| Line 14: | Line 14: | ||
|<math>sin(\omega_0t) </math> | |<math>sin(\omega_0t) </math> | ||
| − | |<math>\frac{\pi}{j}(\delta(\omega - \omega_0) - \delta(\omega+\omega_0)</math> | + | |<math>\frac{\pi}{j}(\delta(\omega - \omega_0) - \delta(\omega+\omega_0))</math> |
|<math> </math> | |<math> </math> | ||
|- | |- | ||
|<math>cos(\omega_0t) </math> | |<math>cos(\omega_0t) </math> | ||
| − | |<math>\ | + | |<math>\pi(\delta(\omega - \omega_0) + \delta(\omega+\omega_0))</math> |
| | | | ||
|- | |- | ||
Revision as of 16:11, 14 November 2018
CTFT of periodic signals and some properties with proofs
- Fourier series of periodic signals
| Function | CTFT | Proof |
|---|---|---|
| $ sin(\omega_0t) $ | $ \frac{\pi}{j}(\delta(\omega - \omega_0) - \delta(\omega+\omega_0)) $ | |
| $ cos(\omega_0t) $ | $ \pi(\delta(\omega - \omega_0) + \delta(\omega+\omega_0)) $ | |
| $ e^{j\omega_0t}u(t) $ | $ 2\pi\delta(\omega - \omega_0) $ |
