Example of Computation of inverse Fourier transform (CT signals)

A practice problem on CT Fourier transform


$ X(\omega) = \frac{j\omega}{7 + j\omega} $

$ x(t) = \frac{1}{2\pi} \int_{-\infty}^{\infty}\frac{j\omega e^{j\omega t}}{7 + j\omega}d\omega $

      $ = \frac{j\omega}{2\pi} \int_{-\infty}^{\infty}\frac{e^{j\omega t}}{7 + j\omega}d\omega $


      $ = \frac{d}{dt}e^{-7t}u(t) $



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