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| + | [[Category:problem solving]] | ||
| + | [[Category:ECE301]] | ||
| + | [[Category:ECE]] | ||
| + | [[Category:Fourier transform]] | ||
| + | [[Category:inverse Fourier transform]] | ||
| + | [[Category:signals and systems]] | ||
| + | == Example of Computation of inverse Fourier transform (CT signals) == | ||
| + | A [[CT_Fourier_transform_practice_problems_list|practice problem on CT Fourier transform]] | ||
| + | ---- | ||
| + | |||
== inverse F.T == | == inverse F.T == | ||
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<math>=e^{j3\pi} + \frac{1}{2\pi}[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> | ||
| + | |||
| + | ---- | ||
| + | [[CT_Fourier_transform_practice_problems_list|Back to Practice Problems on CT Fourier transform]] | ||
Latest revision as of 12:46, 16 September 2013
Example of Computation of inverse Fourier transform (CT signals)
A practice problem on CT Fourier transform
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}] $
