Axial piston pumps work as power supply units in hydraulic systems, assigning great significance to their health management. Model-based method arouses more attention for the inherent physical interpretability. However, most pressure models are confronted with the nonlinear and ill-conditioned terms, posing challenges in obtaining solutions. To address this issue, a spectral domain model is established for simulating dynamic pressure at the outlet port of axial piston pumps. Firstly, pressure build-up equations are derived at the outlet port. Then, Fourier expansions are conducted on the terms in the equations, converting the differential equations into algebraic ones with respect to Fourier coefficients. Additionally, the wear factor is introduced in the proposed model to simulate the faulty response. The experiments involve testing varying degrees of piston wear, demonstrating the feasibility of simulating wear-induced faults. The proposed model successfully captured the increase in rotational frequency amplitude under progressive wear conditions, providing a physical explanation for the fault characteristic.