Fourier Transform Catalog

Time Domain	Frequency Domain	Note
$\text{rect}(t/T)$	$T\text{ sinc}(\omega T/2\pi )$
$e^{-at}u(t)$	$\frac{1}{a+j\omega }$
$e^{a|t|}$	$\frac{2a}{a^2+{\omega }^2}$
$\text{sinc}(t/2\pi )$	$2\pi \text{rect}(\omega )$
$\Delta (t)$	$T^2{\text{ sinc}}^2(\omega T/2\pi )$
${\text{sinc}}^2(t)$	$\Delta (\omega /2\pi )$
$\delta (t)$	$1$
$\delta (t-\tau )$	$e^{-j\omega \tau }$
$1$	$2\pi \delta (\omega )$
$u(t)$	$\pi \delta (\omega )+\frac{1}{j\omega }$
$e^{j{\omega }_{0}t}$	$2\pi \delta (\omega -{\omega }_0)$
$\cos ({\omega }_{0}t)$	$\pi (\delta (\omega -{\omega }_0)+\delta (\omega +{\omega }_0))$
$\sin ({\omega }_{0}t)$	$j\pi (\delta (\omega +{\omega }_0)-\delta (\omega -{\omega }_0))$
${\delta }_T(t)$	${\omega }_0{\delta }_{{\omega }_0}(\omega )$	${\delta }_T(t)$ is the impulse train
$\text{square wave}$	$T\text{ sinc}(\omega T/2\pi ){\delta }_T(t)$