(New page: <math>x(t)=\cos(t)+\jmath\sin(t)</math> ---- <math>|x(t)|=|\cos(t)+\jmath\sin(t)|=\sqrt{\cos^2(t)+\sin^2(t)}=\sqrt{2}</math> <math>E\infty=\int_{-\infty}^\infty |\sqrt{2}|^2\,dt=2t|_...) |
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<math>|x(t)|=|\cos(t)+\jmath\sin(t)|=\sqrt{\cos^2(t)+\sin^2(t)}=\sqrt{2}</math> | <math>|x(t)|=|\cos(t)+\jmath\sin(t)|=\sqrt{\cos^2(t)+\sin^2(t)}=\sqrt{2}</math> | ||
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| + | <math>E\infty</math> | ||
<math>E\infty=\int_{-\infty}^\infty |\sqrt{2}|^2\,dt=2t|_{-\infty}^\infty</math> | <math>E\infty=\int_{-\infty}^\infty |\sqrt{2}|^2\,dt=2t|_{-\infty}^\infty</math> | ||
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<math>E\infty=\infty</math> | <math>E\infty=\infty</math> | ||
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| + | <math>P\infty</math> | ||
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<math>P\infty=lim_{T \to \infty} \ \frac{1}{(2T)}\int|2|^2dt</math> | <math>P\infty=lim_{T \to \infty} \ \frac{1}{(2T)}\int|2|^2dt</math> | ||
Revision as of 19:12, 21 June 2009
$ x(t)=\cos(t)+\jmath\sin(t) $
Magnitude
$ |x(t)|=|\cos(t)+\jmath\sin(t)|=\sqrt{\cos^2(t)+\sin^2(t)}=\sqrt{2} $
$ E\infty $
$ E\infty=\int_{-\infty}^\infty |\sqrt{2}|^2\,dt=2t|_{-\infty}^\infty $
$ E\infty=\infty $
$ P\infty $
$ P\infty=lim_{T \to \infty} \ \frac{1}{(2T)}\int|2|^2dt $
$ P\infty=lim_{T \to \infty} \ \frac{1}{(2T)}*2|_{-T}^T $
$ P\infty=lim_{T \to \infty} \ \frac{1}{(2T)}*2(T-(-T)) $
$ P\infty=lim_{T \to \infty} \ 2 $
$ P\infty=2 $
