## Example of Computation of inverse Fourier transform (CT signals)

A practice problem on CT Fourier transform

$ X(w) = \frac{2sin{3(w-2\pi)}}{w-2\pi}\, $

We already knew that when $ x(t) = \frac{sinWt}{\pi t}, X(w) = 1 for |w|<W. \, $

when$ x(t) = x(t-t_0), X(w) = e^{-jwt_0}X(jw) $

W is 3 , and this was delayed $ 2\pi\, $

So $ x(t) = e^{j2\pi t} $ for $ |t| < 3 \, $

And $ x(t) = 0 \, $ for otherwise