% 
% For illustrative purposes this duplicates the MATLAB code on 
% pig 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; 

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

N  = 512; 
n  = 0:(N-1); 

% our desired signal d(n): 
% 
dn = (0.99.^n) .* sin( 0.1*n*pi + 0.2*pi );   
%dn = sin( 0.01*n*pi + 0.2*pi );   

% the random driving input noise ... used in creating the observed noises v_1(n) and v_2(n) 
% 
v  = 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) 

% get the noised signal to plot i.e. xn
% 
[yw,w,en,xn] = aawienernoisecancelor(dn,a1,a2,v,2,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( [0,256,-4.5,+4.5] ); 
legend( [hd,hdn], { 'd(n)', 'd(n)+v_1(n)' }, 'location', 'north' ); 
saveas( gcf, '../../WriteUp/Graphics/Chapter4/noise_cancelor_fig_1.eps', 'epsc' ); 

% compare our signal approxmation for various filter lengths: 
% 
mArray = [ 4,8,16 ]; a_hands = []; clrs = 'brgkcm'; 
for mi=1:length(mArray),
  thisM = mArray(mi); 
  [yw,w,en,xn] = aawienernoisecancelor(dn,a1,a2,v,mArray(mi),N);   
  %a_hands = [ a_hands, plot(n,en,['-',clrs( mod(mi-1,length(clrs))-1 ) ] );
  figure; plot( n, dn, '-og', 'markersize', 6 ); hold on; 
  plot( n, en, '-xk' ); 
  xlabel( 'n' ); ylabel( 'approximate signal' ); title( ['M=',num2str(thisM)] ); 
  %axis( [0,256,-Inf,+Inf] ); 
  axis( [0,256,-4.5,+4.5] ); 
  saveas( gcf, ['../../WriteUp/Graphics/Chapter4/noise_cancelor_M_',num2str(thisM),'.eps'], 'epsc' ); 
end