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| + | <math>x(t)=4\cos(t)+4\jmath\sin(t)</math> | ||
| + | Compute magnitude of <math>x(t)</math> | ||
| + | |||
| + | <math>|x(t)|=|4\cos(t)+4\jmath\sin(t)|</math> | ||
| + | |||
| + | <math>|x(t)|=\sqrt{16\cos^2(t)+16\sin^2(t)}=4</math> | ||
| + | |||
| + | Compute <math>E\infty</math> | ||
| + | |||
| + | <math>E\infty=\int_{-\infty}^\infty |4|^2\,dt</math> | ||
| + | |||
| + | <math>E\infty=16t|_{-\infty}^\infty</math> | ||
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| + | <math>E\infty=\infty</math> | ||
| + | |||
| + | Compute <math>P\infty</math> | ||
| + | |||
| + | <math>P\infty=lim_{T \to \infty} \ \frac{1}{(2T)}\int|4|^2dt</math> | ||
| + | |||
| + | <math>P\infty=lim_{T \to \infty} \ \frac{1}{(2T)}*16|_{-T}^T</math> | ||
| + | |||
| + | <math>P\infty=lim_{T \to \infty} \ \frac{1}{(2T)}*16(T-(-T))</math> | ||
| + | |||
| + | <math>P\infty=lim_{T \to \infty} \ 16</math> | ||
| + | |||
| + | <math>P\infty=16</math> | ||
Latest revision as of 19:29, 21 June 2009
$ x(t)=4\cos(t)+4\jmath\sin(t) $
Compute magnitude of $ x(t) $
$ |x(t)|=|4\cos(t)+4\jmath\sin(t)| $
$ |x(t)|=\sqrt{16\cos^2(t)+16\sin^2(t)}=4 $
Compute $ E\infty $
$ E\infty=\int_{-\infty}^\infty |4|^2\,dt $ $ E\infty=16t|_{-\infty}^\infty $
$ E\infty=\infty $
Compute $ P\infty $
$ P\infty=lim_{T \to \infty} \ \frac{1}{(2T)}\int|4|^2dt $
$ P\infty=lim_{T \to \infty} \ \frac{1}{(2T)}*16|_{-T}^T $
$ P\infty=lim_{T \to \infty} \ \frac{1}{(2T)}*16(T-(-T)) $
$ P\infty=lim_{T \to \infty} \ 16 $
$ P\infty=16 $
