Improved wavelet packet denoising algorithm using fuzzy threshold and correlation analysis for chaotic signals

The research of an effective denoising algorithm for the actual obtained signals with chaotic characteristics is of great interest to all fields of the subject. To show the true chaotic state and analyze the dynamic characteristics of the chaotic system more accurately, an improved denoising algorithm using wavelet packet is proposed in this paper. Wavelet packet decomposition has an optimal sub-band tree structure, which can be used for local analysis of chaotic signals. Based on the correlation function value differences of wavelet packet coefficients, the algorithm determines the optimal decomposition layer, while the optimal wavelet packet basis is obtained with logarithmic energy entropy as the cost function. Furthermore, on the one hand, it makes efforts to divide wavelet packet coefficients into approximate parts, fuzzy parts and detail parts. On the other, it carries out singular spectrum analysis, the fuzzy threshold and the correlation analysis for the select of these three different types of coefficients in order to retain the dynamic performance of chaotic signals in the greatest extent. To verify the effectiveness of the algorithm, the Lorenz chaotic model is employed to analyzed. Simulation results verify the practicability of the improved denoising algorithm, which can also be well applied to various chaotic signals denoising with different noise levels.