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Consider the signal | Consider the signal | ||
<math>x(t)=cos(t)</math> over the interval 0 to <math>4\pi</math> | <math>x(t)=cos(t)</math> over the interval 0 to <math>4\pi</math> | ||
| − | + | == Average Power == | |
Revision as of 14:17, 5 September 2008
Consider the signal $ x(t)=cos(t) $ over the interval 0 to $ 4\pi $
Average Power
$ Avg. Power = {1\over(t2-t1)}\int_{t_1}^{t_2}\!|x(t)|^2 dt $
$ Avg. Power = {1\over(4\pi-0)}\int_{0}^{4\pi}\!|cos(t)|^2 dt $
$ Avg. Power = {1\over(4\pi)}{1\over2}\int_{0}^{4\pi}\!(1+cos(2t)) dt $
$ Avg. Power = {1\over8\pi}(4\pi+{1\over2}sin(8\pi)) $
$ Avg. Power = {1\over2} $
Energy
$ f(t)=cos(t) $
$ P = \int_{t_1}^{t_2}\!|x(t)|^2\ dt $
$ P = \int_{0}^{4\pi}\!|cos(t)|^2\ dt $
$ P = {1\over2}\int_{0}^{4\pi}\!(1+cos(2t)) dt $
$ P = {1\over2}(4\pi+{1\over2}sin(8\pi)) $
$ P = 2\pi $
