rls.m

solution for the Statistical modelling for digital signal processing by hayes

function [W,E] = rls(x,d,nord,lambda)

%RLS	Recursive Least Squares.

%--- 

%USAGE	[W,E] = rls(x,d,nord,lambda)

%

%           x    : input data to the adaptive filter.

%           d    : desired output

%           nord : number of filter coefficients

%           lambda : exponential forgetting factor

%

%     The output matrix W contains filter coefficients.

%        - The n'th row contains the filter coefficients at time n

%        - The m'th column contains the m'th filter coeff vs. time.

%        - The output vector E contains the error sequence versus time.

%

%  see also LMS and NLMS

%

%---------------------------------------------------------------

% copyright 1996, by M.H. Hayes.  For use with the book 

% "Statistical Digital Signal Processing and Modeling"

% (John Wiley & Sons, 1996).

%---------------------------------------------------------------



delta=0.001;

X=convm(x,nord);

[M,N] = size(X);

if nargin < 4,   lambda = 1.0;   end

P=eye(N)/delta;

W(1,:)=zeros(1,N);

for k=2:M-nord+1;

    z=P*X(k,:)';

    g=z/(lambda+X(k,:)*z);

    alpha=d(k)-X(k,:)*W(k-1,:).';

    W(k,:)=W(k-1,:)+alpha*g.';

    P=(P-g*z.')/lambda;

end;