(New page: == Signal == <font size="4"> <math>f(t)= 2sin(t) \mbox{ from 0 to 2}\pi</math> </font> == Energy == <math>E=\int_{t_1}^{t_2}|x(t)|^2dt </math> <math>E=\int_{0}^{2\pi}|2sin(t)|^2dt</ma...) |
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Latest revision as of 10:48, 4 September 2008
Signal
$ f(t)= 2sin(t) \mbox{ from 0 to 2}\pi $
Energy
$ E=\int_{t_1}^{t_2}|x(t)|^2dt $
$ E=\int_{0}^{2\pi}|2sin(t)|^2dt $
$ E=\int_{0}^{2\pi}|2\Big(2sin^2(t)-1\Big)+2|dt $
$ E=\int_{0}^{2\pi}|-2cos(2t)+2|dt $
$ E=\int_{0}^{2\pi}2cos(2t)+2dt $
$ E=sin(2t)+2t\Big|\begin{matrix}2\pi\\0\end{matrix} $
$ E=\int_{0}^{2\pi}|2sin(t)|^2dt= 4\pi $
Power
$ P=\frac{1}{t_2-t_1}\int_{t_1}^{t_2}|x(t)|^2dt $
$ P=\frac{1}{2\pi-0}\int_{0}^{2\pi}|2sin(t)|^2dt $
$ P=\frac{1}{2\pi}\int_{0}^{2\pi}|2\Big(2sin^2(t)-1\Big)+2|dt $
$ P=\frac{1}{2\pi}\int_{0}^{2\pi}2cos(2t)+2dt $
$ P=\frac{1}{2\pi}\bigg[sin(2t)+2t\Big|\begin{matrix}2\pi\\0\end{matrix}\bigg] $
$ P=\frac{1}{2\pi-0}\int_{0}^{2\pi}|2sin(t)|^2dt=2\pi $
