(Inverse Fourier transform of 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)=2\pi \delta\left ( w- \frac{\pi}{4}\right )    </math>
+
:<math>  X(w)=2\pi \delta\left ( w- \frac{\pi}{4}\right )+2\pi \delta\left ( w+ \frac{\pi}{4}\right )    </math>
  
 
== Inverse Fourier transform of <math>X(w)</math>==
 
== Inverse Fourier transform of <math>X(w)</math>==

Revision as of 18:59, 8 October 2008

Specify a Fourier transform $ X(w) $

$ X(w)=2\pi \delta\left ( w- \frac{\pi}{4}\right )+2\pi \delta\left ( w+ \frac{\pi}{4}\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}2\pi \delta\left ( w- \frac{\pi}{4}\right )e^{j\omega t}d\omega \end{align} $

Alumni Liaison

Ph.D. 2007, working on developing cool imaging technologies for digital cameras, camera phones, and video surveillance cameras.

Buyue Zhang