(New page: == INVERSE FOURIER TRANSFORM == <math> X(\omega) = \delta(\omega) + \delta(\omega - 1) </math> Knowing the formula for the Inverse Fourier transform <math>x(t)=\frac{1}{2\pi}\int_{-\in...) |
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== INVERSE FOURIER TRANSFORM == | == INVERSE FOURIER TRANSFORM == | ||
| − | <math> X(\omega) = \delta(\omega) + \delta(\omega - | + | <math> X(\omega) = \delta(\omega) + \delta(\omega - 3) </math> |
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We can proceed to compute its inverse | We can proceed to compute its inverse | ||
| − | <math> x(t) = \frac{1}{2\pi} \int_{-\infty}^{\infty} (\delta(\omega)e^{j\omega t} + \delta(\omega - | + | <math> x(t) = \frac{1}{2\pi} \int_{-\infty}^{\infty} (\delta(\omega)e^{j\omega t} + \delta(\omega - 3)e^{j\omega t} d\omega \ </math> |
Revision as of 17:08, 8 October 2008
INVERSE FOURIER TRANSFORM
$ X(\omega) = \delta(\omega) + \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)e^{j\omega t} + \delta(\omega - 3)e^{j\omega t} d\omega \ $
