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| + | [[Category:energy]] | ||
| + | [[Category:signal]] | ||
| + | [[Category:ECE]] | ||
| + | [[Category:ECE301]] | ||
| + | [[Category:practice problem]] | ||
| + | |||
| + | |||
| + | ==Problem== | ||
Calculating <math>E_\infty</math> | Calculating <math>E_\infty</math> | ||
<math>x(t)=tu(t)</math> | <math>x(t)=tu(t)</math> | ||
| + | ---- | ||
| + | ==Solution 1== | ||
<math>E_\infty = \int_{-\infty}^\infty |tu(t)|^2\,dt)</math> | <math>E_\infty = \int_{-\infty}^\infty |tu(t)|^2\,dt)</math> | ||
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<math>P_\infty = \infty</math> | <math>P_\infty = \infty</math> | ||
| + | ---- | ||
| + | [[Signal_energy_CT|Back to CT signal energy page]] | ||
Revision as of 15:58, 25 February 2015
Problem
Calculating $ E_\infty $
$ x(t)=tu(t) $
Solution 1
$ 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 $
