(New page: <math>x(t)=\sqrt(t)</math> Compute <math>E\infty</math> and <math>P\infty</math> <math>E\infty=\int_{-\infty}^\infty |x(t)|^2dt</math> <math>E\infty=\int_{-\infty}^\infty |\sqrt(t)|^2d...) |
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<math>E\infty=\int_{-\infty}^0 tdt +\int_{0}^\infty tdt</math> | <math>E\infty=\int_{-\infty}^0 tdt +\int_{0}^\infty tdt</math> | ||
| − | <math>E\ | + | <math>E\infty=0.5 t^2|_{-\infty}^0 + 0.5t^2|_{0}^\infty </math> |
<math>E\infty=\infty</math> | <math>E\infty=\infty</math> | ||
| + | |||
| + | <math>P\infty=\lim_{T->\infty}1/(2T)\int_{-T}^T |x(t)|^2dt</math> | ||
| + | |||
| + | <math>P\infty=\lim_{T->\infty}1/(2T)\int_{-T}^T |\sqrt(t)|^2dt</math> | ||
| + | |||
| + | <math>P\infty=\lim_{T->\infty}1/(2T)*0.5t^2|_{-T}^T</math> | ||
| + | |||
| + | <math>P\infty=\lim_{T->\infty}1/(2T)*(1/2(-T)^2+1/2(T)^2)</math> | ||
| + | |||
| + | <math>P\infty=\lim_{T->\infty}T/4</math> | ||
| + | |||
| + | <math>P\infty=\infty</math> | ||
Latest revision as of 19:44, 17 June 2009
$ x(t)=\sqrt(t) $
Compute $ E\infty $ and $ P\infty $
$ E\infty=\int_{-\infty}^\infty |x(t)|^2dt $
$ E\infty=\int_{-\infty}^\infty |\sqrt(t)|^2dt $
$ E\infty=\int_{-\infty}^\infty tdt $
$ E\infty=\int_{-\infty}^0 tdt +\int_{0}^\infty tdt $
$ E\infty=0.5 t^2|_{-\infty}^0 + 0.5t^2|_{0}^\infty $
$ E\infty=\infty $
$ P\infty=\lim_{T->\infty}1/(2T)\int_{-T}^T |x(t)|^2dt $
$ P\infty=\lim_{T->\infty}1/(2T)\int_{-T}^T |\sqrt(t)|^2dt $
$ P\infty=\lim_{T->\infty}1/(2T)*0.5t^2|_{-T}^T $
$ P\infty=\lim_{T->\infty}1/(2T)*(1/2(-T)^2+1/2(T)^2) $
$ P\infty=\lim_{T->\infty}T/4 $
$ P\infty=\infty $
