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| − | |<math>e^{j\omega_0t} | + | |<math>e^{j\omega_0t} </math> |
|<math>2\pi\delta(\omega - \omega_0) </math> | |<math>2\pi\delta(\omega - \omega_0) </math> | ||
| + | | | ||
| + | |- | ||
| + | |||
| + | |<math> \sum_{k=-\infty}^{\infty}u(t+3k) - u(t-1+3k) </math> | ||
| + | | | ||
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|- | |- | ||
Revision as of 15:13, 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} $ | $ 2\pi\delta(\omega - \omega_0) $ | |
| $ \sum_{k=-\infty}^{\infty}u(t+3k) - u(t-1+3k) $ |
