36 views

0 votes

The exponential Fourier series representation of a continuous-time periodic signal $x(t)$ is defined as

$$x\left ( t \right )=\sum_{k=-\infty }^{\infty }a_{k}e^{jk\omega _{0}t}$$

where $\omega _0$ is the fundamental angular frequency of $x(t)$ and the coefficients of the series are $a_{k}$. The following information is given about $x(t)$ and $a_{k}$.

- $x(t)$ is real and even, having a fundamental period of $6$
- The average value of $x(t)$ is $2$
- $a_{k}=\left\{\begin{matrix} k, & 1\leq k\leq 3\\ 0,& k> 3 \end{matrix}\right.$

The average power of the signal $x(t)$ (rounded off to one decimal place) is ______________