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<math>= \int_{-\infty}^\infty {\sqrt{cos^2(t) + jsin(t)}}^2dt</math> (Magnitude of a Complex Number) | <math>= \int_{-\infty}^\infty {\sqrt{cos^2(t) + jsin(t)}}^2dt</math> (Magnitude of a Complex Number) | ||
| − | <math>= \int_{-\infty}^\infty dt</math> ( | + | <math>= \int_{-\infty}^\infty dt</math> (<math>cos^2(t) + sin^2(t) = 1</math>) |
Revision as of 21:54, 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 $ (Magnitude of a Complex Number)
$ = \int_{-\infty}^\infty dt $ ($ cos^2(t) + sin^2(t) = 1 $)
