Abstract: A mathematical model of amplitude-modulated ship-radiated broad-band noise signal is established based on the principle of Fourier Decomposition, deriving a mathematical expression for modulation spectrum of the ship-radiated noise based on the square demodulation algorithm. Two new conclusions from analysis of the modulation spectrum are obtained based on theoretical analysis and simulation calculation: (1) relationship between demodulation performance and demodulation processing bandwidth: when the modulation depths of different frequency bands of ship-radiated noises received by a sonar are the same, the demodulation performance is positively proportional to bandwidth of the band-pass filter used for demodulation; the wider the band-pass filter bandwidth is, the higher the signal-to-noise (SNR) ratio of the demodulation spectrum is; (2) relationship between broadband demodulation spectrum and sub-band demodulation spectrum: the broadband demodulation spectrum of the ship-radiated noise can be approximately regarded as a sum of different sub-band demodulation spectrums. To verify the two conclusions above, the actual demodulation spectrum of the ship-radiated noise is processed correspondingly, showing that the result is consistent with the result from simulation calculation.