%
% Written by:
% -- 
% John L. Weatherwax                2009-04-21
% 
% email: wax@alum.mit.edu
% 
% Please send comments and especially bug reports to the
% above email address.
% 
%-----

kRange = 0:10; 
r_k = ( (0.9).^(abs(kRange)) ) .* cos( pi * kRange / 4 ); % everything but the k=0 delta component 
r_k(1) = r_k(1) + 1.0 % add back in the delta 

R_x = [ r_k(1), r_k(2) ; r_k(2), r_k(1) ]; 

% for various lookaheads c compute the first-order FIR Wiener predictor 
all_errors = [];
for c = 1:6
  fprintf('c= %d\n', c); 
  right_hand_side = [ r_k(c+1); r_k(c+2) ]
  w = R_x \ right_hand_side 
  xhi = r_k(1) - right_hand_side' * w;
  fprintf('chi= %10.6f\n',xhi);
  all_errors = [ all_errors, xhi ];
end

plot( all_errors, '-o' );