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For a continuous-time signal <br> | For a continuous-time signal <br> | ||
| − | <math>Energy = \int_{t_1}^{t_2} \! |x(t)|^2\ dt </math><br> | + | <math>Energy = \int_{t_1}^{t_2} \! |x(t)|^2\ dt ............. (1)</math><br> |
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</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 the above equation converges, | ||
<math> \lim_{x \to \infty} f(x) = L </math> | <math> \lim_{x \to \infty} f(x) = L </math> | ||
Revision as of 20:53, 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 the above equation converges,
$ \lim_{x \to \infty} f(x) = L $
