Revision as of 20:28, 4 September 2008 by Longja (Talk)

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) $


$ E_\infty = \int_{-\infty}^\infty |e^{j(\pi t-1)}|^2\,dt $


$ E_\infty = \int_{-\infty}^\infty 1,dt $


$ E_\infty = \infty,dt $

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