The exponential Fourier series representation of a continu-ous-time periodic signal $X(t)$ is defined as

$$ x(t)=\sum\limits_{k=-\infty}^{\infty} a_k e^{j k w_0 t} $$

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 $a_k$.

I. $x(t)$ is real and even, having a fundamental period of 6

II. The average value of $x(t)$ is 2

III. $a_k=\left\{\begin{array}{c}k, 1 \leq k \leq 3 \\ 0, k>3\end{array}\right.$

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

Let x(t) be a continuous time periodic signal with fundamental period T = 1 seconds. Let {a_k} be the complex Fourier series coefficients of x(t), where k is integer valued. Consider the following statements about x(3t):

I. The complex Fourier series coefficients of x(3t) are {a_k} where k is integer valued

II. The complex Fourier series coefficients of x(3t) are {3a_k} where k is integer valued

III. The fundamental angular frequency of x(3t) is 6$$\mathrm\pi$$ rad/s

For the three statements above, which one of the following is correct?

The PSD and the power of a signal g(t) are, respectively, S_g($$\omega$$) and P_g. The PSD and the power of the signal ag(t) are, respectively

Which of the following signals is/are periodic?