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| − | + | CTFT of a cosine | |
| − | + | ||
| − | + | <math> | |
| − | + | \begin{align} | |
| − | + | X(f) &=\mathcal{X}(2\pi f) \\ | |
| − | + | &=\pi \left[\delta (2\pi f- \omega_0) + \delta (2\pi f+ \omega_0)\right] \\ | |
| − | + | &=\frac{1}{2} \left[\delta (f - \frac{\omega_0}{2\pi}) + \delta (f + \frac{\omega_0}{2\pi})\right] | |
| + | \end{align} | ||
| + | </math> | ||
| + | |||
| + | <math>Since\ k\delta (kt)=\delta (t),\forall k\ne 0</math> | ||
Revision as of 11:19, 15 September 2010
CTFT of a cosine
$ \begin{align} X(f) &=\mathcal{X}(2\pi f) \\ &=\pi \left[\delta (2\pi f- \omega_0) + \delta (2\pi f+ \omega_0)\right] \\ &=\frac{1}{2} \left[\delta (f - \frac{\omega_0}{2\pi}) + \delta (f + \frac{\omega_0}{2\pi})\right] \end{align} $
$ Since\ k\delta (kt)=\delta (t),\forall k\ne 0 $
