The rigid overhead contact system is characterized by low elasticity and high stress. During long-term operation, the pantograph-catenary system is prone to issues such as component loosening, fatigue, and fracture, which severely affect the current collection quality and operational safety of subways. To address the complex contact behavior of the rigid pantograph-catenary system and the difficulty of accurately characterizing its dynamic interaction process, a combined analysis method integrating power spectral density and load spectrum is proposed. Based on measured dynamic contact force data of the pantograph-catenary system, the contact behavior under train stationary, starting, coasting, and braking conditions is investigated. By applying Fourier transform to convert the time-domain contact force signal into the frequency domain, the power spectral density is calculated, and characteristic frequency and energy distribution indicators are extracted to reveal the amplitude-frequency distribution characteristics and energy variation patterns of the contact force under different operating conditions. The rainflow counting method is employed to perform cycle counting on the contact force time history, compile load spectra under each operating condition, statistically analyze the distributions of load amplitudes and mean values, and extract the main vibration characteristic parameters that lead to pantograph-catenary fatigue failure. The results show that the dynamic contact force of the rigid pantograph-catenary system is primarily concentrated in the low-frequency range of 0~6 Hz, with a high energy proportion in the 0~1 Hz range. The load amplitude is mainly concentrated around 120 N, with low-amplitude, high-frequency periodic load components existing in the range of 0.1~1 N. Significant differences in contact force fluctuation characteristics are observed under different operating conditions, with more intense variations occurring during the starting and braking phases. Through a comprehensive analysis of the contact force amplitude and spectral characteristics, the vibration mechanism of the rigid pantograph-catenary system is revealed, providing a theoretical basis for optimizing the structural design of subway rigid pantograph-catenary systems, conducting fatigue life assessments, and enabling condition monitoring and operational maintenance management of pantograph-catenary systems.