%%%%%%%%%  LMS_Newton  算法  《自適應濾波算法與實現》  98頁

clear all;
% the channel impulse response; 
Hn =[0.8783   -0.5806    0.6537   -0.3223    0.6577   -0.0582   0.2895   -0.2710    0.1278   -0.1508    0.0238   -0.1814   0.2519   -0.0396    0.0423   -0.0152    0.1664   -0.0245   0.1463   -0.0770    0.1304   -0.0148    0.0054   -0.0381    0.0374   -0.0329    0.0313   -0.0253    0.0552  -0.0369   0.0479   -0.0073    0.0305   -0.0138    0.0152   -0.0012  0.0154   -0.0092    0.0177   -0.0161    0.0070   -0.0042  0.0051   -0.0131    0.0059   -0.0041    0.0077   -0.0034   0.0074   -0.0014    0.0025   -0.0056    0.0028   -0.0005   0.0033   -0.0000    0.0022   -0.0032    0.0012   -0.0020   0.0017   -0.0022    0.0004   -0.0011      0          0   ];
Hn=Hn(1:64);
%讀入語音;  it is a column vector;
 r=wavread('C:\Matlab\work\Write_In_Paper\Shi_Yan.wav');
 r=r(1:10000);
% cut the former 5000 points;
% r=sin(2*pi*(1:3000)/40)';
r=r+0.2*randn(size(r));% r is the input noisy signal vector;
% the output signal vector;
output=conv(r,Hn);  N=length(r);
d=output;
k=length(Hn);   % k is the order of the fikter;
 % the filter coeffients vector;
error=zeros(N,1);  
DB_error=error;
delta=0.1;  alfa=0.03; mu=0.01;
I=eye(k,k);
inv_R=delta*I;
w=zeros(k,1);
   for i=k:N
       x=r(i:-1:i-k+1);
       e=d(i)-x'*w;
       inv_R=1/(1-alfa)*(inv_R-(inv_R*(x*x')*inv_R)/((1-alfa)/alfa+x'*multiply(inv_R,x)));
       w=w+2*mu*e*multiply(inv_R,x);
       error(i)=error(i)+e^2;
   end;
      figure;
      DB_error=10*log10(error);
      plot(DB_error,'r');   %%%% 本圖和下圖都是 LMS_Newton算法，只是參數不同
      
      
      
      error=zeros(N,1);
delta=0.01;  alfa=0.01; mu=0.009;
I=eye(k,k);
inv_R=delta*I;
w=zeros(k,1);
   for i=k:N
       x=r(i:-1:i-k+1);
       e=d(i)-x'*w;
       inv_R=1/(1-alfa)*(inv_R-(inv_R*(x*x')*inv_R)/((1-alfa)/alfa+x'*multiply(inv_R,x)));
       w=w+2*mu*e*multiply(inv_R,x);
       error(i)=error(i)+e^2;
   end;
      
      hold on;
      DB_error=10*log10(error);
      plot(DB_error,'y');
      
      
     %%%%%%%%%%%%%%  對比 LMS_Newton算法和基本LMS算法的收斂性
       %%%%%%   下圖是基本LMS算法
      mu=0.01;
      win=zeros(1,k)';  % the filter coeffients vector;
      error=zeros(1,N)';
      DB_error=error;
for i=k:N
    input=r(i:-1:i-k+1);  % intercept the input vector;
    e=output(i)-win'*input;
    win=win+mu*e*input;
    error(i)=error(i)+e^2;
end;
    hold on;
    DB_error=10*log10(error);
    plot(DB_error,'b');