(→Specify a Fourier transform X(w)) |
(→Specify a Fourier transform X(w)) |
||
| Line 1: | Line 1: | ||
== Specify a Fourier transform <math>X(w)</math> == | == Specify a Fourier transform <math>X(w)</math> == | ||
| − | :<math> X(w)=\frac{1}{4+w} </math> | + | :<math> X(w)=2\pi \delta\left ( w- \frac{1}{4+w}\right ) </math> |
== Inverse Fourier transform of <math>X(w)</math>== | == Inverse Fourier transform of <math>X(w)</math>== | ||
Revision as of 17:54, 8 October 2008
Specify a Fourier transform $ X(w) $
- $ X(w)=2\pi \delta\left ( w- \frac{1}{4+w}\right ) $
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} $
