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} $ | $ 2\pi\delta(\omega - \omega_0) $ | |
| $ \sum_{k=-\infty}^{\infty}u(t+5k) - u(t-1+5k) $ |
