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

$X(\omega ) = \delta(\omega ) + \delta(\omega - 5) + \delta(\omega - 5)\,$

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

$= \frac{1}{2\pi}\int_{-\infty}^{\infty}\delta(\omega )e^{j\omega t}d\omega + \frac{1}{2\pi}\int_{-\infty}^{\infty}\delta(\omega - 5)e^{j\omega t}d\omega + \frac{1}{2\pi}\int_{-\infty}^{\infty}\delta(\omega + 5)e^{j\omega t}d\omega\,$

$= \frac{1}{2\pi}*1 + \frac{1}{2\pi}*e^{5jt} + \frac{1}{2\pi}*e^{-5jt}\,$

$= \frac{1}{2\pi} * (1 + 2cos(5t))\,$

I'll add another one when i have time

## Alumni Liaison

Abstract algebra continues the conceptual developments of linear algebra, on an even grander scale.

Dr. Paul Garrett