Difference between revisions of "HW1.5 Paul Scheffler - The Energy and Power of a Signal ECE301Fall2008mboutin" - Rhea

Revision as of 15:03, 4 September 2008

Energy

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

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

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

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

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

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

$ P = 8\pi $