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Tabla de la transformada de Fourier
1
1
1
δ
(
t
)
\delta(t)
δ
(
t
)
1
1
1
δ
(
ω
)
\delta(\omega)
δ
(
ω
)
1
1
1
δ
(
ω
)
\delta(\omega)
δ
(
ω
)
2
a
a
2
+
4
π
2
ω
2
\dfrac{2a}{a^{2}+4\pi^{2}\omega^{2}}
a
2
+
4
π
2
ω
2
2
a
e
−
a
∣
t
∣
e^{-a|t|}
e
−
a
∣
t
∣
2
a
a
2
+
4
π
2
ω
2
\dfrac{2a}{a^{2}+4\pi^{2}\omega^{2}}
a
2
+
4
π
2
ω
2
2
a
e
−
π
ω
2
e^{-\pi\omega^{2}}
e
−
π
ω
2
e
−
π
t
2
e^{-\pi t^{2}}
e
−
π
t
2
e
−
π
ω
2
e^{-\pi\omega^{2}}
e
−
π
ω
2
π
e
−
π
2
ω
2
\sqrt{\pi}\,e^{-\pi^{2}\omega^{2}}
π
e
−
π
2
ω
2
e
−
t
2
e^{-t^{2}}
e
−
t
2
π
e
−
π
2
ω
2
\sqrt{\pi}\,e^{-\pi^{2}\omega^{2}}
π
e
−
π
2
ω
2
π
e
−
2
π
∣
ω
∣
\pi\,e^{-2\pi|\omega|}
π
e
−
2
π
∣
ω
∣
1
1
+
t
2
\dfrac{1}{1+t^{2}}
1
+
t
2
1
π
e
−
2
π
∣
ω
∣
\pi\,e^{-2\pi|\omega|}
π
e
−
2
π
∣
ω
∣
sinc
(
ω
)
=
sin
(
π
ω
)
π
ω
\operatorname{sinc}(\omega)=\dfrac{\sin(\pi\omega)}{\pi\omega}
sinc
(
ω
)
=
π
ω
sin
(
π
ω
)
Π
(
t
)
(
∣
t
∣
<
1
2
)
\Pi(t)\ \ (|t|<\tfrac12)
Π
(
t
)
(
∣
t
∣
<
2
1
)
sin
(
π
ω
)
π
ω
\dfrac{\sin(\pi\omega)}{\pi\omega}
π
ω
sin
(
π
ω
)
δ
(
ω
−
ω
0
)
+
δ
(
ω
+
ω
0
)
2
\dfrac{\delta(\omega-\omega_0)+\delta(\omega+\omega_0)}{2}
2
δ
(
ω
−
ω
0
)
+
δ
(
ω
+
ω
0
)
cos
(
2
π
ω
0
t
)
\cos(2\pi\omega_0 t)
cos
(
2
π
ω
0
t
)
δ
(
ω
−
ω
0
)
+
δ
(
ω
+
ω
0
)
2
\dfrac{\delta(\omega-\omega_0)+\delta(\omega+\omega_0)}{2}
2
δ
(
ω
−
ω
0
)
+
δ
(
ω
+
ω
0
)
1
a
+
2
π
i
ω
\dfrac{1}{a+2\pi i\omega}
a
+
2
π
iω
1
e
−
a
t
θ
(
t
)
e^{-at}\,\theta(t)
e
−
a
t
θ
(
t
)
1
a
−
2
π
i
ω
\dfrac{1}{a-2\pi i\omega}
a
−
2
π
iω
1