基于多尺度小波变换的变步长LMS滤波算法

摘要

对LMS自适应算法、基于抽样函数的变步长LMS算法和基于多尺度小波变换的自适应滤波算法进行了研究,在此基础上把变步长LMS算法与多尺度小波变换相结合,产生了新算法.该算法一方面可以克服固定步长LMS算法在收敛速度与收敛精度方面与步长因子的矛盾；另一方面,小波变换的引入减少了输入向量自相关矩阵的条件数,提高了收敛速度、跟踪性能和稳定性.最后对算法的性能进行了计算机仿真比较,仿真结果表明:基于多尺度小波变换的变步长LMS滤波算法具有较快的收敛速度和更强的抑噪能力.%The paper represents a new algorithm from the mergence of the variable step size LMS algorithm and the multi-scale wavelet transform on the basis of studies of LMS algorithm, variable step size LMS algorithm based on sample function ,and LMS adaptive filtering algorithm based on multi-scale wavelet transform. On one hand,this new algorithm can overcome the contradiction between the fixed step size LMS algorithm' s speed and accuracy of convergence and its step factors. On the other hand, the introduction of wavelet reduce the conditions of auto-correlation matrix of the input vector, and improve the speed, tracking performance and stability of contradication. Finally, the algorithm is compared by computer simulation, the simulation results show that a adaptive LMS algorithm with variable step based on multi-scale wavelet transform has faster convergence speed, better performance, and stronger robustness against noise and disturbance.