| Line 5: | Line 5: | ||
<math> X(\omega) = \int_{-\infty}^{\infty} \delta (t+1)e^{-j \omega t} + \int_{-\infty}^{\infty} \delta (t-1)e^{-j \omega t} dt </math> | <math> X(\omega) = \int_{-\infty}^{\infty} \delta (t+1)e^{-j \omega t} + \int_{-\infty}^{\infty} \delta (t-1)e^{-j \omega t} dt </math> | ||
| − | <math> X(\omega) = e^{j \omega}+ e^{-j \omega} = \frac{1}{2} (e^ {j \ omega} + e^ {-j \ omega})^2 | + | <math> X(\omega) = e^{j \omega}+ e^{-j \omega} = \frac{1}{2} (e^ {j \omega} + e^ {-j \omega})^2 |
Revision as of 17:09, 24 October 2008
Fourier Transform of delta functions
$ x(t) = \delta (t+1) + \delta (t-1) $
$ X(\omega) = \int_{-\infty}^{\infty} \delta (t+1)e^{-j \omega t} + \int_{-\infty}^{\infty} \delta (t-1)e^{-j \omega t} dt $
$ X(\omega) = e^{j \omega}+ e^{-j \omega} = \frac{1}{2} (e^ {j \omega} + e^ {-j \omega})^2 $
