Difference between revisions of "HW1.5 Nicholas Browdues - Signal Power and Energy ECE301Fall2008mboutin" - Rhea

Revision as of 14:07, 5 September 2008

Energy

Consider the signal $ x(t)=cos(t) $ over the interval 0 to $ 4\pi $

$ E = {1\over(t2-t1)}\int_{t_1}^{t_2}\!|x(t)|^2 dt $

$ E = {1\over(4\pi-0)}\int_{0}^{4\pi}\!|cos(t)|^2 dt $

$ E = {1\over(4\pi)}{1\over2}\int_{0}^{4\pi}\!(1+cos(2t)) dt $

$ E = {1\over8\pi}(4\pi+{1\over2}sin(8\pi)) dt $

$ E = {2} $

Power

$ f(t)=2cos(t) $

$ P = \int_{t_1}^{t_2}\!|f(t)|^2\ dt $

$ P = \int_{0}^{2\pi}\!|2cos(t)|^2\ dt $

$ P = (4){1\over2}\int_{0}^{2\pi}\!1+cos(2t) dt $

$ P = (4){1\over2}(2\pi+{1\over2}sin(2*2\pi) $

$ P = 4\pi $