语音信号 lms算法原理和代码编写

1 关键词

2 代码  http://blog.csdn.net/future_fighter/archive/2008/04/27/2334181.aspx

3 代码  http://hi.baidu.com/haixinguan/blog/item/202636d1fea20ed6562c8430.html

4 代码 http://bbs.matwav.com/viewthread.php?tid=832092

5 符号http://love4ningning.spaces.live.com/Blog/cns!1pof7_u11lF7-54HJZno4f-Q!306.entry

特殊符号表

'   (在这里,表示倒置)      ^2 表示乘方                    ∂  如何输入偏微分符号

× · 查阅 http://baike.baidu.com/view/428845.htm

构成自适应数字滤波器的基本部件是自适应线性组合器，如图 8-1 的所示。设线性组合
的 M 个输入为 x(k-1),……x(k-M) 其输出 y(k)  是这些输入加权后的线性组合，即:

              m    

y(k)=∑x(k-i)*wi

         i=1

定义权向量:

W=[w1 ,w2 ,w3,w4,….wm]';                     m×1向量

X(k) =[x(k-1),x(k-2),x(k-3),…..x(k-m)]'   ;  m×1向量

令d(k)为所希望的相应,则定义了误差信号

                        ε(k)=d(k)-y(k)

                          =d(k)-W' *X(k) 

ε(k) ^2= d(k)^2-2d(k)*X(k)'*W +W'X(k)X(k)'W

E{ε(k) ^2} = E{d(k)^2}-2E{d(k)X(k)'}W+W'E{X(k)X(k)'}W

定义了互相关函数向量

                         RXd   RXd=E{d(k)·X(k)'} 

定义自相关函数矩阵                    

                     RXX      RXX =E{X(k)·X(k)'}

关于这个问题

                                                                                                                            >> w=[1 2 3 4 5 6 7 8 9]

                                                                                                        w = 

                                                                                                                 1     2     3     4     5     6     7     8     9

                                                                                                     >> mean(w)

                                                                                                         ans =

                                                                                                                       5

                                                                                                     >> mean(w*w')

                                                                                                          ans =

                                                                                                                        285

                                                                                                      >>

E{ε(k) ^2}=E{d(k)^2}-2RXd'·W+W'·RXX·W

显然,E{ε(k) ^2}=F(W ),而且是一个关于W 的二次函数

对W 求导数:

▽ (k)=▽ E{ε(k) ^2}=[ ∂E{ε(k) ^2} /∂w1 ,     ∂E{ε(k) ^2} /∂w2 ,..... ,  ∂E{ε(k) ^2} /∂ wm ]