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| − | == | + | ==Energy== |
| − | + | We will find the energy in one cycle of the cosine waveform. | |
| − | + | ||
| + | <math>E=\int_0^{2\pi}{|cos(t)|^2dt}</math> | ||
| − | |||
| + | <math>=\frac{1}{2}\int_0^{2\pi}(1+cos(2t))dt</math> | ||
| − | |||
| + | <math>=\frac{1}{2}(t+\frac{1}{2}sin(2t))|_{t=0}^{t=2\pi}</math> | ||
| − | |||
| + | <math>=\frac{1}{2}(2\pi+0-0-0)</math> | ||
| − | <math> | + | |
| − | + | <math>=\pi</math> | |
Revision as of 15:34, 3 September 2008
Signal
$ y(t)=exp(t) $
Energy
We will find the energy in one cycle of the cosine waveform.
$ E=\int_0^{2\pi}{|cos(t)|^2dt} $
$ =\frac{1}{2}\int_0^{2\pi}(1+cos(2t))dt $
$ =\frac{1}{2}(t+\frac{1}{2}sin(2t))|_{t=0}^{t=2\pi} $
$ =\frac{1}{2}(2\pi+0-0-0) $
$ =\pi $
