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| − | <math>x(t) =\sqrt x < | + | <math>x(t) =\sqrt x </math> |
| − | <math>P_\infty</math> | + | <math>E_\infty = \int_{-\infty}^\infty x(t) dt</math> |
| + | |||
| + | <math>E_\infty = \int_{-\infty}^\infty \sqrt x dt | ||
| + | |||
| + | E_\infty = \int_{-\infty}^0 j \sqrt -x dt + \int_0^\infty \sqrt x dt</math> | ||
| + | |||
| + | Solving for the two parts of <math>E_\inf</math>: | ||
| + | |||
| + | <math>\int_{-\infty}^0 j \sqrt -x dt = \dfrac {0 + \infty}{2}</math> and <math>\int_0^\infty \sqrt t dt = \dfrac{\infty + 0}{2} </math> | ||
| + | |||
| + | Therefore: | ||
| + | <math>E_\infty = \infty</math> | ||
| + | |||
| + | |||
| + | |||
| + | |||
| + | Solving for <math>P_\infty</math> | ||
| + | |||
| + | <math>P_\infty = \lim_{t\to\infty} \int_{-t}^t x(t)d\tau</math> | ||
| + | |||
| + | <math>P_\infty = \lim_{t\to\infty} \int_{-t}^t \sqrt t d\tau</math> | ||
Revision as of 07:48, 22 June 2009
$ x(t) =\sqrt x $
$ E_\infty = \int_{-\infty}^\infty x(t) dt $
$ E_\infty = \int_{-\infty}^\infty \sqrt x dt E_\infty = \int_{-\infty}^0 j \sqrt -x dt + \int_0^\infty \sqrt x dt $
Solving for the two parts of $ E_\inf $:
$ \int_{-\infty}^0 j \sqrt -x dt = \dfrac {0 + \infty}{2} $ and $ \int_0^\infty \sqrt t dt = \dfrac{\infty + 0}{2} $
Therefore: $ E_\infty = \infty $
Solving for $ P_\infty $
$ P_\infty = \lim_{t\to\infty} \int_{-t}^t x(t)d\tau $
$ P_\infty = \lim_{t\to\infty} \int_{-t}^t \sqrt t d\tau $
