Optimal mother wavelet selection for a stochastic resynthesis of the sound textures

Continuous wavelet transform is a powerful and versatile tool for signal analysis, outperforming short-time Fourier transform in the task of non-stationary, transient signals analysis. However, the method’s performance is heavily influenced by the choice of a mother wavelet function, which is most often made by the experience-supported intuition, followed by the trial-and-error procedure. Numerous attempts to optimize the problem are not universal by any means, as its solution is determined by a particular application, acquired data, and other system requirements. One very specific example is wavelet-based statistical analysis, performed for the needs of the stochastic resynthesis of sound textures, which requires minimal decomposition and precise time localization of the individual acoustic events, components of a complex texture. This work presents the automated mother wavelet function optimization system, which performs the optimal selection based on the reference audio signal. The algorithm iterates through a wide set of commonly used functions and compares the wavelet packet decomposition trees in search of the single node, containing the most information possible, with the use of the entropy-based criterion. After performing the procedure, reference signal is resynthesized with coefficients of the selected wavelet function and then calculation of normalized root mean square error serves as a verification of the results. Conclusions contain both the advantages and the limitations of the proposed solution together with the possible improvements and the directions of future research.