(New page: == Signal Energy == The signal energy expanded from <math>t_1\!</math> to <math>t_2\!</math> is defined as <math>E = \int_{t_1}^{t_2} \! |f(t)|^2\ dt</math>. <br> <br> The following is an ...) |
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<br><br><math> = (1/4)[e^{4t}]_{t=0}^{t=2} \!</math> | <br><br><math> = (1/4)[e^{4t}]_{t=0}^{t=2} \!</math> | ||
<br><br><math> = (1/4)(e^8 -1)\!</math> | <br><br><math> = (1/4)(e^8 -1)\!</math> | ||
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+ | == Average Signal Power== | ||
+ | The average signal power over an interval <math>[t_1,t_2]\!</math> is defined as <math>P_avg= |
Revision as of 13:20, 4 September 2008
Signal Energy
The signal energy expanded from $ t_1\! $ to $ t_2\! $ is defined as $ E = \int_{t_1}^{t_2} \! |f(t)|^2\ dt $.
The following is an example problem to find the signal energy for $ x(t)=e^{2t}\! $ on $ [0,2]\! $:
$ E = \int_{0}^{2} |e^{2t}|^2\ dt \! $
$ = \int_{0}^{2} e^{4t}\ dt \! $
$ = (1/4)[e^{4t}]_{t=0}^{t=2} \! $
$ = (1/4)(e^8 -1)\! $
Average Signal Power
The average signal power over an interval $ [t_1,t_2]\! $ is defined as $ P_avg= $