Abstract—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.