一个二阶FIR的LMS自适应滤波器消除正弦干扰我要分享

A second order FIR LMS adaptive filter for sinusoidal interference cancellation

阶次图 陷波滤波器 陷波-抑制 陷波法 噪音抑制

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代码分类: 智能算法

开发平台: matlab

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代码描述

中文说明:

传统的宽带信号中抑制正弦干扰的方法是采用陷波器(notch filter),为此需要精确知道干扰正弦的频率.然而当干扰正弦频率是缓慢变化时,且选频率特性要求十分尖锐时,则最好采用自适应噪声抵消的方法.下图是用一个二阶FIR的LMS自适应滤波器消除正弦干扰的一个方案。该代码实现了以下功能:

1) 借助MATLAB画出了滤波器的误差性能曲面和误差性能曲面的等值曲线;

2) 给出了最陡下降法以及LMS算法的计算公式;

3) 用MATLAB产生了方差为0.05, 均值为0白噪音S(n),并画出某次采样得到的波形;

4) 根据 2)中的公式,并利用 3)中产生的S(n),在 1)中的误差性能曲面的等值曲线上叠加画出了采用最陡下降法以及LMS法时H(n)的在叠代过程中的轨迹曲线;

5)用MATLAB计算并画出了LMS法时误差随时间n的变化曲线(对应S(n)的某一次的一次实现)和e(n)波形;

6)在 1)中的误差性能曲面的等值曲线上,叠加画出采用LMS法得到的100次实验中的H(n)的平均值的轨迹曲线;

7)最终对结果进行了分析,具体见压缩包的word文档。


English Description:

The traditional method to suppress sinusoidal interference in wideband signal is to use notch filter, so it is necessary to know the frequency of interference sinusoid accurately. However, when the frequency of interference sinusoid changes slowly and the frequency selection characteristic is very sharp, it is better to use adaptive noise cancellation method. The figure below is a scheme to eliminate sinusoidal interference with a second-order fir LMS adaptive filter. The code realizes the following functions:
1) With the help of MATLAB, the error performance surface of the filter and the equivalent curve of the error performance surface are drawn;
2) The calculation formulas of steepest descent method and LMS algorithm are given;
3) The white noise s (n) with variance of 0.05 and mean value of 0 is generated by MATLAB, and the waveform of a certain sampling is drawn;
4) According to the formula in 2) and using the S (n) generated in 3), the trajectory curve of H (n) in the iterative process is drawn by superposition on the equivalent curve of the error performance surface in 1) using the steepest descent method and LMS method;
5) Matlab is used to calculate and draw the curve of LMS error with time n (corresponding to a realization of S (n)) and E (n) waveform;
6) On the equivalent curve of error performance surface in 1), the trajectory curve of average value of H (n) in 100 experiments obtained by LMS method is superimposed and drawn;
7) Finally, the results are analyzed. See the word document of the compressed package for details.


代码预览

DSPII_USTC_实验一

.................\DSP.doc

.................\DSP.m