Nonlinear behaviour of a direct current (DC) driven semiconductor-gas discharge plasma is investigated experimentally. The setup consists of two planar electrodes separated by a gap of 1 mm. Plasma glow is generated between a semiconductor cathode and a transparent anode using nitrogen gas at partial atmospheric pressure. Nonlinear behavior of the discharge is investigated by varying the applied DC voltage while monitoring the plasma current (I), voltage (V), and the optical emission, (i.e., amplified voltage measurements obtained using a photodiode and an amplifier). The discharge behaves oscillatory in time. By increasing the applied voltage, the system evolves into higher frequency oscillations with sub-harmonics. In fact, period doublings are observed in these systems, as shown in earlier publications by our research group. In this study, we investigate the mode coupling nature of these oscillations using a Fourier transform based spectral analysis.