基于LMS自适应滤波器的MATLAB实现

基于LMS自适应滤波器的MATLAB实现

文档编号:JD141 字数:12133,页数:33

摘要
数字滤波器在数字信号处理中的应用广泛，是数字信号处理的重要基础。自适应滤波器可以不必事先给定信号及噪声的自相关函数,它可以利用前一时刻已获得的滤波器参数自动地调节现时刻的滤波器参数使得滤波器输出和未知的输入之间的均方误差最小化,从而它可以实现最优滤波。
自适应滤波器的算法有很多,有RLS（递归最小二乘法）和LMS（最小均方算法）等。自适应LMS算法是一种很有用且很简单的估计梯度的方法,在信号处理中得到广泛应用。
本文档主要研究了自适应滤波器的基本结构和原理，然后介绍了最小均方误差算法(LMS算法)，并完成了一种基于MATLAB平台的自适应LMS自适应滤波器的设计,同时实现了对信号进行初步的降噪处理。
通过仿真，我们实现了LMS自适应滤波算法，并从结果得知步长和滤波器的阶数是滤波器中很重要的两个参数，并通过修改它们证实了这一点，其中步长影响着收敛时间，而且阶数的大小也会大大地影响自适应滤波器的性能。
关键字：自适应滤波器 MATLAB LMS 仿真

The Realization of Adaptive Filter Based on LMS by Applying MATLAB
Abstract
Digital filter which is widely used is the important basement of the digital signal processing. Adaptive filter can adjust its coefficients automatically to minimize the mean-square error between its output and that of an unknown input, unnecessary to know the autocorrelation functions of signal and noise in advance, hence it can realize linearly optimum filtering.
Adaptive filter has many different algorithms such as RLS(Recursive Least Square) and LMS(Least Mean-Square) algorithms. Algorithm of adaptive LMS is a simple and very useful method which is used to estimate gradient. It has been widely applied in the signal processing areas.
This paper introduces the structure and the principle of the adaptive filter, and then introduces the LMS algorithm, at the same time, it has completed the design of adaptive LMS filter based on MATLAB platform and realized to decrease noise in signal processing.
Through the simulations, we realize the algorithm of adaptive LMS. Moreover, we can understand there exist two very important parameters, step-size and filter order M through the results. We also demonstrate that how the step-size affects the convergence rate toward the unknown system, and how the filter order M affects the performance of adaptive filter by changing these two parameters.
Keywords: Adaptive Filter MATLAB LMS Simulation

目    录
摘    要 I
Abstract   II
目    录   III
第一章绪论 1
1.1 滤波器概述   1
1.2数字滤波器   1
1.3 滤波器发展 1
1.4 小结   2
第二章 LMS自适应滤波器   3
2.1 自适应滤波器   3
2.2 自适应滤波器设计原理 3
2.3 自适应滤波器的结构及LMS算法   4
2.3.1 自适应滤波器结构 4
2.3.2 LMS算法   5
2.4 小结   11
第三章仿真软件 MATLAB 简介   12
3.1 MATLAB的概况    12
3.1.1 MATLAB产生的历史背景   12
3.1.2 MATLAB的语言特点 13
3.2 MATLAB仿真的基本流程 15
3.3 小结   16
第四章 LMS自适应滤波器的MATLAB实现   17
4.1 自适应滤波器出现的意义   17
4.2 自适应滤波器的实现    17
4.2.1 最速下降法的仿真   17
4.2.2 LMS算法的MATLAB仿真    18
4.2.2.1 基于LMS算法的自适应滤波器设计 18
4.2.2.2 对LMS算法参数的分析研究    20
4.3 小结    .23
第五章结论以及展望   24
参考文献   25

附录 26
致谢 28

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