durbin.m

统计自适应信号处理的matlab程序

function [a,k,Po]=durbin(r,M)
%
% Programmed by: Dimitris Manolakis, 1998
%
%-----------------------------------------------------------
% Copyright 2000, by Dimitris G. Manolakis, Vinay K. Ingle,
% and Stephen M. Kogon.  For use with the book
% "Statistical and Adaptive Signal Processing"
% McGraw-Hill Higher Education.
%-----------------------------------------------------------

% Input: r(m), 0<=m<=M
% Output:
a=zeros(M+1,1);  % Prediction error filter
k=zeros(M,1);    % Lattice parameters
Po=zeros(M+1,1); % LP MMSE for 0<=m<=M

% Initialization
P=r(1);
Po(1)=P;
beta=r(2);
k(1)=-beta/P;
a(1)=k(1);
P=P+beta*k(1);
Po(2)=P;

% Recursion
for m=2:M
  beta=(r(2:m))'*flipud(a(1:m-1))+r(m+1); % eq. ()
  k(m)=-beta/P;                           % eq. ()
  a(1:m)=[(a(1:m-1))' 0]'...
     +[(flipud(a(1:m-1)))' 1]'*k(m);      % eq. ()
  P=P+beta*k(m);                          % eq. ()
  Po(m+1)=P;
end

a(2:M+1)=a(1:M);
a(1)=1;