| Line 1: | Line 1: | ||
== INVERSE FOURIER TRANSFORM == | == INVERSE FOURIER TRANSFORM == | ||
| − | <math> X(\omega) = \delta(\omega) + \delta(\omega - 3) </math> | + | <math> X(\omega) = \delta(\omega - 1) + \delta(\omega - 3) </math> |
Knowing the formula for the Inverse Fourier transform | Knowing the formula for the Inverse Fourier transform | ||
| − | <math>x(t)=\frac{1}{2\pi}\int_{-\infty}^{\infty}X(\omega)e^{j\omega t}d\omega \,</math> | + | <math>x(t)=\frac{1}{2\pi}\int_{-\infty}^{\infty}X(\omega - 1)e^{j\omega t}d\omega \,</math> |
We can proceed to compute its inverse | We can proceed to compute its inverse | ||
| − | <math> x(t) = \frac{1}{2\pi} \int_{-\infty}^{\infty} (\delta(\omega)e^{j\omega t} + \delta(\omega - 3)e^{j\omega t} d\omega \ </math> | + | <math> 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 \ </math> |
Revision as of 17:08, 8 October 2008
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 - 1)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 \ $
