(Signal Energy)
(Signal Energy)
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find the signal energy of <math>x(t)=e^{4t}\!</math> on <math>[0,1]\!</math>
 
find the signal energy of <math>x(t)=e^{4t}\!</math> on <math>[0,1]\!</math>
  
<math>E=\int_{0}^{1} |e^(4t)|^2 dt \!</math>
+
<math>E = \int_{0}^{1} |e^{4t}|^2\ dt \!</math>
  
 
<math>E=\int_{0}^{1}e^(8t)dt \!</math>
 
<math>E=\int_{0}^{1}e^(8t)dt \!</math>

Revision as of 08:50, 5 September 2008

Signal Energy

$ E=\int_{t_1}^{t_2}x(t)dt $

find the signal energy of $ x(t)=e^{4t}\! $ on $ [0,1]\! $

$ E = \int_{0}^{1} |e^{4t}|^2\ dt \! $

$ E=\int_{0}^{1}e^(8t)dt \! $

$ = \frac{1}{8}[e^{8t}]_{t=0}^{t=1} \! $ $ = \frac{1}{8}(e^8 -1)\! $

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