INVERSE FOURIER TRANSFORM
$ X(\omega) = \delta(\omega - 1) + \delta(\omega - 3) $
Knowing the formula for the Inverse Fourier transform
$ x(t)=\frac{1}{2\pi}\int_{-\infty}^{\infty}X(\omega)e^{j\omega t}d\omega \, $
We can proceed to compute its inverse
$ x(t) = \frac{1}{2\pi} \int_{-\infty}^{\infty} \delta(\omega - 1)e^{j\omega t} + \delta(\omega - 3)e^{j\omega t} d\omega \ $
$ x(t) = \frac{1}{2\pi}[e^{jt}+ e^{3jt}] $
