(New page: ==Inverse Fourier Transforms== If we have a Fourier series <math>X(\omega)</math>, then <math>x(t)=\frac{1}{2\pi}\int_{-\infty}^{\infty}X(\omega)e^{j\omega t}d\omega</math> ==Example== <...) |
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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 Fourier Transforms== | ==Inverse Fourier Transforms== | ||
If we have a Fourier series <math>X(\omega)</math>, then | If we have a Fourier series <math>X(\omega)</math>, then | ||
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<math>x(t)=4cos(\frac{3\pi}{2}t)</math> | <math>x(t)=4cos(\frac{3\pi}{2}t)</math> | ||
| + | ---- | ||
| + | [[CT_Fourier_transform_practice_problems_list|Back to Practice Problems on CT Fourier transform]] | ||
Latest revision as of 12:43, 16 September 2013
Example of Computation of inverse Fourier transform (CT signals)
A practice problem on CT Fourier transform
Inverse Fourier Transforms
If we have a Fourier series $ X(\omega) $, then
$ x(t)=\frac{1}{2\pi}\int_{-\infty}^{\infty}X(\omega)e^{j\omega t}d\omega $
Example
$ X(\omega)=4\pi\delta(\omega-\frac{3\pi}{2})+4\pi\delta(\omega+\frac{3\pi}{2}) $
$ x(t)=\frac{1}{2\pi}\int_{-\infty}^{\infty}4\pi\delta(\omega-\frac{3\pi}{2})e^{j\omega t}+4\pi\delta(\omega+\frac{3\pi}{2})d\omega $
$ x(t)=2\int_{-\infty}^{\infty}\delta(\omega-\frac{3\pi}{2})e^{j\omega t}+delta(\omega+\frac{3\pi}{2})d\omega $
$ x(t)=2e^{j\frac{3\pi}{2}t}+2e^{j\frac{-3\pi}{2}} $
$ x(t)=4[\frac{e^{j\frac{3\pi}{2}t}+e^{-j\frac{3\pi}{2}}}{2}] $
$ x(t)=4cos(\frac{3\pi}{2}t) $
