| CTFT of a sine |
| $ X(f)=\mathcal{X}(2\pi f)=\frac{\pi}{i} \left[\delta (2\pi f- \omega_0) - \delta (2\pi f+ \omega_0)\right]=\frac{1}{2i} \left[\delta (f - \frac{\omega_0}{2\pi}) - \delta (f + \frac{\omega_0}{2\pi})\right] \ $ |
| $ Since\ k\delta (kt)=\delta (t),\forall k\ne 0 $ |
