(New page: Property: if <math>E_{\infty}</math> is finite, then <math>P_\infty</math> equals to zero. ---- Proof: <math>E_\infty = \int^{+\infty}_{-\infty}|x(t)|^2 dt</math> <math>P_\infty = \displ...) |
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Latest revision as of 16:21, 21 June 2009
Property: if $ E_{\infty} $ is finite, then $ P_\infty $ equals to zero.
Proof:
$ E_\infty = \int^{+\infty}_{-\infty}|x(t)|^2 dt $
$ P_\infty = \displaystyle\lim_{T\to\infty} \dfrac{1}{2T} \int^{+T}_{-T}{|x(t)|^2}{dt} $
We see from the equations above that,
$ P_\infty = \displaystyle\lim_{T\to\infty} \dfrac{E_\infty}{2T} $
For $ E_{\infty} < {\infty} $, we got that,
$ P_\infty = \displaystyle\lim_{T\to\infty} \dfrac{E_\infty}{2T} = 0 $
