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<math>= \int_{-\infty}^\infty |cos(t) + jsin(t)|^2dt</math> (Euler's Formula) | <math>= \int_{-\infty}^\infty |cos(t) + jsin(t)|^2dt</math> (Euler's Formula) | ||
| − | <math>= \int_{-\infty}^\infty (\sqrt{cos^2(t) + jsin(t)})^2dt</math> (Euler's Formula) | + | <math>= \int_{-\infty}^\infty ( \sqrt{cos^2(t) + jsin(t)} )^2dt</math> (Euler's Formula) |
Revision as of 21:51, 4 September 2008
Signal
$ x(t) = e^{jt} $
Energy
$ E_\infty = \int_{-\infty}^\infty |x(t)|^2dt $
$ = \int_{-\infty}^\infty |e^{jt}|^2dt $
$ = \int_{-\infty}^\infty |cos(t) + jsin(t)|^2dt $ (Euler's Formula)
$ = \int_{-\infty}^\infty ( \sqrt{cos^2(t) + jsin(t)} )^2dt $ (Euler's Formula)
