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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 TRANSFORM == | == INVERSE FOURIER TRANSFORM == | ||
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Knowing the formula for the Inverse Fourier transform | Knowing the formula for the Inverse Fourier transform | ||
| − | <math>x(t)=\frac{1}{2\pi}\int_{-\infty}^{\infty}X(\omega | + | <math>x(t)=\frac{1}{2\pi}\int_{-\infty}^{\infty}X(\omega)e^{j\omega t}d\omega \,</math> |
We can proceed to compute its inverse | We can proceed to compute its inverse | ||
| − | <math> x(t) = \frac{1}{2\pi} \int_{-\infty}^{\infty} | + | <math> x(t) = \frac{1}{2\pi} \int_{-\infty}^{\infty} \delta(\omega - 1)e^{j\omega t} + \delta(\omega - 3)e^{j\omega t} d\omega \ </math> |
<math> x(t) = \frac{1}{2\pi}[e^{jt}+ e^{3jt}]</math> | <math> x(t) = \frac{1}{2\pi}[e^{jt}+ e^{3jt}]</math> | ||
| + | |||
| + | |||
| + | ---- | ||
| + | [[CT_Fourier_transform_practice_problems_list|Back to Practice Problems on CT Fourier transform]] | ||
Latest revision as of 12:52, 16 September 2013
Example of Computation of inverse Fourier transform (CT signals)
A practice problem on CT Fourier transform
INVERSE FOURIER TRANSFORM
$ X(\omega) = \delta(\omega - 1) + \delta(\omega - 3) $
Knowing the formula for the Inverse Fourier transform
$ x(t)=\frac{1}{2\pi}\int_{-\infty}^{\infty}X(\omega)e^{j\omega t}d\omega \, $
We can proceed to compute its inverse
$ x(t) = \frac{1}{2\pi} \int_{-\infty}^{\infty} \delta(\omega - 1)e^{j\omega t} + \delta(\omega - 3)e^{j\omega t} d\omega \ $
$ x(t) = \frac{1}{2\pi}[e^{jt}+ e^{3jt}] $
