(New page: Compute the Inverse Fourier transform of: <math>\mathcal{X}(\omega)=3\pi \delta (\omega-\pi)</math> Using the Formula for Inverse Fourier Transforms: <math> \mathcal{F}^{-1}(\mathcal{X}...) |
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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]] | ||
| + | ---- | ||
Compute the Inverse Fourier transform of: | Compute the Inverse Fourier transform of: | ||
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=\frac{3\pi}{2\pi}e^{j\pi t}=1.5e^{j\pi t} | =\frac{3\pi}{2\pi}e^{j\pi t}=1.5e^{j\pi t} | ||
</math> | </math> | ||
| + | |||
| + | ---- | ||
| + | [[CT_Fourier_transform_practice_problems_list|Back to Practice Problems on CT Fourier transform]] | ||
Latest revision as of 12:48, 16 September 2013
Example of Computation of inverse Fourier transform (CT signals)
A practice problem on CT Fourier transform
Compute the Inverse Fourier transform of:
$ \mathcal{X}(\omega)=3\pi \delta (\omega-\pi) $
Using the Formula for Inverse Fourier Transforms:
$ \mathcal{F}^{-1}(\mathcal{X}(\omega))= x(t)= \frac{1}{2\pi}\int_{-\infty}^{\infty}\mathcal{X}(\omega)e^{j\omega t} \,d\omega $
So:
$ x(t)= \frac{1}{2\pi}\int_{-\infty}^{\infty}3\pi \delta (\omega-\pi)e^{j\omega t} \,d\omega $ Using sifting property:
$ =\frac{3\pi}{2\pi}e^{j\pi t}=1.5e^{j\pi t} $
