Line 32: | Line 32: | ||
<math>P\infty=lim\bullet T\rightarrow\infty~~1</math> | <math>P\infty=lim\bullet T\rightarrow\infty~~1</math> | ||
<math>P\infty=1</math> | <math>P\infty=1</math> | ||
+ | |||
+ | [https://kiwi.ecn.purdue.edu/rhea/index.php/Computing_E_infinity_and_P_infinity Return to Computing E infinity and P infinity] |
Revision as of 07:09, 17 June 2009
Work By Ryne Rayburn (rrayburn)
$ x(t)=\sqrt{t} $
$ E\infty=\int|x(t)|^2dt $ (from $ -\infty $ to $ \infty $)
$ E\infty=\int|\sqrt{t}|^2dt=\int tdt $(from $ 0 $ to $ \infty $ due to sqrt limiting to positive Real numbers) $ E\infty=.5*t^2| $(from $ 0 $ to $ \infty $) $ E\infty=.5(\infty^2-0^2)=\infty $
$ P\infty=lim\bullet T\rightarrow\infty*1/(2T)\int|x(t)|^2dt $ (from $ -T $ to $ T $)
$ P\infty=lim\bullet T\rightarrow\infty~~1/(2T)\int|\sqrt{t}|^2dt=\int tdt $ (from $ 0 $ to $ T $) $ P\infty=lim\bullet T\rightarrow\infty~~1/(2T)*.5t^2| $(from $ 0 $ to $ T $) $ P\infty=lim\bullet T\rightarrow\infty~~1/(2T)*(.5T^2) $ $ P\infty=lim\bullet T\rightarrow\infty~~(.25T)=\infty $
$ x(t)=\cos(t)+\jmath\sin(t) $
$ |x(t)|=|\cos(t)+\jmath\sin(t)|=\sqrt{\cos^2(t)+\sin^2(t)}=1 $
$ E\infty=\int|x(t)|^2dt $ (from $ -\infty $ to $ \infty $)
$ E\infty=\int|1|^2dt=t| $(from $ -\infty $ to $ \infty $) $ E\infty=\infty $
$ P\infty=lim\bullet T\rightarrow\infty~~1/(2T)\int|x(t)|^2dt $ (from $ -T $ to $ T $)
$ P\infty=lim\bullet T\rightarrow\infty~~1/(2T)\int|1|^2dt $ $ P\infty=lim\bullet T\rightarrow\infty~~1/(2T)*t| $(from $ -T $ to $ T $) $ P\infty=lim\bullet T\rightarrow\infty~~1/(2T)*(T-(-T)) $ $ P\infty=lim\bullet T\rightarrow\infty~~1 $ $ P\infty=1 $