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CTFT of a impulse train
$ X(f)=\mathcal{X}(2\pi f)=\frac{2\pi}{T}\sum^{\infty}_{k=-\infty}\delta(2\pi f-\frac{2\pi k}{T})=\frac{1}{T}\sum^{\infty}_{k=-\infty}\delta(f-\frac{k}{T})\ $
$ Since\ k\delta (kt)=\delta (t),\forall k\ne 0 $
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