(New page: Compute <math>E\infty</math> and <math>P\infty</math> <math>E\infty=\int_{-\infty}^\infty |x(t)|^2dt</math> <math>E\infty=\int_{-\infty}^\infty |\sqrt(t)|^2dt</math> <math>E\infty=\i...) |
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+ | Compute <math>E\infty</math> | ||
− | + | <math>x(t)=\cos(t)+j*\sin(t)</math> | |
− | + | ||
<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 |\ | + | <math>E\infty=\int_{-\infty}^\infty |\cos(t)+j\sin(t)|^2dt</math> |
+ | |||
+ | <math>E\infty=\int_{-\infty}^\infty |e^{j*t}|^2dt</math> | ||
+ | |||
+ | <math>E\infty=\int_{-\infty}^\infty |e^2*e^{j*t}|dt</math> | ||
+ | |||
+ | <math>E\infty=e^2/j*|e^{j*t}|_{-\infty}^{\infty}</math> | ||
+ | |||
+ | <math>E\infty=e^2/j*(\infty-0)</math> | ||
+ | |||
+ | <math>E\infty=\infty</math> | ||
+ | |||
+ | Compute <math>P\infty</math> | ||
+ | |||
+ | <math>x(t)=\cos(t)+j*\sin(t)</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 |\cos(t)+j\sin(t)|^2dt</math> | ||
+ | |||
+ | <math>P\infty=\lim_{T \to \infty}\int_{-T}^T|e^{j*t}|^2dt</math> | ||
+ | |||
+ | <math>P\infty=\lim_{T \to \infty}\frac{1}{2*T}\int_{-T}^T|e^2*e^{j*t}|dt</math> | ||
+ | |||
+ | <math>P\infty=\lim_{T \to \infty}\frac{1}{2*T}\int_{-T}^T|e^2*e^{j*t}|dt</math> | ||
+ | |||
+ | <math>P\infty=\lim_{T \to \infty}\frac{\int_{-\infty}^\infty |e^2*e^{j*t}|dt}{2*T}</math> | ||
+ | |||
+ | <math>P\infty=\frac{d(\int_{-\infty}^\infty |e^2*e^{j*t}|dt)}{d(2*T)}</math> | ||
+ | |||
+ | <math>P\infty=\frac{e^{2*j*t}}{2}</math> | ||
− | <math> | + | <math>P\infty=\infty</math> |
Latest revision as of 16:24, 21 June 2009
Compute $ E\infty $
$ x(t)=\cos(t)+j*\sin(t) $
$ E\infty=\int_{-\infty}^\infty |x(t)|^2dt $
$ E\infty=\int_{-\infty}^\infty |\cos(t)+j\sin(t)|^2dt $
$ E\infty=\int_{-\infty}^\infty |e^{j*t}|^2dt $
$ E\infty=\int_{-\infty}^\infty |e^2*e^{j*t}|dt $
$ E\infty=e^2/j*|e^{j*t}|_{-\infty}^{\infty} $
$ E\infty=e^2/j*(\infty-0) $
$ E\infty=\infty $
Compute $ P\infty $
$ x(t)=\cos(t)+j*\sin(t) $
$ 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 |\cos(t)+j\sin(t)|^2dt $
$ P\infty=\lim_{T \to \infty}\int_{-T}^T|e^{j*t}|^2dt $
$ P\infty=\lim_{T \to \infty}\frac{1}{2*T}\int_{-T}^T|e^2*e^{j*t}|dt $
$ P\infty=\lim_{T \to \infty}\frac{1}{2*T}\int_{-T}^T|e^2*e^{j*t}|dt $
$ P\infty=\lim_{T \to \infty}\frac{\int_{-\infty}^\infty |e^2*e^{j*t}|dt}{2*T} $
$ P\infty=\frac{d(\int_{-\infty}^\infty |e^2*e^{j*t}|dt)}{d(2*T)} $
$ P\infty=\frac{e^{2*j*t}}{2} $
$ P\infty=\infty $