From envelope detection to cyclostationary methods: Enhancing propeller noise analysis by negative entropy.

Propeller cavitation is an important source of underwater-radiated noise that can carry modulation features related to a vessel's propulsion system. These features are commonly extracted using detection of envelope modulation on noise (DEMON). The performance of DEMON is highly sensitive to the arbitrary selection of the bandpass filter. Multiband DEMON improves performance by uniformly combining subbands but, at the same time, limits this benefit by overlooking the distinction between informative and noise-dominated bands. This study evaluates two cyclostationary representations, the cyclic modulation spectrum and fast spectral correlation, and introduces spectral negative entropy as a subband weighting function to overcome the limitations of DEMON-based methods. The weighting emphasizes subbands whose envelope spectra are more strongly structured. The proposed fast spectral correlation weighted by spectral negative entropy achieves the same detection probability at a 3.5 dB lower input signal-to-noise ratio than DEMON and 1 dB lower than multiband DEMON, with a 25% improvement in detection signal-to-noise ratio. Tests on DeepShip vessel recordings show 1-3 dB gains in dominant band contrast relative to uniform averaging. These results indicate that entropy-based subband weighting improves the contrast and interpretability of modulation-related features in passive sonar analysis.