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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>= t|_{-\infty}^\infty</math> | ||
| + | |||
| + | <math>= \infty - (-\infty)</math> | ||
| + | |||
| + | <math>= \infty</math> | ||
Revision as of 21:55, 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 $
$ = t|_{-\infty}^\infty $
$ = \infty - (-\infty) $
$ = \infty $
