Fourier Transform (FT) and Inverse

The Fourier transform of a signal $x(t)\in{\bf C}$, $t\in(-\infty,\infty)$, is defined as

$$X(\omega) \isdef \int_{-\infty}^\infty x(t) e^{-j\omega t} dt \protect$$ (3.1)

and its inverse is given by

$$x(t) = \frac{1}{2\pi}\int_{-\infty}^\infty X(\omega) e^{j\omega t} d\omega \protect$$ (3.2)