| Line 15: | Line 15: | ||
|<math>sin(\omega_0t) </math> | |<math>sin(\omega_0t) </math> | ||
|<math>\frac{1}{2j}e^{j\omega_0 t} - \frac{1}{2j}e^{-j\omega_0 t} </math> | |<math>\frac{1}{2j}e^{j\omega_0 t} - \frac{1}{2j}e^{-j\omega_0 t} </math> | ||
| − | | | + | |<math> </math> |
|- | |- | ||
Revision as of 15:08, 14 November 2018
CT Fourier Series for periodic signals and some properties with proofs
- Fourier series of periodic signals
| Function | Fourier Series | Proof |
|---|---|---|
| $ sin(\omega_0t) $ | $ \frac{1}{2j}e^{j\omega_0 t} - \frac{1}{2j}e^{-j\omega_0 t} $ | |
| $ cos(\omega_0t) $ | $ \frac{1}{2}e^{j\omega_0 t} + \frac{1}{2}e^{-j\omega_0 t} $ | |
| $ e^{j\omega_0t}u(t) $ | $ 2\pi\delta(\omega - \omega_0) $ |
