The signal feature of propeller cavitation noise during acceleration or deceleration procedure can be used to passively detect and classify moving vessels and underwater vehicles in the port regions. By analyzing the chirp periodicity of the variation of propeller wake velocity under acceleration situation, this paper presents a time domain expression of the modulation envelope signal of the accelerating propeller noise, treating the signal as a Gaussian-shaped chirp periodic pulse train with increasing trend and fluctuating pulse amplitude. The paper investigates the characteristics of simplified fractional Fourier transform (SFRFT) spectrum of the chirp periodic signal, and thus obtains the relation between the chirp periodic signal and its chirp harmonics under the conditions of underwater passive detection. Furthermore, the experimental data of the cavitation tunnel satisfy the results obtained by simulation, which verifies the correctness of the proposed signal model.