(New page: <math>X(\omega) = 2\pi e^{4j\omega}\,</math> We kenw that the Fourier transformation of <math>x(t - t_o)\,</math> is equal to <math>e^{-j\omega t_o} X(\omega)\,</math> Using this propert...) |
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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]] | ||
| + | ---- | ||
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<math>X(\omega) = 2\pi e^{4j\omega}\,</math> | <math>X(\omega) = 2\pi e^{4j\omega}\,</math> | ||
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<math>x(t) = \delta(t+4)\,</math> | <math>x(t) = \delta(t+4)\,</math> | ||
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| + | ---- | ||
| + | [[CT_Fourier_transform_practice_problems_list|Back to Practice Problems on CT Fourier transform]] | ||
Latest revision as of 12:42, 16 September 2013
Example of Computation of inverse Fourier transform (CT signals)
A practice problem on CT Fourier transform
$ X(\omega) = 2\pi e^{4j\omega}\, $
We kenw that the Fourier transformation of $ x(t - t_o)\, $ is equal to $ e^{-j\omega t_o} X(\omega)\, $
Using this property, we can solve the question
$ X(\omega) = 2\pi e^{4j\omega} Y(\omega)\, $ where $ Y(\omega) = 1\, $
$ y(t) = \delta(t)\, $
$ x(t) = \frac{1}{2\pi} \int^{\infty}_{-\infty}2\pi e^{4j\omega} Y(\omega) dw\, $
$ x(t) = \int^{\infty}_{-\infty}e^{4j\omega} Y(\omega) dw\, $
$ x(t) = \hat{f} (e^{4j\omega } Y(\omega))\, $
$ x(t) = \delta(t+4)\, $
