I need to calculate the following inverse Fourier transform:
$$G(t) = \frac{1}{\sqrt{2 \pi}} {\int _{- \infty} ^{+ \infty}} \dfrac{1 - e^{-i \omega T}}{i \omega} \; e^{i \omega t} \, \mathrm{d} \omega$$
with $T \in \mathrm{R}_+$
Now, the solution is supposed to be
$$ G(t) = \sqrt{\frac{\pi}{2}} \left( \mathrm{sign}(t) - \mathrm{sign}(t - T) \right)$$
but I've idea of how to get there.