Revision as of 17:09, 8 October 2008 by Cdleon (Talk)

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 - 1)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}] $

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