The Analysis And Application Of Adaptive Filtering Algorithm Based On Wavelet Transform

To systematize the theory of adaptive filtering technique based on wavelet transform, the algorithm of this technique has been researched deeply and systematically by this dissertation. Its theory has been analyzed, its algorithm has been classified, and the advanced algorithm has been derived and verified. Furthermore the application of adaptive filtering algorithm based on wavelet transform in the nonlinear system identification has become a new way to identify the nonlinear system successfully.Firstly, after the deep research on adaptive filtering algorithm, wavelet decomposition and other relative theories, the characteristics and advantages of adaptive filtering algorithm based on wavelet transform is summarized. Algorithm structure and application mode are proposed as two innovative ways to classify this technique. Meanwhile, working principle and suitable application areas are illustrate. Secondly, the D-LMS (Decomposition Least Mean Square) algorithm, which is more advanced than other filtering algorithm, is developed. According to the theory of Sigmoid function, a novel changed-step D-LMS algorithm is deduced from the advanced D-LMS algorithm. At last, this research builds some simulation models, and by the MATLAB software, the nonlinear system identification results of both algorithms are obtained. The experimental results show that both adaptive filtering algorithms based on wavelet transform can identify nonlinear systems well. They can also meet the demands of high convergence rate, fast tracking speed, and low steady misadjustment noise after convergence. Moreover, more accurate data can be obtained by the changed-step D-LMS algorithm. Therefore it fits for these systems required exactness, such as ultra-precision manipulator, high-precision magnetically suspended table, ultra-precision turning, and so on.