HW1.5 Sangwan Han - Energy and Power ECE301Fall2008mboutin - Rhea

I assumed $ x(t)=\cos(4t) $ and time interval 0 to $ 5\pi $

Energy

$ x(t) = \cos(4t) $

$ E=\int_{t1}^{t2} |x(t)|^2\, dt $

$ E=\int_{0}^{5\pi} |\cos(4t)|^2\, dt $

$ E=\frac{1}{2}\int_{0}^{5\pi} |1+\cos(8t)|^2\, dt $

$ E=\frac{1}{2}\times|t+\frac{1}{8}\sin(8t)|\ t = 0 to 5\pi $

$ =\frac{1}{2} \times (5\pi + 0 - 0-0) $

$ =\frac{5}{2}\times\pi $

Power