(→Power and Energy Problem) |
(→Power and Energy Problem) |
||
| Line 11: | Line 11: | ||
* Bonus Problem! | * Bonus Problem! | ||
| + | |||
<math>x(t) = e^{j(\pi t-1)}</math> | <math>x(t) = e^{j(\pi t-1)}</math> | ||
| + | |||
<math>P_\infty = \lim_{T \to \infty} (\frac{1}{2T} \int_{-T}^T |e^{j(\pi t-1)}|^2\,dt)</math> | <math>P_\infty = \lim_{T \to \infty} (\frac{1}{2T} \int_{-T}^T |e^{j(\pi t-1)}|^2\,dt)</math> | ||
<math>P_\infty = \lim_{T \to \infty} (\frac{1}{2T} \int_{-T}^T 1\,dt)</math> | <math>P_\infty = \lim_{T \to \infty} (\frac{1}{2T} \int_{-T}^T 1\,dt)</math> | ||
| + | |||
| + | |||
| + | <math>P_\infty = \lim_{T \to \infty} (\frac{1}{2T} 2T)</math> | ||
| + | |||
| + | |||
| + | <math>P_\infty = 1</math> | ||
| + | |||
| Line 27: | Line 36: | ||
| − | <math>E_\infty = \infty | + | <math>E_\infty = \infty</math> |
Revision as of 21:30, 4 September 2008
Power and Energy Problem
$ x(t) = 3\cos(4t + \frac{\pi}{3}) $
$ P_\infty = \lim_{T \to \infty} (\frac{1}{2T} \int_{-T}^T |3\cos(4t + \frac{\pi}{3})|^2\,dt) $
$ E_\infty = \int_{-\infty}^\infty |3\cos(4t + \frac{\pi}{3})|^2\,dt $
- Bonus Problem!
$ x(t) = e^{j(\pi t-1)} $
$ P_\infty = \lim_{T \to \infty} (\frac{1}{2T} \int_{-T}^T |e^{j(\pi t-1)}|^2\,dt) $
$ P_\infty = \lim_{T \to \infty} (\frac{1}{2T} \int_{-T}^T 1\,dt) $
$ P_\infty = \lim_{T \to \infty} (\frac{1}{2T} 2T) $
$ P_\infty = 1 $
$ E_\infty = \int_{-\infty}^\infty |e^{j(\pi t-1)}|^2\,dt $
$ E_\infty = \int_{-\infty}^\infty 1,dt $
$ E_\infty = \infty $
