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| + | Calculating <math>E_\infty</math> | ||
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<math>x(t)=tu(t)</math> | <math>x(t)=tu(t)</math> | ||
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<math>E_\infty =\infty-0 = \infty</math> | <math>E_\infty =\infty-0 = \infty</math> | ||
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| + | Calculating <math>P_\infty</math> | ||
<math>P_\infty = lim_{T \to \infty} \ \frac{1}{2T} \int_{-T}^T |tu(t)|^2\,dt</math> | <math>P_\infty = lim_{T \to \infty} \ \frac{1}{2T} \int_{-T}^T |tu(t)|^2\,dt</math> | ||
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<math>P_\infty = lim_{T \to \infty} \ \frac{1}{2T} \int_{0}^T t^2\,dt</math> | <math>P_\infty = lim_{T \to \infty} \ \frac{1}{2T} \int_{0}^T t^2\,dt</math> | ||
| − | <math>P_\infty = lim_{T \to \infty} \ \frac{1}{2T} \frac{t^3}{3}\bigg]_0^\infty</math> | + | <math>P_\infty = lim_{T \to \infty} \ \frac{1}{2T} \frac{t^3}{3}\bigg]_0^T</math> |
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| + | <math>P_\infty = lim_{T \to \infty} \ \frac{1}{2T} \frac{T^3}{3}</math> | ||
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| + | <math>P_\infty = lim_{T \to \infty} \ \frac{T^2}{6}</math> | ||
<math>P_\infty = \infty</math> | <math>P_\infty = \infty</math> | ||
Revision as of 19:57, 21 June 2009
Calculating $ E_\infty $
$ x(t)=tu(t) $
$ E_\infty = \int_{-\infty}^\infty |tu(t)|^2\,dt) $
$ E_\infty = \int_{0}^\infty t^2\,dt) $
$ E_\infty =\frac{t^3}{3}\bigg]_0^\infty) $
$ E_\infty =\infty-0 = \infty $
Calculating $ P_\infty $
$ P_\infty = lim_{T \to \infty} \ \frac{1}{2T} \int_{-T}^T |tu(t)|^2\,dt $
$ P_\infty = lim_{T \to \infty} \ \frac{1}{2T} \int_{0}^T t^2\,dt $
$ P_\infty = lim_{T \to \infty} \ \frac{1}{2T} \frac{t^3}{3}\bigg]_0^T $
$ P_\infty = lim_{T \to \infty} \ \frac{1}{2T} \frac{T^3}{3} $
$ P_\infty = lim_{T \to \infty} \ \frac{T^2}{6} $
$ P_\infty = \infty $
