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<math> X(\omega) = \int_{-\infty}^{\infty} \delta (t+1)e^{-j \omega t} + \int_{-\infty}^{\infty} \delta (t-1)e^{-j \omega t} dt </math>
 
<math> X(\omega) = \int_{-\infty}^{\infty} \delta (t+1)e^{-j \omega t} + \int_{-\infty}^{\infty} \delta (t-1)e^{-j \omega t} dt </math>
  
<math> X(\omega) = e^{j \omega}+ e^{-j \omega} = \frac{1}{2} (e^ {j \omega} + e^ {-j \omega})^2
+
<math> X(\omega) = e^{j \omega}+ e^{-j \omega} = \frac{1}{2} (e^ {j \omega} + e^ {-j \omega})^2 </math>
 +
 
 +
<math> X(omega) = 2cos(\omega)

Revision as of 17:10, 24 October 2008

Fourier Transform of delta functions

$ x(t) = \delta (t+1) + \delta (t-1) $

$ X(\omega) = \int_{-\infty}^{\infty} \delta (t+1)e^{-j \omega t} + \int_{-\infty}^{\infty} \delta (t-1)e^{-j \omega t} dt $

$ X(\omega) = e^{j \omega}+ e^{-j \omega} = \frac{1}{2} (e^ {j \omega} + e^ {-j \omega})^2 $

$ X(omega) = 2cos(\omega) $

Alumni Liaison

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

Buyue Zhang