(New page: == inverse F.T == assume <math>X(\omega) = 7\pi\delta(\omega-3\pi)+\delta(\omega+5\pi)-\delta(\omega-7\pi)\!</math>) |
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<math>X(\omega) = 7\pi\delta(\omega-3\pi)+\delta(\omega+5\pi)-\delta(\omega-7\pi)\!</math> | <math>X(\omega) = 7\pi\delta(\omega-3\pi)+\delta(\omega+5\pi)-\delta(\omega-7\pi)\!</math> | ||
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| + | == answer == | ||
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| + | <math>x(t)= \frac{1}{2\pi}\int_{-\infty}^{\infty}7\pi\delta(\omega-3\pi)+\delta(\omega+5\pi) - \delta(\omega-7\pi)e^{jwt}dw</math> | ||
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| + | <math>=\frac{1}{2\pi}[2\pi^{j3\pi t} + e^{-j5\pi t}- e^{j7\pi t}]</math> | ||
| + | |||
| + | <math>=e^{j3\pi} + \frac{1}{2\pi}[e^{-j5\pi t}-e^{j7\pi t}]</math> | ||
Revision as of 15:15, 7 October 2008
inverse F.T
assume
$ X(\omega) = 7\pi\delta(\omega-3\pi)+\delta(\omega+5\pi)-\delta(\omega-7\pi)\! $
answer
$ x(t)= \frac{1}{2\pi}\int_{-\infty}^{\infty}7\pi\delta(\omega-3\pi)+\delta(\omega+5\pi) - \delta(\omega-7\pi)e^{jwt}dw $
$ =\frac{1}{2\pi}[2\pi^{j3\pi t} + e^{-j5\pi t}- e^{j7\pi t}] $
$ =e^{j3\pi} + \frac{1}{2\pi}[e^{-j5\pi t}-e^{j7\pi t}] $
