(New page: Compute the inverse fourier transform of the fourier transform below: <math>\,\mathcal{X}(\omega)= \delta(\omega - 3\pi) e^{-t}\,</math> <math>\,x(t)=\frac{1}{2\pi}\int_{-\infty}^{\inft...) |
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<math>\,x(t)=\frac{1}{2\pi}\int_{-\infty}^{\infty}\mathcal{X}(\omega)e^{j\omega t}\,d\omega \,</math> | <math>\,x(t)=\frac{1}{2\pi}\int_{-\infty}^{\infty}\mathcal{X}(\omega)e^{j\omega t}\,d\omega \,</math> | ||
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| + | <math>\,x(t)=\frac{1}{2\pi}\int_{-\infty}^{\infty} \delta(\omega - 3\pi) e^{-t} e^{j\omega t}\,d\omega \,</math> | ||
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| + | <math>\,x(t)=\frac{1}{2\pi}\int_{-\infty}^{\infty} \delta(\omega - 3\pi) e^{(j\omega - 1)t}\,d\omega \,</math> | ||
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| + | <math>\,x(t)=\frac{1}{2\pi} e^{(j(-3/pi) - 1)t}\,d\omega \,</math> | ||
Revision as of 09:51, 6 October 2008
Compute the inverse fourier transform of the fourier transform below:
$ \,\mathcal{X}(\omega)= \delta(\omega - 3\pi) e^{-t}\, $
$ \,x(t)=\frac{1}{2\pi}\int_{-\infty}^{\infty}\mathcal{X}(\omega)e^{j\omega t}\,d\omega \, $
$ \,x(t)=\frac{1}{2\pi}\int_{-\infty}^{\infty} \delta(\omega - 3\pi) e^{-t} e^{j\omega t}\,d\omega \, $
$ \,x(t)=\frac{1}{2\pi}\int_{-\infty}^{\infty} \delta(\omega - 3\pi) e^{(j\omega - 1)t}\,d\omega \, $
$ \,x(t)=\frac{1}{2\pi} e^{(j(-3/pi) - 1)t}\,d\omega \, $
