Introduction:
The Fourier series represents the decomposition of a periodic function into a sum of sinusoidal functions. The coefficients of the Fourier series determine the amplitudes and phases of these sinusoidal components. In this question, we are given that the Fourier series coefficients of a signal are periodic and we need to determine the nature of the signal.

Explanation:

1. Definition of Fourier Series:
The Fourier series of a periodic function f(t) with period T is given by:
f(t) = a0/2 + Σ(an*cos(nω0t) + bn*sin(nω0t))
where ω0 = 2π/T and an and bn are the Fourier coefficients.

2. Periodicity of Fourier Series Coefficients:
If the Fourier series coefficients an and bn are periodic, it means that they repeat after a certain number of harmonics. In other words, the coefficients have a periodic pattern with a fundamental period.

3. Continuous-time vs. Discrete-time:
Continuous-time signals are defined for all real values of time, while discrete-time signals are defined only at discrete time instants. The nature of the signal (continuous-time or discrete-time) is determined by the domain of the signal.

4. Continuous-time, periodic signal:
If the Fourier series coefficients are periodic, it implies that the signal can be represented as a sum of sinusoids with periodic amplitudes and phases. This corresponds to a continuous-time, periodic signal.

5. Discrete-time, periodic signal:
If the Fourier series coefficients are periodic, it implies that the signal can be represented as a sum of sinusoids with periodic amplitudes and phases. In the discrete-time domain, this corresponds to a periodic signal.

6. Elimination of options:
a) Continuous-time, periodic: This option is incorrect because it does not account for the possibility of a discrete-time signal.
c) Continuous-time, non-periodic: This option is incorrect because the periodicity of the Fourier series coefficients implies a periodic signal.
d) Discrete-time, non-periodic: This option is incorrect because the periodicity of the Fourier series coefficients implies a periodic signal.

Conclusion:
Based on the periodicity of the Fourier series coefficients, the signal must be a discrete-time, periodic signal (option B).