Fast Wavelet Transform Algorithms for Sonar Signal Analysis

In active sonar, received echoes are composed of multiple replicas of transmitted sonar signal with time delays and attenuations through multipath. In non-stationary scenarios, different multipath also exhibits different scaling. This phenomenon provides a way to explicitly resolve the multipath components given the availability of a rational orthogonal wavelet (ROW) analysis framework. This paper establishes the ground work of a wavelet-based multipath resolving structure by tackling the fast wavelet transform (FWT) filter bank (FB) design for ROWs. A review of different FWT algorithms in terms of scaling, translation and computational complexity is presented. The proposed FWT FB design for ROWs enables practical applications of the multipath/Doppler resolving structure in both active and passive sonar signal analysis. A simplified model for active sonar signal multipath resolving is presented to demonstrate the multipath resolving mechanism.