(New page: Let the signal <math>X(\omega)</math> be equal to: <math>X(\omega) = \delta(\omega) + \delta(\omega - 2) - \delta(\omega - 3) \,</math> The Inverse Fourier Transform of a signal in Cont...) |
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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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Let the signal <math>X(\omega)</math> be equal to: | Let the signal <math>X(\omega)</math> be equal to: | ||
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<math>x(t) = \frac{1}{2\pi}(e^{j\omega t} +e^{j2\omega t} - e^{j3\omega t}) \,</math> | <math>x(t) = \frac{1}{2\pi}(e^{j\omega t} +e^{j2\omega t} - e^{j3\omega t}) \,</math> | ||
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| + | ---- | ||
| + | [[CT_Fourier_transform_practice_problems_list|Back to Practice Problems on CT Fourier transform]] | ||
Latest revision as of 11:46, 16 September 2013
Example of Computation of inverse Fourier transform (CT signals)
A practice problem on CT Fourier transform
Let the signal $ X(\omega) $ be equal to:
$ X(\omega) = \delta(\omega) + \delta(\omega - 2) - \delta(\omega - 3) \, $
The Inverse Fourier Transform of a signal in Continuous Time is:
$ x(t)=\frac{1}{2\pi}\int_{-\infty}^{\infty}X(\omega)e^{j\omega t}d\omega \, $
Using this, we obtain:
$ x(t)=\frac{1}{2\pi}\int_{-\infty}^{\infty}(\delta(\omega)e^{j\omega t} + \delta(\omega - 2)e^{j\omega t} - \delta(\omega - 3)e^{j\omega t}) d\omega \, $
$ x(t) = \frac{1}{2\pi}(e^{j\omega t} +e^{j2\omega t} - e^{j3\omega t}) \, $
