## Example of Computation of inverse Fourier transform (CT signals)

Compute the inverse fourier transform of the fourier transform below:

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

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

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

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

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

## Alumni Liaison

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

Francisco Blanco-Silva