CTFT of a periodic function |
$ X(f)=\mathcal{X}(2\pi f)=2\pi\sum^{\infty}_{k=-\infty}a_{k}\delta(2\pi f-kw_{0})=\sum^{\infty}_{k=-\infty}a_{k}\delta(f-\frac{kw_{0}}{2\pi}) $ |
$ Since\ k\delta (kt)=\delta (t),\forall k\ne 0 $ |
CTFT of a periodic function |
$ X(f)=\mathcal{X}(2\pi f)=2\pi\sum^{\infty}_{k=-\infty}a_{k}\delta(2\pi f-kw_{0})=\sum^{\infty}_{k=-\infty}a_{k}\delta(f-\frac{kw_{0}}{2\pi}) $ |
$ Since\ k\delta (kt)=\delta (t),\forall k\ne 0 $ |