% 
% For illustrative purposes this duplicates the MATLAB code on 
% page XXX from the book but specified for the problem 4.4.2 on epage XXX
% 
% 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; 

randn('seed',0); rand('seed',0); 

N  = 2^10;
n  = 0:(N-1); 

% our desired signal d(n): 
% 
dn = (0.99.^n) .* sin( 0.1*n*pi + 0.2*pi );   
%dn = sin( 0.1*n*pi + 0.2*pi );   

% the random driving input noise ... used in creating the observed noises v_1(n) and v_2(n) 
% 
v  = 0.1*randn(1,N);                              
                                              
% the coefficients of the ARMA(1,1) models for v_1(n) and v_2(n)  
% 
a1 =  0.8;
a2 = -0.95;

% plot the pure signal d(n) with the noised signal d(n) + v_1(n)
% 
fo=figure; 
hd=plot( n, dn, '-og', 'markersize', 6 ); hold on;    % <- the pure signal d(n) 

M=2; 

% get the observed noised signal to plot i.e. xn
% 
alpha_dum = 0.0; 
[yw,w,en,xn] = aaWNC_with_leaking_signal(dn,alpha_dum,a1,a2,v,M,N);
hdn=plot( n, xn, '-xr' ); 
xlabel( 'n' ); ylabel( 'measured signal' ); title( 'the pure signal and the signal with noise' );
%axis( [0,256,-Inf,+Inf] ); 
axis tight; 
legend( [hd,hdn], { 'd(n)', 'd(n)+v_1(n)' }, 'location', 'north' ); 
saveas( gcf, '../../WriteUp/Graphics/Chapter4/prob_4_4_2_NC_fig_1.eps', 'epsc' ); 

%M = 16; 
M = 64; 

% compare our signal approxmation for various amounts of signal leakage:
% 
alphaArray = [ 0.05, 0.1, 0.3, 0.6, 1.0 ]; alphas_to_save = [ 0.05, 0.3, 1.0 ]; 
for mi=1:length(alphaArray),
  thisALPHA = alphaArray(mi); 
  [yw,w,en,xn] = aaWNC_with_leaking_signal(dn,thisALPHA,a1,a2,v,M,N);   
  figure; plot( n, dn, '-og', 'markersize', 6 ); hold on; %(fh); 
  plot( n, en, '-xk' ); 
  xlabel( 'n' ); ylabel( 'approximate signal' ); title( ['alpha=',num2str(thisALPHA)] ); 
  %axis( [0,256,-Inf,+Inf] ); 
  axis tight; 
  if( ismember( thisALPHA, alphas_to_save ) )
    saveas( gcf, ['../../WriteUp/Graphics/Chapter4/prob_4_4_2_NC_a_',num2str(thisALPHA),'.eps'], 'epsc' ); 
  end
end