Study And Implement On LMS Adaptive Filtering Algorithm Based On Multi-scale Wavelet Transform

Adaptive filtering algorithm is one of the most active research in modern signal processing field. Least Mean Square (LMS) algorithm is used widely in adaptive filter. Although classical LMS algorithm has simple complexity and is easy to be implemented, its convergence speed is very slow. In order to speedup the convergence process, one can increase the step size, but at the same time, the steady state error will be large and the algorithm may even become unstable. Fixed step size cannot result in fast convergence speed and low residual error simultaneously. In order to solve this problem, people present a lot of modified LMS algorithms. There are two famous research direction of algorithms that are summarized, one is variable step size LMS algorithm, the other one is transform-domain LMS algorithm. The method that a wavelet is introduced into the adaptive filtering has a prosperous future in the adaptive filtering of time-varying and rapid changing signal because the wavelet has the good capacity to decrease the correlation property of the input vector, and possesses the characteristics of multi-resolution and time-frequency localization. The main achievement in this thesis can be summarized as follows:1. Expatiate adaptive filtering technology and the basic principle of LMS algorithm, discuss the convergence range of step size factor in LMS algorithm, analyze the merits and demerits of LMS adaptive filtering algorithms, and present two variable step sizeLMS algorithm--VSS and MVSS algorithms, theoretical analysis and computersimulation demonstrate their performance.2. Analysis the characteristics of time-frequency localization of wavelet transform, expatiate Mallat fast algorithm and multiple-resolution analysis, discuss multi-scale wavelet decomposition and reconstruction.3. The multiple-scale wavelet transform theory is introduced into the LMS adaptive filtering algorithm. The linear filter is represented by a set of orthogonal wavelets. The paper analysis the principle and convergence speed and conditions of the LMS adaptive filtering algorithm based on multiple-scale wavelet transform. Theoretical analysis and simulations show that the MSWT-LMS algorithm converges faster than the classical LMS adaptive filtering. The spectrum dynamic range of auto-correlation matrix of the input vector is decreased so that the convergence speed of the LMS algorithm is improved.4. The variable step size LMS algorithm and the multiple-scale wavelet transform are merged into the adaptive filtering system. A novel method is proposed in this paper, that is, a LMS adaptive filtering algorithm with modified variable step size based on multiple-scale wavelet transform (MSWT-MVSS-LMS). The novel algorithm can decrease the conditions of auto-correlation matrix of the input vector, as well as resolve the contradiction that fixed step size cannot result in fast convergence speed and low residual error simultaneously. Experimental results demonstrate that the new algorithm has not only better convergence property but also better stable mean square errors than the former algorithms.5. The novel algorithm is applied to speech signal noise cancellation system. Experimental results demonstrate that the MSWT-MVSS-LMS algorithm can overcome the deficiency of classical speech signal adaptive noise cancellation system that has a slow convergence speed and a large maladjustment and the large spectrum dynamic range of auto-correlation matrix of the input vector.