The application of the robust discrete wavelet transform to underwater sound

This paper proposes the use of robust discrete wavelet transform (RDWT) as a solution to a signal processing problem of to detect transient features in the sound recordings that contain interference as well as multipaths. The discrete wavelet transform (DWT) was used to detect signal in the underwater. In underwater and a multipaths environment where numbers signal components arrive with arbitrary delays, we use the RDWT in detection. We adopt the RDWT instead of using DWT for two reasons. The first one is that the spectrum of the shifted signal is the same as the unshifted version when using the RDWT. The second one is that while the RDWT provides a solution to the translation invariance problem, it maintains the DWT´s attractive attributes, such as efficiency and suited for transients. Since each subband should preserves its energy when using the RDWT in a multipaths environment, summary features of its robust wavelet decomposition are the same as the unshifted version. By an adaptive model of the background interference, using recursive density estimation of the joint distribution of certain summary features of its robust wavelet decomposition, we may detect the transient in a multipaths and a background underwater sound environment.