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(Unit Impulse)
(Repsonse of the CT system)
 
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== Unit Impulse ==
 
== Unit Impulse ==
  
<math> h(t) = u(t-1) ,\</math>
+
<math> h(t) = u(t-1) \,</math><br>
 +
 
 +
<math> H(s) = \int^{\infty}_{-\infty} u(t-1)e^{-jw_0 t} dt\,</math><br>
 +
 
 +
<math> H(s) = \int^{\infty}_{1}e^{-jw_0 t} dt\,</math><br>
 +
 
 +
<math> H(s) = \frac{1}{jw_0}</math><br>
 +
 
 +
 
 +
== Repsonse of the CT system  ==
 +
 
 +
<math> x(t) = cos({\frac{2\pi t}{3}})+ 4sin({\frac{5\pi t}{3}})\,</math><br>
 +
 
 +
<math> y(t) = H(s)x(t)\,</math><br>
 +
 
 +
<math> y(t) = \frac{1}{j4}e^{\frac{2j2\pi t}{6}} - \frac{1}{j4}e^{\frac{-2j2\pi t}{6}} - \frac{2}{5}e^{\frac{2j5\pi t}{6}}  -\frac{2}{5}e^{\frac{-2j5\pi t}{6}}</math>

Latest revision as of 17:48, 25 September 2008

Unit Impulse

$ h(t) = u(t-1) \, $

$ H(s) = \int^{\infty}_{-\infty} u(t-1)e^{-jw_0 t} dt\, $

$ H(s) = \int^{\infty}_{1}e^{-jw_0 t} dt\, $

$ H(s) = \frac{1}{jw_0} $


Repsonse of the CT system

$ x(t) = cos({\frac{2\pi t}{3}})+ 4sin({\frac{5\pi t}{3}})\, $

$ y(t) = H(s)x(t)\, $

$ y(t) = \frac{1}{j4}e^{\frac{2j2\pi t}{6}} - \frac{1}{j4}e^{\frac{-2j2\pi t}{6}} - \frac{2}{5}e^{\frac{2j5\pi t}{6}} -\frac{2}{5}e^{\frac{-2j5\pi t}{6}} $

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BSEE 2004, current Ph.D. student researching signal and image processing.

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