(→Inverse Fourier transform of X(w)) |
(→Inverse Fourier transform of X(w)) |
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== Inverse Fourier transform of <math>X(w)</math>== | == Inverse Fourier transform of <math>X(w)</math>== | ||
:<math>\begin{align} x(t)&=\frac{1}{2\pi}\int_{-\infty}^{\infty}X( \omega)e^{j\omega t}d\omega | :<math>\begin{align} x(t)&=\frac{1}{2\pi}\int_{-\infty}^{\infty}X( \omega)e^{j\omega t}d\omega | ||
| − | \\& =\frac {1}{2\pi}\int_{-\infty}^{\infty}\left (\frac{1}{4+ | + | \\& =\frac {1}{2\pi}\int_{-\infty}^{\infty}\left (\frac{1}{4+w}\right )e^{j\omega t}d\omega |
Revision as of 17:52, 8 October 2008
Specify a Fourier transform $ X(w) $
- $ X(w)=\frac{1}{4+jw} $
Inverse Fourier transform of $ X(w) $
- $ \begin{align} x(t)&=\frac{1}{2\pi}\int_{-\infty}^{\infty}X( \omega)e^{j\omega t}d\omega \\& =\frac {1}{2\pi}\int_{-\infty}^{\infty}\left (\frac{1}{4+w}\right )e^{j\omega t}d\omega \end{align} $
