(Specify a Fourier transform X(w))
(Specify a Fourier transform X(w))
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== 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 18:54, 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} $

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