Example of Computation of Fourier transform of a CT SIGNAL
A practice problem on CT Fourier transform
Fourier Transform
Signal: x(t) = $ e^{3|t-1|} $
$ X(j \omega) = \int_{-\infty}^{\infty} x(t) e^{-j\omega t} dt \! $
$ = \int_{-\infty}^{\infty} e^{2|t-1|} e^{-j\omega t} dt \! $
$ = \int_{1}^{\infty} e^{2|t-1|} e^{-j\omega t} dt \! $ + $ \int_{-\infty}^{1} e^{2|t-1|} e^{-j\omega t} dt \! $
= $ \frac{e^{-j \omega}}{2 + j \omega} + \frac{e^{-j \omega}}{2 - j \omega} $
= $ \frac{4e^{-j \omega}}{4 + \omega ^2} ---- [[CT_Fourier_transform_practice_problems_list|Back to Practice Problems on CT Fourier transform]] $
