% 
% For illustrative purposes this duplicates the MATLAB code on 
% epage 73 from the book but specified for the problem 4.3.2 on epage 
% 
% Written by:
% -- 
% John L. Weatherwax                2008-11-24
% 
% email: wax@alum.mit.edu
% 
% Please send comments and especially bug reports to the
% above email address.
% 
%-----

addpath( '../../AdaptiveFilteringCode/' ); 

clear functions; 
clear; 
%clc; 
close all; drawnow; 

M      = 2; 
N      = 200; 

sigmaV2 = 0.15;                          % <- the variance of the noise v(n)
v       = sqrt(sigmaV2)*randn(1,N);

x      = randn(1,N);                     % <- input data sequance x(n) (zero mean, variance one)

b      = [ 0.9, 0.25 ];                  % <- the unknown filter coeffients 
b      = [ 1, 0.38 ];

sysout = filter( b, 1, x ); 
dn     = sysout + v; 
rx     = aasamplebiasedautoc(x,M); 
Rx     = toeplitz(rx);                   % <- this should approximate the identity 
fprintf('Is Rx close to the identity matrix ... %d\n', norm( Rx-eye(M) ) < 1e-1 ); 
pdx    = xcorr(x,dn,'biased'); 
p      = pdx((N-(M-1)):N);    
p      = fliplr(p);                      % <- this should approximate [ b0, b1 ] 
fprintf('Is p close to the vector b ... %d\n', norm( p(1:2) - b ) < 1e-1 ); 
%w      = inv(Rx)*p.'; 
w      = Rx\p(:); 
fprintf('Is w close to the vector b ... %d\n', norm( w(1:2).' - b ) < 1e-1 ); 

dnc    = aasamplebiasedautoc(dn,1); 
jmin   = dnc - p*w; 

fprintf('\n'); 
fprintf( 'the original filter coefficients were = \n'); 
disp(b); 
fprintf('the optimal filter values found are w = \n'); 
disp(w.'); 
fprintf( 'the minumum J value is = \n'); 
disp(jmin);