Underwater sound detection based on Hilbert transform pairs of wavelet bases

We designed a new algorithm to detect multipath signals in underwater environments. The underwater sounds can be thought to comprise of acoustical signals of interest superimposed on a background of underwater noise. Though there are no obvious distribution assumptions which can be made to model underwater sound, the use of recursive density estimator of the initial underwater background noise, reconstructed by the discrete wavelet transform (DWT), can be considered to establish an empirical model for it. In a multipath environment, where signals are arbitrarily time delayed, the lack of translation invariance drawback of DWT is a pitfall for the model established. This paper proposes to use a Hilbert transform pairs of wavelet bases based on infinite-product formula and spectral factorization in dual-tree discrete wavelet transform structure (HISDT DWT) as a solution to it. The performance of the HISDT DWT exhibiting much better shift invariance than the DWT is illustrated. By utilizing the HISDT DWT to establish the recursive density estimator of the underwater background noise, the ability of detecting a multipath signal in an underwater environment were improved compared to that of by using the DWT's.