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Total Energy:

$ E_{\infty} = \int^{\infty}_{-\infty} |x(t)|^2 dt = \lim_{T\to\infty} \int^T_{-T} |x(t)|^2 dt $

Average Power:

$ P_{\infty} = \lim_{T\to\infty} \frac{1}{2T} \int^T_{-T} |x(t)|^2 dt $

Therefore if

$ E_{\infty} < \infty $,

$ P_{\infty} = \lim_{T\to\infty} \frac{E_{\infty}}{2T} = 0 $

-Bill Snow

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