(New page: == Equations == Energy of a Signal: <math>E = {1\over(t2-t1)}\int_{t_1}^{t_2} \! |f(t)|^2 dt</math> Power of a Signal: <math>P = \int_{t_1}^{t_2} \! |f(t)|^2\ dt</math> === Energy === ...) |
(No difference)
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Latest revision as of 16:54, 4 September 2008
Equations
Energy of a Signal: $ E = {1\over(t2-t1)}\int_{t_1}^{t_2} \! |f(t)|^2 dt $
Power of a Signal: $ P = \int_{t_1}^{t_2} \! |f(t)|^2\ dt $
Energy
$ E = {1\over(t2-t1)}\int_{t_1}^{t_2} \! |sin(t)|^2 dt $
$ E = {1\over4\pi} * [t - {1\over2}sin(2t)]_{t=0}^{t=2\pi} $
$ E = {1\over{4\pi}} * [ 2\pi - {1\over2}\sin(4\pi) - ( 0 - {1\over2}\sin(0) ) ] $
$ E = {1\over{4\pi}} * [2\pi] $
$ E = {1\over2} $
Power
$ P = \int_{t_1}^{t_2} \! |sin(t)|^2\ dt $
$ P = \int_0^{2\pi} \! |{(1-\cos(2t))\over 2}| dt $
$ P = {1\over 2}\int_0^{2\pi} \! |1-\cos(2t)| dt $
$ P = {1\over 2}t - {1\over 4}\sin(2t) )\mid_0^{2\pi} $
$ P = {1\over 2}(2\pi) - {1\over 4}\sin(2*2\pi) - [{1\over 2}(0) - {1\over 4}\sin(2*0)] $
$ P = \pi $
