% 
% 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.
% 
%-----

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

R_x = [ 1, 0.7; 0.7, 1 ]; 
p = [ 0.7, 0.5 ].'; 

[Q,Lambda] = eig(R_x); 

%lambda_max = max(diag(Lambda)); 
lambda_max = Lambda(2,2);

1/lambda_max

pxdp = (Q.') * p; 

% now plot the "convergence" or not of these weights
%
n = 0:25;

% these should converge: 
mu = 0.5; 
w1 = -pxdp(1) * (0.7071/0.3) * ( 1 - ( 1- 0.6 * mu ).^n ) + pxdp(2) * (0.7071/1.7) * ( 1 - ( 1- 3.4 * mu ).^n ) ; 
w2 =  pxdp(1) * (0.7071/0.3) * ( 1 - ( 1- 0.6 * mu ).^n ) + pxdp(2) * (0.7071/1.7) * ( 1 - ( 1- 3.4 * mu ).^n ) ; 

figure; 
hw1=plot( n, w1, '-go' ); hold on; 
hw2=plot( n, w2, '-gx' ); 

% these should NOT converge: 
mu = 0.7; 
w1 = -(0.7071/0.3) * ( 1 - ( 1- 0.6 * mu ).^n ) + (0.7071/1.7) * ( 1 - ( 1- 3.4 * mu ).^n ) ; 
w2 =  (0.7071/0.3) * ( 1 - ( 1- 0.6 * mu ).^n ) + (0.7071/1.7) * ( 1 - ( 1- 3.4 * mu ).^n ) ; 

hw3=plot( n(1:20), w1(1:20), '-ro' ); 
hw4=plot( n(1:20), w2(1:20), '-rx' ); 

grid on; xlabel('n index'); ylabel('filter weights w(n)'); 
axis( [1,n(end),-1.0,+1.0] ); 

saveas( gcf, '../../WriteUp/Graphics/Chapter6/prob_6_2_3', 'epsc' );