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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> |
<math> = \frac{1}{8}[e^{8t}]_{t=0}^{t=1} \!</math> | <math> = \frac{1}{8}[e^{8t}]_{t=0}^{t=1} \!</math> | ||
<math> = \frac{1}{8}(e^8 -1)\!</math> | <math> = \frac{1}{8}(e^8 -1)\!</math> | ||
Revision as of 08:49, 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)\! $
