$$xleft( t ight) in R$$
$$xleft( t ight) in P$$
$$xleft( t ight) in left( {C - R} ight)$$
The information given is not sufficient to draw any conclusion about x(t)
Answer is Right!
Answer is Wrong!
The correct answer is $\boxed{\text{D. The information given is not sufficient to draw any conclusion about }x(t)}$.
The magnitude and phase of the complex Fourier series coefficient $a_k$ of a periodic signal $x(t)$ are shown in the figure. However, the information given is not sufficient to determine whether $x(t)$ is a real-valued or complex-valued signal.
If $x(t)$ is a real-valued signal, then its complex Fourier series coefficients $a_k$ will be real numbers. However, if $x(t)$ is a complex-valued signal, then its complex Fourier series coefficients $a_k$ may be real or complex numbers.
Therefore, the information given is not sufficient to draw any conclusion about $x(t)$.