% A test script for ao/noisegen2D
% 
% DESCRIPTION: Run noisegen2D with mdc2 models and test procedure accuracy
% 
% L. Ferraioli 04-02-2009
% 
% $Id: test_ao_noisegen2D_mdc2.m,v 1.1 2009/04/20 14:31:43 luigi Exp $
% 

%% General use variables and vectors

f = logspace(-6,log10(5),300);
f = f.';
fs = 10;
Nsecs = 1e5; % number of seconds
Nfft = 1e5; % number of samples for the fft
pls  = plist('Nfft', Nfft,'Order',0); % plist for spectra

%% MDC2 Models

b = ao(plist('built-in','mdc2r2_fd_ltpnoise','f',f,'fs',fs));
CSD = [b(1) b(2);conj(b(2)) b(3)];

%% Make white noise

a1 = ao(plist('tsfcn', 'randn(size(t))', 'fs', fs, 'nsecs', Nsecs));
a2 = ao(plist('tsfcn', 'randn(size(t))', 'fs', fs, 'nsecs', Nsecs));
a1.setYunits('m');
a2.setYunits('m');
a = [a1 a2];

% axx = a.cpsd(pls);

%% 
iplot(a)

%% some ploting

iplot(axx)

iplot(CSD(1,1),CSD(1,2),CSD(2,1),CSD(2,2))

%% Noise generation

pl = plist(...
    'csd11', CSD(1,1), ...
    'csd12', CSD(1,2), ...
    'csd21', CSD(2,1), ...
    'csd22', CSD(2,2), ...
    'MaxIter', 80, ...
    'PoleType', 2, ...
    'MinOrder', 30, ...
    'MaxOrder', 40, ...
    'Weights', 2, ...
    'Plot', false,...
    'FITTOL', 1e-5,...
    'MSEVARTOL', 1e-2,...
    'UseSym', 0,...
    'Disp', false);

ac = noisegen2D(a, pl);

%% Checking results and starting data

% iplot(a)
iplot(ac)

%% Making cross-spectrum

acxx1 = ac(1).psd(pls);
acxx2 = ac(2).psd(pls);
acxx12 = cpsd(ac(1),ac(2),pls);
acch = ac.cohere(pls);

%% Plotting spectra

% iplot(acxx);

iplot(abs(acxx1),abs(CSD(1,1))) % model data need to be multiplied by 2 because acxx is the onesided cpsd
iplot(abs(acxx12),abs(CSD(1,2)))
iplot(abs(acxx2),abs(CSD(2,2)))

iplot(abs(acxx1),abs(acxx12),abs(acxx2))

%% Plotting coherence

iplot(acch,(abs(CSD(1,2)).^2)./(CSD(1,1).*CSD(2,2)))

%%

m1=mean(acxx(2,2).data.y(end-10,end)) % calculate average on the tail of channel 2
m2=mean(CSD(2,2).data.y(end-5,end))% calculate average on the tail of channel 2
m1/m2 % verify that the ratio is near 1

%% 
% ************************************************************************
% Some more analysis for testing the accuracy of noise generation procedure
% ************************************************************************

%% Extracting filters from data

Filt11 = find(ac(1).procinfo,'Filt11');
Filt12 = find(ac(1).procinfo,'Filt12');
Filt21 = find(ac(2).procinfo,'Filt21');
Filt22 = find(ac(2).procinfo,'Filt22');

%% Calculating filters responses

tr11 = resp(Filt11,plist('f',f));
rFilt11 = tr11(1);
for ii = 2:numel(tr11)
  rFilt11 = rFilt11 + tr11(ii);
end
rFilt11.setName('rFilt11', 'internal');

tr12 = resp(Filt12,plist('f',f));
rFilt12 = tr12(1);
for ii = 2:numel(tr12)
  rFilt12 = rFilt12 + tr12(ii);
end
rFilt12.setName('rFilt12', 'internal');

tr21 = resp(Filt21,plist('f',f));
rFilt21 = tr21(1);
for ii = 2:numel(tr21)
  rFilt21 = rFilt21 + tr21(ii);
end
rFilt21.setName('rFilt21', 'internal');

tr22 = resp(Filt22,plist('f',f));
rFilt22 = tr22(1);
for ii = 2:numel(tr22)
  rFilt22 = rFilt22 + tr22(ii);
end
rFilt22.setName('rFilt22', 'internal');

%% Obtaining transfer functions

% calculating transfer functions from data
pl  = plist('Nfft', Nt);
etf11 = tfe(a(1),ac(1),pl);
etf12 = tfe(a(2),ac(1),pl);
etf21 = tfe(a(1),ac(2),pl);
etf22 = tfe(a(2),ac(2),pl);

%% Comparing Filters Responses with estimated TFs (e-TFs)

% Comparing filters responses and calculated TFs
pl = plist('Legends', {'Filter Response','e-TF'});
iplot(rFilt11,etf11,pl)
iplot(rFilt12,etf12,pl)
iplot(rFilt21,etf21,pl)
iplot(rFilt22,etf22,pl)

%% Filtering data separately

% This operation is performed internally to the noisegen2D. Output data are
% then obtained by b1 = b11 + b12 and b2 = b21 + b22
b11 = filter(a1,plist('filter',Filt11,'bank','parallel'));
b12 = filter(a2,plist('filter',Filt12,'bank','parallel'));
b21 = filter(a1,plist('filter',Filt21,'bank','parallel'));
b22 = filter(a2,plist('filter',Filt22,'bank','parallel'));

%% Extracting transfer functions from separately filtered data se-TFs

etf11 = tfe(a1,b11,pls);
etf12 = tfe(a2,b12,pls);
etf21 = tfe(a1,b21,pls);
etf22 = tfe(a2,b22,pls);

%% Comparing separately-estimated TFs (se-TFs) with filter responses

pl = plist('Legends', {'Filter Response','se-TF'});
iplot(rFilt11,etf11,pl)
iplot(rFilt12,etf12,pl)
iplot(rFilt21,etf21,pl)
iplot(rFilt22,etf22,pl)

%% Comparing filters with TFs obtained by eigendecomposition

% This function output transfer functions as they are obtained by the
% eigendecomposition process. i.e. before the fitting process

icsd11 = CSD(1,1).data.y*fs/2;
icsd12 = CSD(1,2).data.y*fs/2;
icsd21 = CSD(2,1).data.y*fs/2;
icsd22 = CSD(2,2).data.y*fs/2;

[tf11,tf12,tf21,tf22] = utils.math.eigcsd(icsd11,icsd12,icsd21,icsd22,'USESYM',0,'DIG',50,'OTP','TF');

% Making AOs
eigtf11 = ao(fsdata(f,tf11,fs));
eigtf12 = ao(fsdata(f,tf12,fs));
eigtf21 = ao(fsdata(f,tf21,fs));
eigtf22 = ao(fsdata(f,tf22,fs));

%% Comparing eig-TFs with output filters

% Compare TFs before and after the fitting process

pl = plist('Legends', {'eig-TF','Filter Response'});
iplot(eigtf11,rFilt11,pl)
iplot(eigtf12,rFilt12,pl)
iplot(eigtf21,rFilt21,pl)
iplot(eigtf22,rFilt22,pl)

%% Phase difference between eig-TFs and output filters

% checking that phase differences between TFs are preserved by the fitting
% process
eigph1 = unwrap(angle(eigtf11)-angle(eigtf21));
eigph1.setYunits('rad')
filtph1 = unwrap(angle(rFilt11)-angle(rFilt21));
filtph1.setYunits('rad')
eigph2 = unwrap(angle(eigtf22)-angle(eigtf12));
eigph2.setYunits('rad')
filtph2 = unwrap(angle(rFilt22)-angle(rFilt12));
filtph2.setYunits('rad')

pl = plist('Legends',{'eig-TF','Filter'},'YScales',{'All','lin'});
iplot(eigph1+2*pi,filtph1,pl)
iplot(eigph2,filtph2,pl)


%% Comparing eig-TFs with se-TFs

% Compare eigendecomposition results with separately estimated TFs (se-TFs)
pl = plist('Legends', {'eig-TF','se-TF'});
iplot(eigtf11,etf11(1,2),pl)
iplot(eigtf12,etf12(1,2),pl)
iplot(eigtf21,etf21(1,2),pl)
iplot(eigtf22,etf22(1,2),pl)

%% Phase difference between eig-TFs and se-TFs

% checking that phase differences between TFs are preserved by the fitting
% process also for the filtered data (se-TFs)
eigph1 = unwrap(angle(eigtf11)-angle(eigtf21));
filtph1 = unwrap(angle(etf11(1,2))-angle(etf21(1,2)));
eigph2 = unwrap(angle(eigtf22)-angle(eigtf12));
filtph2 = unwrap(angle(etf22(1,2))-angle(etf12(1,2)));

pl = plist('Legends',{'eig-TF \Delta\phi','se-TF \Delta\phi'},'YScales',{'All','lin'});
iplot(eigph1,filtph1,pl)
iplot(eigph2,filtph2,pl)

% END