## INVERSE FOURIER TRANSFORM

$X(\omega) = \delta(\omega - 1) + \delta(\omega - 3)$

Knowing the formula for the Inverse Fourier transform

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

We can proceed to compute its inverse

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

$x(t) = \frac{1}{2\pi}[e^{jt}+ e^{3jt}]$

## Alumni Liaison

Ph.D. 2007, working on developing cool imaging technologies for digital cameras, camera phones, and video surveillance cameras.