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  1. x[n]=d^[n]=e[n]+s^[n]*y[n]
  2. y[n]=w[n]*x[n]
  3. x'[n]=s^[n]*x[n]
  4. w[n+1]=w[n]+u.e[n].x'[n]
  5. e[n]=d[n]-y'[n]
  6.    
  7. %%%%%%%%%% Initalize Wz %%%%%%%%%%
  8.     Wz = zeros(M,1);          % adaptive filter weigths; coloumn array
  9.  
  10.     %%%%%%%%%% Initalize step size mu %%%%%%%%%%
  11.     % Initialize "mu"
  12.  
  13.     %%%%%%%%%% Initialize input %%%%%%%%%%
  14.     % Initialize input "x[n]" of length"N"
  15.  
  16.     %%%%%%%%%% Generate desired response %%%%%%%%%%
  17.     % Generate the desired response d[n]
  18.  
  19.     %%%%%%%%%% Generate x'[n] %%%%%%%%%%
  20.     x_prime = conv(Szh,x);           % x'[n] = x[n]*s^[n]
  21.  
  22.     % Make sure that x and d are coloumn arrays
  23.     x = x(:);
  24.     d = d(:);
  25.  
  26.     %%%%%%%%%% FBFXLMS algorithm %%%%%%%%%%
  27.     for n=M:N
  28.         x_reverse = x(n:-1:n-M+1);        % input in reverse order
  29.         x_prime_reverse = x_prime(n:-1:n-M+1);      % x'[n] in reverse order    
  30.         y = Wz'*x_reverse;                % y[n] = w[n]*x[n];
  31.         y_prime = conv(Sz,y);             % y'[n] = y[n]*s[n]
  32.         e(n) = d(n)-y_prime(n);           % update error: e[n]=d[n]-y'[n]
  33.         Wz = Wz+mu*x_prime_reverse*(e(n));         % update weigths
  34.     end
  35.  
  36.     %%%%%%%%%% generate y''[n] %%%%%%%%%%
  37.     y_second = conv(Szh,y);      % y'[n] = y[n]*s[n]
  38.  
  39.     %%%%%%%%%% generate x[n] %%%%%%%%%%
  40.     x = e + y_second;            % x[n] = d^[n] = e[n]+y''[n]
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