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Over an infinite period of time <br> | Over an infinite period of time <br> | ||
<math>Energy(\infty) = \lim_{T \to \infty} \int_{-T}^{T} \! |x(t)|^2\ dt = \int_{-\infty}^{\infty} \! |x(t)|^2\ dt .......... (2)</math> <br><br> | <math>Energy(\infty) = \lim_{T \to \infty} \int_{-T}^{T} \! |x(t)|^2\ dt = \int_{-\infty}^{\infty} \! |x(t)|^2\ dt .......... (2)</math> <br><br> | ||
| − | If | + | If Equation 2 converges, Energy is finite. <br> |
| − | <math> \lim_{ | + | If Equation 2 diverges, Energy is infinite. <br><br> |
| + | <math>P(\infty)=\lim_{T \to \infty} {\frac{E(\infty)}{2T}} = 0 ................ Finite-energy Signal</math><br> | ||
| + | <math>P(\infty0 > 0 ................ Infinite-energy Signal</math><br> | ||
| + | Not Periodic ..................... Neither Finite nor Infinite.<br> | ||
Latest revision as of 21:00, 4 September 2008
For a continuous-time signal
$ Energy = \int_{t_1}^{t_2} \! |x(t)|^2\ dt ............. (1) $
Over an infinite period of time
$ Energy(\infty) = \lim_{T \to \infty} \int_{-T}^{T} \! |x(t)|^2\ dt = \int_{-\infty}^{\infty} \! |x(t)|^2\ dt .......... (2) $
If Equation 2 converges, Energy is finite.
If Equation 2 diverges, Energy is infinite.
$ P(\infty)=\lim_{T \to \infty} {\frac{E(\infty)}{2T}} = 0 ................ Finite-energy Signal $
$ P(\infty0 > 0 ................ Infinite-energy Signal $
Not Periodic ..................... Neither Finite nor Infinite.
