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)} $


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