Example of Computation of inverse Fourier transform (CT signals)

A practice problem on CT Fourier transform


Compute the inverse fourier transform of the fourier transform below:

$ \,\mathcal{X}(\omega)= \delta(\omega - 3\pi) e^{-t}\, $


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

$ \,x(t)=\frac{1}{2\pi}\int_{-\infty}^{\infty} \delta(\omega - 3\pi) e^{-t} e^{j\omega t}\,d\omega \, $

$ \,x(t)=\frac{1}{2\pi}\int_{-\infty}^{\infty} \delta(\omega - 3\pi) e^{(j\omega - 1)t}\,d\omega \, $

$ \,x(t)=\frac{1}{2\pi} e^{(j(-3\pi) - 1)t}\, $


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Alumni Liaison

Ph.D. on Applied Mathematics in Aug 2007. Involved on applications of image super-resolution to electron microscopy

Francisco Blanco-Silva