| Line 7: | Line 7: | ||
<math>\begin{align} | <math>\begin{align} | ||
| − | \left|\cos(5t)\right|^{2} = \cos^2(5t) | + | \left|\cos(5t)\right|^{2} = \cos^2(5t) \\ |
\cos^2(5t) = \frac{1-\cos(10t)}{2} | \cos^2(5t) = \frac{1-\cos(10t)}{2} | ||
\end{align}</math> | \end{align}</math> | ||
| Line 13: | Line 13: | ||
<math> | <math> | ||
\begin{align} | \begin{align} | ||
| − | E_{\infty} &=\int_{-\infty}^\infty \cos^2(5t) dt | + | E_{\infty} &=\int_{-\infty}^\infty \cos^2(5t) dt |
| + | &=\int_{-\infty}^\infty \frac{1-\cos(10t)}{2} dt | ||
\end{align} | \end{align} | ||
</math> | </math> | ||
Revision as of 18:20, 1 December 2018
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 \end{align} $
