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<math>x(t)=\sqrt(2t)</math> | <math>x(t)=\sqrt(2t)</math> | ||
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Compute <math>E\infty</math> | Compute <math>E\infty</math> | ||
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<math>E\infty=0</math> | <math>E\infty=0</math> | ||
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| + | Compute <math>P\infty</math> | ||
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| + | <math>P\infty=\lim_{T \to \infty}\frac{1}{2*T}\int_{-T}^T |x(t)|^2dt</math> | ||
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| + | <math>P\infty=\lim_{T \to \infty}\frac{1}{2*T}\int_{-T}^T |\sqrt(2t)|^2dt</math> | ||
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| + | <math>P\infty=\lim_{T \to \infty}\frac{1}{2*T}\int_{-T}^T|2t|dt</math> | ||
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| + | <math>P\infty=\lim_{T \to \infty}\frac{|t^2|_{-T }^{T}}{2*T}</math> | ||
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| + | <math>P\infty=\lim_{T \to \infty}\frac{T^2-(-T)^2}{2*T }</math> | ||
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| + | <math>P\infty=0</math> | ||
-Tylor Thompson | -Tylor Thompson | ||
Revision as of 18:17, 21 June 2009
$ x(t)=\sqrt(2t) $
Compute $ E\infty $
$ E\infty=\int_{-\infty}^\infty |x(t)|^2dt $
$ E\infty=\int_{-\infty}^\infty |\sqrt(2t)|^2dt $
$ E\infty=\int_{-\infty}^\infty |2t|dt $
$ E\infty=|t^2|_{-\infty}^{\infty} $
$ E\infty= \infty-\infty $
$ E\infty=0 $
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)|^2dt $
$ P\infty=\lim_{T \to \infty}\frac{1}{2*T}\int_{-T}^T|2t|dt $
$ P\infty=\lim_{T \to \infty}\frac{|t^2|_{-T }^{T}}{2*T} $
$ P\infty=\lim_{T \to \infty}\frac{T^2-(-T)^2}{2*T } $
$ P\infty=0 $
-Tylor Thompson
