{2a}{a^{2}+4\pi^{2}\omega^{2}}eate^{-a|t|}2aa2+4π2ω2\dfrac{2a}{a^{2}+4\pi^{2}\omega^{2}}
eπω2e^{-\pi\omega^{2}}eπt2e^{-\pi t^{2}}eπω2e^{-\pi\omega^{2}}
πeπ2ω2\sqrt{\pi}\,e^{-\pi^{2}\omega^{2}}et2e^{-t^{2}}πeπ2ω2\sqrt{\pi}\,e^{-\pi^{2}\omega^{2}}
πe2πω\pi\,e^{-2\pi|\omega|}11+t2\dfrac{1}{1+t^{2}}πe2πω\pi\,e^{-2\pi|\omega|}
sinc(ω)=sin(πω)πω\operatorname{sinc}(\omega)=\dfrac{\sin(\pi\omega)}{\pi\omega}Π(t)  (t<12)\Pi(t)\ \ (|t|<\tfrac12)sin(πω)πω\dfrac{\sin(\pi\omega)}{\pi\omega}
δ(ωω0)+δ(ω+ω0)2\dfrac{\delta(\omega-\omega_0)+\delta(\omega+\omega_0)}{2}cos(2πω0t)\cos(2\pi\omega_0 t)δ(ωω0)+δ(ω+ω0)2\dfrac{\delta(\omega-\omega_0)+\delta(\omega+\omega_0)}{2}
1a+2πiω\dfrac{1}{a+2\pi i\omega}eatθ(t)e^{-at}\,\theta(t)1a2πiω\dfrac{1}{a-2\pi i\omega}