Example of Computation of Fourier transform of a CT SIGNAL
A practice problem on CT Fourier transform
$ x(t)=e^{-3t} u(t-3) u(t+3) $
$ X(w) = \int^{\infty}_{- \infty}x(t)e^{-jwt} dt $
$ = \int^{\infty}_{- \infty} e^{-3t} u(t-3) u(t+3) e^{-jwt} dt $
$ = \int^{3}_{-3} e^{-(3 + jw)t} dt $
$ [\frac{e^{-(3 + jw)t}}{-(3 + jw)}]_{-3}^{3} $
$ \frac{e^{-(9 + 3jw)}}{-(3 + jw)} - \frac{e^{(9 + 3jw)}}{-(3 + jw)} $
