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| align="left" style="padding-left: 0em;" | CTFT of a complex exponential | | align="left" style="padding-left: 0em;" | CTFT of a complex exponential | ||
| + | |- | ||
| + | |<math>x(t)=e^{i\omega_0 t}</math> | ||
|- | |- | ||
|<math>X(f)= \mathcal{X}(2\pi f)=2\pi \delta (2\pi f-\omega_0)</math> | |<math>X(f)= \mathcal{X}(2\pi f)=2\pi \delta (2\pi f-\omega_0)</math> | ||
Revision as of 15:59, 9 September 2010
| CTFT of a complex exponential |
| $ x(t)=e^{i\omega_0 t} $ |
| $ X(f)= \mathcal{X}(2\pi f)=2\pi \delta (2\pi f-\omega_0) $ |
| $ Since\text{ } k\delta (kt)=\delta (t),\forall k\ne 0 $ |
| $ X(f)=\delta (f-\frac{\omega_0}{2\pi}) $ |
