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<math>\,\mathcal{X}(\omega)=e^{-|\omega +3|} + e^{j(\omega + 5)}\delta(\omega - \pi)\,</math> | <math>\,\mathcal{X}(\omega)=e^{-|\omega +3|} + e^{j(\omega + 5)}\delta(\omega - \pi)\,</math> | ||
| − | |||
== Answer == | == Answer == | ||
| − | <math>\,x(t)=\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> |
| + | |||
| + | <math>\,x(t)=\int_{-\infty}^{\infty} | ||
Revision as of 19:46, 5 October 2008
Compute the inverse Fourier transform of the following signal using the integral formula:
$ \,\mathcal{X}(\omega)=e^{-|\omega +3|} + e^{j(\omega + 5)}\delta(\omega - \pi)\, $
Answer
$ \,x(t)=\frac{1}{2\pi}\int_{-\infty}^{\infty}\mathcal{X}(\omega)e^{j\omega t}\,d\omega \, $
$ \,x(t)=\int_{-\infty}^{\infty} $
