METHOD OF DETERMINING THE OPTIMAL WAVELET BASIS FOR SPEECH SIGNAL PRO-CESSING - Lavrynenko, Oleksandr (Science-based technologies, 2025)
This paper considers a method for selecting the optimal wavelet function as the basis of wavelet transform. Existing approaches to the optimal selection of the mother wavelet function for processing speech signals are based on the criterion of the minimum entropy of wavelet coefficients, and have one major drawback, which is that entropy is characterized only by the probability distribution of the appearance of certain wavelet coefficients in the speech signal. This fact does not allow the existing approach to be considered optimal, since it does not take into account the accuracy of speech signal reconstruction by wavelet coefficients. Thus, the developed method for determining the optimal wavelet basis takes into account not only the absolute entropy index, but also its effect on the reconstruction of the speech signal, which will be based on finding the optimal value of the adaptive threshold filtering of the wavelet coefficients of the speech signal, where objective quantitative metrics, such as the root mean square error of the input and processed signals, as well as the energy of the wavelet coefficients before and after thresholding, will serve as a functional assessment of the signal reconstruction error. The proposed method shows an algorithm for analyzing wavelet spectra with different wavelet functions in order to evaluate their suitability for optimal processing of speech signals in the tasks of filtering, compression, coding, synthesis and speech recognition. As a result, it is shown that in the task of processing speech signals using wavelet analysis, the Meyer wavelet is the most optimal. The paper presents the developed optimality criterion for selecting the generating wavelet function as the basis of the wavelet transform. The criterion is based on the determination of the local energy density of the frequency distribution of the wavelet spectrum of the speech signal and on the possibility to reconstruct the signal using the inverse wavelet transform with the smallest error. The study showed that the efficiency of the developed method increased by 20.5 % or 1.4 times, in contrast to the existing method based on the minimum entropy criterion is 52.1 %, and amounted to 72.6 %.