Mercurial > hg > ltpda

view m-toolbox/test/utils/test_ndeigcsd.m @ 0:f0afece42f48

Find changesets by keywords (author, files, the commit message), revision number or hash, or revset expression.
Import.
author Daniele Nicolodi <nicolodi@science.unitn.it>
date Wed, 23 Nov 2011 19:22:13 +0100
parents
children
line wrap: on
line source

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% TEST ndeigcsd
% 
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% HISTORY:     23-04-2009 L Ferraioli
%                 Creation
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%



%% 2 Dim Test

%%% Define startinf TFs

fs = 10;
f = [logspace(-6,log10(fs/2),2000)]';

% Model Stefano TF11
dRes11 = [2.44554138162509e-011 - 1.79482547894083e-011i;
2.44554138162509e-011 + 1.79482547894083e-011i;
2.66402334803101e-009 +  1.1025122049153e-009i;
2.66402334803101e-009 -  1.1025122049153e-009i;
-7.3560293387644e-009;
-1.82811618589835e-009 - 1.21803627800855e-009i;
-1.82811618589835e-009 + 1.21803627800855e-009i;
1.16258677367555e-009;
1.65216557639319e-016;                         
-1.78092396888606e-016;
-2.80420398962379e-017;
9.21305973049041e-013 - 8.24686706827269e-014i;
9.21305973049041e-013 + 8.24686706827269e-014i;
5.10730060739905e-010 - 3.76571756625722e-011i;
5.10730060739905e-010 + 3.76571756625722e-011i;
3.45893698149735e-009;
3.98139182134446e-014 - 8.25503935419059e-014i;
3.98139182134446e-014 + 8.25503935419059e-014i;
-1.40595719147164e-011];

dPoles11 = [0.843464045655194 - 0.0959986292915475i;
0.843464045655194 + 0.0959986292915475i;
0.953187595424927 - 0.0190043625473383i;
0.953187595424927 + 0.0190043625473383i;
0.967176277937188;
0.995012027005247 - 0.00268322602801729i;
0.995012027005247 + 0.00268322602801729i;
0.996564761885673;
0.999999366165445;
0.999981722418555;
0.999921882627659;
0.999624431675213 - 0.000813407848742761i;
0.999624431675213 + 0.000813407848742761i;
0.997312006278751 - 0.00265611346834941i;
0.997312006278751 + 0.00265611346834941i;
0.990516544257531;
0.477796923118318 - 0.311064085401834i;
0.477796923118318 + 0.311064085401834i;
0];

dDTerms11 = 0;

% Model Stefano TF12
dRes12 = [1.44258422208796e-017 + 7.07359428613009e-019i;
1.44258422208796e-017 - 7.07359428613009e-019i;
-3.4918408053655e-021 - 1.05662874569329e-021i;
-3.4918408053655e-021 + 1.05662874569329e-021i;
-7.61773292876976e-021;
4.84357724603939e-020 + 2.38824204294595e-019i;
4.84357724603939e-020 - 2.38824204294595e-019i;
-4.07088520945753e-020 - 2.31474543846105e-019i;
-4.07088520945753e-020 + 2.31474543846105e-019i;
8.73316588658882e-023;
-5.21840635377469e-020;
1.8461911504859e-023;                         
5.20105247464461e-020;
-4.68960092394415e-022;
-1.44261407664171e-017 +  6.8922564526833e-019i;
-1.44261407664171e-017 -  6.8922564526833e-019i;
3.13688133935426e-022];

dPoles12 = [0.477546340377332 -     0.310830571032376i;
          0.477546340377332 +     0.310830571032376i;
           0.99790715414307 -    0.0028490561287024i;
           0.99790715414307 +    0.0028490561287024i;
          0.998014205354671                         ;
          0.999585354543332 -  0.000780408757425194i;
          0.999585354543332 +  0.000780408757425194i;
           0.99966003029931 -  0.000830944038363768i;
           0.99966003029931 +  0.000830944038363768i;
          0.999962770401331                         ;
          0.999981881865521                         ;
          0.999999365763457                         ;
          0.999981706320212                         ;
           0.99992421574188                         ;
          0.477898460791003 +     0.311001926610074i;
          0.477898460791003 -     0.311001926610074i;
                          0];
dDTerms12 = 0;

% Model Stefano Tf21
dRes21 = [-1.80035241582968e-016 + 1.99543917791863e-015i;
     -1.80035241582968e-016 - 1.99543917791863e-015i;
     -1.85590889333759e-013 - 1.23844418827409e-014i;
     -1.85590889333759e-013 + 1.23844418827409e-014i;
      5.03656596876842e-013                         ;
     -2.62470963499904e-013 + 2.30024232938878e-012i;
     -2.62470963499904e-013 - 2.30024232938878e-012i;
     -9.83780507870955e-018                         ;
      3.40426735130194e-021                         ;
      9.78322351492755e-018                         ;
     -1.65010934542937e-020                         ;
      2.60918565203438e-015 +  1.0546609464659e-015i;
      2.60918565203438e-015 -  1.0546609464659e-015i;
      3.18105585405455e-014 + 2.48839990780042e-013i;
      3.18105585405455e-014 - 2.48839990780042e-013i;
      3.23021641947666e-013                         ;
      4.81265000078114e-016 - 3.18269170053848e-017i;
      4.81265000078114e-016 + 3.18269170053848e-017i;
      5.16260024128201e-018];

dPoles21 = [0.872004077421604 -     0.110344282822693i;
          0.872004077421604 +     0.110344282822693i;
          0.956884129232757 -    0.0225532091775074i;
          0.956884129232757 +    0.0225532091775074i;
          0.966514825697177                         ;
          0.995140550419744 -  0.000755127639524413i;
          0.995140550419744 +  0.000755127639524413i;
          0.999981802194393                         ;
           0.99999936576546                         ;
          0.999981722418555                         ;
          0.999921882627659                         ;
          0.999624431675213 +  0.000813407848742761i;
          0.999624431675213 -  0.000813407848742761i;
          0.997312006278751 +   0.00265611346834941i;
          0.997312006278751 -   0.00265611346834941i;
          0.990516544257531                         ;
          0.477796923118318 +     0.311064085401834i;
          0.477796923118318 -     0.311064085401834i;
                          0];
                        
dDTerms21 = 0;

% Model Stefano Tf22
dRes22 = [1.1284521501259e-014;
     -3.72133611555879e-014 - 2.08232683444075e-014i;
     -3.72133611555879e-014 + 2.08232683444075e-014i;
      9.84930639106637e-014 - 1.46640810672565e-013i;
      9.84930639106637e-014 + 1.46640810672565e-013i;
      2.51323684013671e-014                         ;
     -5.64078525288305e-014                         ;
     -1.62476406586366e-014                         ;
     -1.08424815979566e-011 + 8.32328079357669e-012i;
     -1.08424815979566e-011 - 8.32328079357669e-012i;
      2.41831559776112e-011];
    
dPoles22 = [0.988511243978897;
          0.997305870640646 +   0.00211760900132725i;
          0.997305870640646 -   0.00211760900132725i;
          0.999626453270255 +    0.0008125673525946i;
          0.999626453270255 -    0.0008125673525946i;
          0.999999366366222                         ;
          0.999981706320212                         ;
           0.99992421574188                         ;
          0.477898460791003 -     0.311001926610074i;
          0.477898460791003 +     0.311001926610074i;
                          0];
                        
dDTerms22 = 0;

% response calculation

pfparams.type = 'disc';
pfparams.freq = f;
pfparams.fs = 10;

% TF11
pfparams.res = dRes11;
pfparams.pol = dPoles11;
pfparams.dterm = dDTerms11;
pfr = utils.math.pfresp(pfparams);
mtf11 = pfr.resp;

% TF12
pfparams.res = dRes12;
pfparams.pol = dPoles12;
pfparams.dterm = dDTerms12;
pfr = utils.math.pfresp(pfparams);
mtf12 = pfr.resp;

% TF21
pfparams.res = dRes21;
pfparams.pol = dPoles21;
pfparams.dterm = dDTerms21;
pfr = utils.math.pfresp(pfparams);
mtf21 = pfr.resp;

% TF22
pfparams.res = dRes22;
pfparams.pol = dPoles22;
pfparams.dterm = dDTerms22;
pfr = utils.math.pfresp(pfparams);
mtf22 = pfr.resp;

% CSD calculation with Papoulis Method Style
% csd11 = mtf11.*conj(mtf11)+mtf12.*conj(mtf12);
% csd12 = mtf11.*conj(mtf21)+mtf12.*conj(mtf22);
% csd22 = mtf22.*conj(mtf22)+mtf21.*conj(mtf21);
% csd21 = conj(csd12);

% CSD = zeros(2,2,length(f));
% for hh = 1:length(f)
%   CSD(:,:,hh) = [csd11(hh) csd12(hh);csd21(hh) csd22(hh)];
% end

% CSD = zeros(2,2,length(f));
% for hh = 1:length(f)
%   CSD(:,:,hh) = [csd11(hh) 0;0 csd22(hh)];
% end


%% Get CSD Model

fs = 10;
f = [logspace(-6,log10(fs/2),2000)]';

% currPath = cd;
% cd MDC1 % assuming to start from ..\ltpda\software\m-toolbox\test
% [TF,CSD] = mdc1_tf_models(plist('f',f,'fs',fs));
% cd(currPath)

% get noise psd shapes
% parameters names
parnames = {'DH','S11','S1D','SD1','SDD','Dh1','Dh2','w1','w2',...
  'TH','Th1','Th2'};

% nominal params values
parvalues = {1,1,0,-1e-4,1,1,1,-1.3e-6,-2.0e-6,0.35,0.25,0.28};

% Noise model
N = matrix(plist('built-in','mdc3_ifo2ifo_noise'));

% evalueat model
[rw,cl]=size(N.objs);
for ii=1:rw
  for jj=1:cl
    N.objs(ii,jj).setParams(parnames,parvalues);
    N.objs(ii,jj).setXvals(f);
    sp(ii,jj)=eval(N.objs(ii,jj));
    if ii==jj
      sp(ii,jj)= abs(sp(ii,jj));
    end
  end
end

csd11 = sp(1,1).y;
csd12 = sp(1,2).y;
csd21 = sp(2,1).y;
csd22 = sp(2,2).y;

CSD = zeros(2,2,length(f));
for hh = 1:length(f)
  CSD(:,:,hh) = [csd11(hh) csd12(hh);csd21(hh) csd22(hh)];
end

%% Eigcsd 2-dim

h = utils.math.ndeigcsd(CSD,'MTD','PAP');

%% Test eigenshuffle

[l,m,npts] = size(CSD);

% Finding suppression  
k = min(sqrt(csd11./csd22));
if k>=1
  suppr = floor(k);
else
  n=0;
  while k<1
    k=k*10;
    n=n+1;
  end
  k = floor(k);
  suppr = k*10^(-n);
end

supmat = [1 0;0 suppr];
% isupmat = [1 0;0 1/suppr];
isupmat = inv(supmat);

PP = CSD;
for ii=1:npts
  PP(:,:,ii)=supmat*CSD(:,:,npts)*supmat;
end

[V,D] = eigenshuffle(CSD);
h = ones(l,m,npts);

for ii=1:npts
  HH = isupmat*V(:,:,ii)*sqrt(diag(D(:,ii)));
  h(:,:,ii) = HH;
end

%% Plot CSD

% CSD calculation
ncsd11 = squeeze(h(1,1,:).*conj(h(1,1,:))+h(1,2,:).*conj(h(1,2,:)));
ncsd12 = squeeze(h(1,1,:).*conj(h(2,1,:))+h(1,2,:).*conj(h(2,2,:)));
ncsd22 = squeeze(h(2,2,:).*conj(h(2,2,:))+h(2,1,:).*conj(h(2,1,:)));
ncsd21 = conj(csd12);

figure()
loglog(f,abs(csd11),'k')
hold on
grid on
loglog(f,abs(ncsd11),'r')

figure()
loglog(f,abs(csd12),'k')
hold on
grid on
loglog(f,abs(ncsd12),'r')

figure()
semilogx(f,angle(csd12),'k')
hold on
grid on
semilogx(f,angle(ncsd12),'r')

figure()
loglog(f,abs(csd22),'k')
hold on
grid on
loglog(f,abs(ncsd22),'r')

%% plot TFs

figure()
loglog(f,abs(mtf11),'k')
hold on
grid on
loglog(f,abs(squeeze(h(1,1,:))),'r')

figure()
loglog(f,abs(mtf12),'k')
hold on
grid on
loglog(f,abs(squeeze(h(1,2,:))),'r')

figure()
loglog(f,abs(mtf21),'k')
hold on
grid on
loglog(f,abs(squeeze(h(2,1,:))),'r')

figure()
loglog(f,abs(mtf22),'k')
hold on
grid on
loglog(f,abs(squeeze(h(2,2,:))),'r')

%% plot TFs phase

figure()
semilogx(f,angle(mtf11),'k')
hold on
grid on
semilogx(f,angle(squeeze(h(1,1,:))),'r')

figure()
semilogx(f,angle(mtf12),'k')
hold on
grid on
semilogx(f,angle(squeeze(h(1,2,:))),'r')

figure()
semilogx(f,angle(mtf21),'k')
hold on
grid on
semilogx(f,angle(squeeze(h(2,1,:))),'r')

figure()
semilogx(f,angle(mtf22),'k')
hold on
grid on
semilogx(f,angle(squeeze(h(2,2,:))),'r')



%% 3 Dim Test


% sampling frequency
fs = 1; % Hz
% frequency vector
f = logspace(-6,log10(0.5),300);
f = f.';

%%% Set the 3 channel model

% d = [1 -1.1 0.5 0.02];
% 
% h11 = miir(1e-1.*[1 -0.5],d,fs);
% h12 = miir(1e-4.*[0 -0.5],d,fs);
% h13 = miir(1e-2.*[1 0.2],d,fs);
% 
% h21 = miir(1e-3.*[0 0.4],d,fs);
% h22 = miir(1e-5.*[1 -0.6],d,fs);
% h23 = miir(1e-6.*[1 0.3],d,fs);
% 
% h31 = miir(1e-4.*[0 0.1 -0.2],d,fs);
% h32 = miir(1e-7.*[0 -0.6],d,fs);
% h33 = miir(1e-5.*[1 0.05 0.3],d,fs);


h11 = pzmodel(plist('GAIN', [0.01], 'POLES', [pz(9.9999999999999995e-007,NaN) pz(0.01,NaN) pz(0.02,NaN)], 'ZEROS', [pz(0.0001,NaN) pz(0.002,NaN)]));
h12 = pzmodel(plist('GAIN', [0.0001], 'POLES', [pz(0.10000000000000001,NaN) pz(0.0030000000000000001,NaN) pz(0.0050000000000000001,NaN) pz(1.0000000000000001e-005,NaN)], 'ZEROS', [pz(0.00050000000000000001,NaN) pz(0.001,NaN)]));
h13 = pzmodel(plist('GAIN', [0.00001], 'POLES', [pz(5.0000000000000004e-006,NaN) pz(0.02,NaN)], 'ZEROS', pz(0.00040000000000000002,NaN)));

h21 = pzmodel(plist('GAIN', [0.00001], 'POLES', [pz(5.0000000000000004e-006,NaN) pz(0.10000000000000001,NaN) pz(0.050000000000000003,NaN)], 'ZEROS', [pz(0.002,NaN) pz(0.00020000000000000001,NaN)]));
h22 = pzmodel(plist('GAIN', [0.001], 'POLES', [pz(0.01,NaN) pz(9.9999999999999995e-008,NaN) pz(0.002,NaN) pz(0.001,NaN)], 'ZEROS', [pz(1.0000000000000001e-005,NaN) pz(2.0000000000000002e-005,NaN) pz(5.0000000000000002e-005,NaN) pz(0.20000000000000001,NaN)]));
h23 = pzmodel(plist('GAIN', [0.0001], 'POLES', [pz(0.01,NaN) pz(0.029999999999999999,NaN) pz(0.10000000000000001,NaN) pz(5.0000000000000002e-005,NaN)], 'ZEROS', [pz(0.0001,NaN) pz(0.0050000000000000001,NaN)]));

h31 = pzmodel(plist('GAIN', [0.001], 'POLES', [pz(0.01,NaN) pz(0.029999999999999999,NaN) pz(0.10000000000000001,NaN) pz(0.00050000000000000001,NaN)], 'ZEROS', [pz(0.0001,NaN) pz(0.0050000000000000001,NaN)]));
h32 = pzmodel(plist('GAIN', [0.00001], 'POLES', [pz(0.01,NaN) pz(0.029999999999999999,NaN) pz(0.10000000000000001,NaN) pz(0.00050000000000000001,NaN) pz(0.00029999999999999997,NaN)], 'ZEROS', [pz(0.002,NaN) pz(0.059999999999999998,NaN)]));
h33 = pzmodel(plist('GAIN', [0.05], 'POLES', [pz(0.0001,NaN) pz(9.9999999999999995e-008,NaN) pz(0.002,NaN)], 'ZEROS', [pz(3.0000000000000001e-005,NaN) pz(5.0000000000000002e-005,NaN) pz(0.10000000000000001,NaN)]));

%%% TFs resps

% filters response
plresp = plist('f',f);

rh11 = resp(h11,plresp);
rh12 = resp(h12,plresp);
rh13 = resp(h13,plresp);

rh21 = resp(h21,plresp);
rh22 = resp(h22,plresp);
rh23 = resp(h23,plresp);

rh31 = resp(h31,plresp);
rh32 = resp(h32,plresp);
rh33 = resp(h33,plresp);

% iplot(rh11,rh12,rh13)
% iplot(rh21,rh22,rh23)
% iplot(rh31,rh32,rh33)

% iplot(rh11,rh22,rh33)

%%% Spectra calculation with Kay style method

% Note that the definition of cross-spectral matrix follows that of s M
% Kay, Modern Spectral Estimation
fs = 1; % Hz
% csd11 
G11 = rh11.y.*conj(rh11.y) + rh12.y.*conj(rh12.y) + rh13.y.*conj(rh13.y);
G11 = ao(plist('xvals', f, 'yvals', G11, 'fs', fs, 'dtype', 'fsdata', 'yunits', unit('m^2').*unit('Hz^-1')));
G11.setName;

% csd12
G12 = conj(rh11.y).*rh21.y + conj(rh12.y).*rh22.y + conj(rh13.y).*rh23.y;
G12 = ao(plist('xvals', f, 'yvals', G12, 'fs', fs, 'dtype', 'fsdata', 'yunits', unit('m^2').*unit('Hz^-1')));
G12.setName;

% csd13
G13 = conj(rh11.y).*rh31.y + conj(rh12.y).*rh32.y + conj(rh13.y).*rh33.y;
G13 = ao(plist('xvals', f, 'yvals', G13, 'fs', fs, 'dtype', 'fsdata', 'yunits', unit('m^2').*unit('Hz^-1')));
G13.setName;

% csd21
G21 = conj(G12);
G21.setName;

% csd22
G22 = rh21.y.*conj(rh21.y) + rh22.y.*conj(rh22.y) + rh23.y.*conj(rh23.y);
G22 = ao(plist('xvals', f, 'yvals', G22, 'fs', fs, 'dtype', 'fsdata', 'yunits', unit('m^2').*unit('Hz^-1')));
G22.setName;

% csd23
G23 = conj(rh21.y).*rh31.y + conj(rh22.y).*rh32.y + conj(rh23.y).*rh33.y;
G23 = ao(plist('xvals', f, 'yvals', G23, 'fs', fs, 'dtype', 'fsdata', 'yunits', unit('m^2').*unit('Hz^-1')));
G23.setName;

% csd31
G31 = conj(G13);
G31.setName;

% csd32
G32 = conj(G23);
G32.setName;

% csd33
G33 = conj(rh31.y).*rh31.y + conj(rh32.y).*rh32.y + conj(rh33.y).*rh33.y;
G33 = ao(plist('xvals', f, 'yvals', G33, 'fs', fs, 'dtype', 'fsdata', 'yunits', unit('m^2').*unit('Hz^-1')));
G33.setName;

% iplot(G11,G12,G13,G22,G23,G33)

% iplot(G11,G22,G33)

%%% Build CSD matrix

CSD = zeros(3,3,length(f));
for hh = 1:length(f)
  CSD(:,:,hh) = [G11.y(hh) G12.y(hh) G13.y(hh);G21.y(hh) G22.y(hh) G23.y(hh);G31.y(hh) G32.y(hh) G33.y(hh)];
end

% for hh = 1:length(f)
%   CSD(:,:,hh) = [G11.y(hh) 0 0;0 G22.y(hh) 0;0 0 G33.y(hh)];
% end

%%% 3-dim Eigcsd with kay method stule
h = utils.math.ndeigcsd(CSD,'MTD','KAY');

% %%% Eigenshuffle
% 
% [l,m,kk] = size(CSD);
% suppr = ones(l,l);
% for ii = 2:l
%   k = ones(l,1);
%   
%   for jj = ii-1:-1:1
%     k(jj) = min(sqrt(CSD(jj,jj,:)./CSD(ii,ii,:)));
%     if k(jj)>=1
%       suppr(jj,ii) = floor(k(jj));
%     else
%       n=0;
%       while k(jj)<1
%         k(jj)=k(jj)*10;
%         n=n+1;
%       end
%       k(jj) = floor(k(jj));
%       suppr(jj,ii) = k(jj)*10^(-n);
%       %       suppr(ii) = suppr(ii)*suppr(ii-1);
%     end
%   end
%   %     csuppr(ii) = prod(suppr(:,ii));
% end
% csuppr = prod(suppr,2);
% supmat = diag(csuppr);
% % ssup = rot90(rot90(supmat));
% ssup = supmat;
% % ssup = eye(3);
% % ssup = supmat*supmat.';
% issup = inv(ssup);
% 
% for jj = 1:kk
%   nCSD(:,:,jj) = ssup*CSD(:,:,jj)*ssup;
% end
% 
% [Vseq,Dseq] = eigenshuffle(nCSD);
% 
% % get h = V*sqrt(D);
% [nn,mm,kk] = size(Vseq);
% h = zeros(nn,mm,kk);
% for dd = 1:kk
% %   h(:,:,dd) = rot90(issup*Vseq(:,:,dd)*sqrt(diag(Dseq(:,dd))));
%   h(:,:,dd) = issup*Vseq(:,:,dd)*sqrt(diag(Dseq(:,dd)));
% end

%% Build TF AOs

nh11 = ao(plist('xvals', f, 'yvals', squeeze(h(1,1,:)), 'fs', fs, 'dtype', 'fsdata'));
nh11.setName;

nh12 = ao(plist('xvals', f, 'yvals', squeeze(h(1,2,:)), 'fs', fs, 'dtype', 'fsdata'));
nh12.setName;

nh13 = ao(plist('xvals', f, 'yvals', squeeze(h(1,3,:)), 'fs', fs, 'dtype', 'fsdata'));
nh13.setName;

nh21 = ao(plist('xvals', f, 'yvals', squeeze(h(2,1,:)), 'fs', fs, 'dtype', 'fsdata'));
nh21.setName;

nh22 = ao(plist('xvals', f, 'yvals', squeeze(h(2,2,:)), 'fs', fs, 'dtype', 'fsdata'));
nh22.setName;

nh23 = ao(plist('xvals', f, 'yvals', squeeze(h(2,3,:)), 'fs', fs, 'dtype', 'fsdata'));
nh23.setName;

nh31 = ao(plist('xvals', f, 'yvals', squeeze(h(3,1,:)), 'fs', fs, 'dtype', 'fsdata'));
nh31.setName;

nh32 = ao(plist('xvals', f, 'yvals', squeeze(h(3,2,:)), 'fs', fs, 'dtype', 'fsdata'));
nh32.setName;

nh33 = ao(plist('xvals', f, 'yvals', squeeze(h(3,3,:)), 'fs', fs, 'dtype', 'fsdata'));
nh33.setName;

iplot(rh11,nh11)
iplot(rh12,nh12)
iplot(rh13,nh13)
iplot(rh21,nh21)
iplot(rh22,nh22)
iplot(rh23,nh23)
iplot(rh31,nh31)
iplot(rh32,nh32)
iplot(rh33,nh33)

%% Build CSD AOs

% Note that the definition of cross-spectral matrix follows that of s M
% Kay, Modern Spectral Estimation

% csd11 
H11 = nh11.y.*conj(nh11.y) + nh12.y.*conj(nh12.y) + nh13.y.*conj(nh13.y);
H11 = ao(plist('xvals', f, 'yvals', H11, 'fs', fs, 'dtype', 'fsdata', 'yunits', unit('m^2').*unit('Hz^-1')));
H11.setName;

% csd12
H12 = conj(nh11.y).*nh21.y + conj(nh12.y).*nh22.y + conj(nh13.y).*nh23.y;
H12 = ao(plist('xvals', f, 'yvals', H12, 'fs', fs, 'dtype', 'fsdata', 'yunits', unit('m^2').*unit('Hz^-1')));
H12.setName;

% csd13
H13 = conj(nh11.y).*nh31.y + conj(nh12.y).*nh32.y + conj(nh13.y).*nh33.y;
H13 = ao(plist('xvals', f, 'yvals', H13, 'fs', fs, 'dtype', 'fsdata', 'yunits', unit('m^2').*unit('Hz^-1')));
H13.setName;

% csd21
H21 = conj(H12);
H21.setName;

% csd22
H22 = nh21.y.*conj(nh21.y) + nh22.y.*conj(nh22.y) + nh23.y.*conj(nh23.y);
H22 = ao(plist('xvals', f, 'yvals', H22, 'fs', fs, 'dtype', 'fsdata', 'yunits', unit('m^2').*unit('Hz^-1')));
H22.setName;

% csd23
H23 = conj(nh21.y).*nh31.y + conj(nh22.y).*nh32.y + conj(nh23.y).*nh33.y;
H23 = ao(plist('xvals', f, 'yvals', H23, 'fs', fs, 'dtype', 'fsdata', 'yunits', unit('m^2').*unit('Hz^-1')));
H23.setName;

% csd31
H31 = conj(H13);
H31.setName;

% csd32
H32 = conj(H23);
H32.setName;

% csd33
H33 = conj(nh31.y).*nh31.y + conj(nh32.y).*nh32.y + conj(nh33.y).*nh33.y;
H33 = ao(plist('xvals', f, 'yvals', H33, 'fs', fs, 'dtype', 'fsdata', 'yunits', unit('m^2').*unit('Hz^-1')));
H33.setName;

iplot(G11,H11)
iplot(G12,H12)
iplot(G13,H13)
iplot(G22,H22)
iplot(G23,H23)
iplot(G33,H33)