Difference between revisions of "E infinty & P infinty - Ryne Rayburn (rrayburn)" - Rhea

Revision as of 07:05, 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 $