Application of Harmonic Wavelets to Processing Oscillating Hydroacoustic Signals

Abstract

The paper is devoted to the application of specific functions called harmonic wavelets, which are aimed at processing a wide range of oscillating hydroacoustic signals including multiharmonic and transient signals. We provide basics of the harmonic wavelet transform and a two-stage algorithm for computing wavelet coefficients based on the discrete Fourier transform. We introduce a special efficiency factor of applying these wavelets to oscillating hydroacoustic signals. Application of harmonic wavelets is efficient for processing oscillating hydroacoustic signals since harmonic wavelets have similarities with these types of signals. In many cases the best basis is the basis that has high correlation with the investigated signals since signal representation in such a basis will require a small number of components. We devote special attention to a very important practical task - denoising of oscillating signals using special statistical criteria and wavelet-based thresholding.