(making pretty) |
(fixing mistake) |
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| − | <math>x(t)=\sqrt(2t)</math> | + | <math>x(t)=\sqrt(2t)u(t)</math> |
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<math>E\infty=\int_{-\infty}^\infty |x(t)|^2dt</math> | <math>E\infty=\int_{-\infty}^\infty |x(t)|^2dt</math> | ||
| − | <math>E\infty=\int_{-\infty}^\infty |\sqrt(2t)|^2dt</math> | + | <math>E\infty=\int_{-\infty}^\infty |\sqrt(2t)u(t)|^2dt</math> |
| − | <math>E\infty=\int_{-\infty}^\infty | | + | <math>E\infty=\int_{-\infty}^\infty |2tu(t)|dt</math> |
<math>E\infty=\int_{0}^\infty 2tdt</math> | <math>E\infty=\int_{0}^\infty 2tdt</math> | ||
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<math>P\infty=\lim_{T \to \infty}\frac{1}{2*T}\int_{-T}^T |x(t)|^2dt</math> | <math>P\infty=\lim_{T \to \infty}\frac{1}{2*T}\int_{-T}^T |x(t)|^2dt</math> | ||
| − | <math>P\infty=\lim_{T \to \infty}\frac{1}{2*T}\int_{-T}^T |\sqrt(2t)|^2dt</math> | + | <math>P\infty=\lim_{T \to \infty}\frac{1}{2*T}\int_{-T}^T |\sqrt(2t)u(t)|^2dt</math> |
| − | <math>P\infty=\lim_{T \to \infty}\frac{1}{2*T}\int_{-T}^T| | + | <math>P\infty=\lim_{T \to \infty}\frac{1}{2*T}\int_{-T}^T|2tu(t)|dt</math> |
<math>P\infty=\lim_{T \to \infty}\frac{1}{2*T}\int_{0}^T2tdt</math> | <math>P\infty=\lim_{T \to \infty}\frac{1}{2*T}\int_{0}^T2tdt</math> | ||
Revision as of 07:58, 22 June 2009
$ x(t)=\sqrt(2t)u(t) $
Compute $ E\infty $
$ E\infty=\int_{-\infty}^\infty |x(t)|^2dt $
$ E\infty=\int_{-\infty}^\infty |\sqrt(2t)u(t)|^2dt $
$ E\infty=\int_{-\infty}^\infty |2tu(t)|dt $
$ E\infty=\int_{0}^\infty 2tdt $
$ E\infty=t^2|_{0}^{\infty} $
$ E\infty= \infty-0 $
$ E\infty=\infty $
Compute $ P\infty $
$ P\infty=\lim_{T \to \infty}\frac{1}{2*T}\int_{-T}^T |x(t)|^2dt $
$ P\infty=\lim_{T \to \infty}\frac{1}{2*T}\int_{-T}^T |\sqrt(2t)u(t)|^2dt $
$ P\infty=\lim_{T \to \infty}\frac{1}{2*T}\int_{-T}^T|2tu(t)|dt $
$ P\infty=\lim_{T \to \infty}\frac{1}{2*T}\int_{0}^T2tdt $
$ P\infty=\lim_{T \to \infty}\frac{|t^2|_{0}^{T}}{2*T} $
$ P\infty=\lim_{T \to \infty}\frac{T^2-0}{2*T} $
$ P\infty=\lim_{T \to \infty}\frac{T}{2} $
$ P\infty=\infty $
-Tylor Thompson
