(New page: {| | align="left" style="padding-left: 0em;" | CTFT of a periodic function |- | <math> X(f)=\mathcal{X}(2\pi f)=2\pi\sum^{\infty}_{k=-\infty}a_{k}\delta(w-kw_{0})=\sum^{\infty}_{k=-\inf...) |
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| align="left" style="padding-left: 0em;" | CTFT of a periodic function | | align="left" style="padding-left: 0em;" | CTFT of a periodic function | ||
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| − | | <math> X(f)=\mathcal{X}(2\pi f)=2\pi\sum^{\infty}_{k=-\infty}a_{k}\delta( | + | | <math> 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})</math> |
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| <math>Since\ k\delta (kt)=\delta (t),\forall k\ne 0</math> | | <math>Since\ k\delta (kt)=\delta (t),\forall k\ne 0</math> | ||
|} | |} | ||
Revision as of 16:47, 9 September 2010
| 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 $ |
