Computation of Energy and Power of a CT sinusoidal signal - Rhea

Problem

Compute the energy and the power of the CT sinusoidal signal below:

$ x(t)= \cos (5t) $

Solution

$ \begin{align} \left|\cos(5t)\right|^{2} = \cos^2(5t) \\ \cos^2(5t) = \frac{1+\cos(10t)}{2} \end{align} $

$ \begin{align} E_{\infty} &=\int_{-\infty}^\infty \cos^2(5t) dt \\ &=\int_{-\infty}^\infty \frac{1+\cos(10t)}{2} dt \\ &=\int_{-\infty}^\infty \frac{1}{2} + {\frac{1}{2}}\cos(5t) dt \\ \end{align} $