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CTFT of a periodic function
$ X(f)=\mathcal{X}(2\pi f)=2\pi\sum^{\infty}_{k=-\infty}a_{k}\delta(w-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 $
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