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−% Training session Topic 5 exercise 02
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−% 
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−% System identification in z-domain 2
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−% 
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−% 1) Load fsdata object from file
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−% 2) Fit loaded TF data with zDomainFit and fixed order
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−% 3) Compare results
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−% 
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−% L FERRAIOLI 22-02-09
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−%
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−% $Id: TrainigSession_T5_Ex02.m,v 1.3 2009/02/25 18:18:45 luigi Exp $
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−%
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−%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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−
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−%% 1) load fsdata
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−
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−% load AO from file
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−rfilt = ao(plist('filename', 'topic5\T5_Ex02_rfilt.xml'));
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−iplot(rfilt)
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−
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−%% 2) Fitting TF - fixed model order
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−
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−% Loaded fsdata are the response of an order 19 partial fractioned filter.
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−% We now try to fitting the loaded filter response with zDomainFit with a
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−% fixed model order.
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−% We set Autosearch to off, in this case the function do not perform
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−% accuracy test but simply run how far maximum number of iteration is
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−% reached. Model order is fixed by minorder parameter. 
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−
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−plfit1 = plist('FS',10,... % Sampling frequency for the model filters
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−  'AutoSearch','off',... % Automatically search for a good model
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−  'StartPolesOpt','c1',... % Define the properties of the starting poles - complex distributed in the unitary circle
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−  'maxiter',30,... % maximum number of iteration per model order
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−  'minorder',19,... % fixed model order
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−  'weightparam','abs',... % assign weights as 1./abs(data)
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−  'Plot','on',... % set the plot on or off
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−  'ForceStability','on',... % force to output a stable ploes model
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−  'CheckProgress','off'); % display fitting progress on the command window
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−
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−% Do the fit
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−fobj = zDomainFit(rfilt,plfit1);
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−% setting input and output units for fitted model
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−
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−%% 3) Compare results
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−
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−% Extracting residues and poles from fit results
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−fRes = zeros(numel(fobj),1); % fit residue vector initialization
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−fPoles = zeros(numel(fobj),1); % fit poles vector initialization
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−
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−% extracting data from fitted filters
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−for ii = 1:numel(fobj)
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−  fRes(ii,1) = fobj(ii).a(1);
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−  fPoles(ii,1) = -1*fobj(ii).b(2);
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−end
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−[fRes,idx] = sort(fRes);
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−fPoles = fPoles(idx);
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−
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−% starting model residues and poles
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−mRes = [2.44554138162509e-011 - 1.79482547894083e-011i;
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−2.44554138162509e-011 + 1.79482547894083e-011i;
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−2.66402334803101e-009 +  1.1025122049153e-009i;
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−2.66402334803101e-009 -  1.1025122049153e-009i;
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−-7.3560293387644e-009;
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−-1.82811618589835e-009 - 1.21803627800855e-009i;
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−-1.82811618589835e-009 + 1.21803627800855e-009i;
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−1.16258677367555e-009;
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−1.65216557639319e-016;                         
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−-1.78092396888606e-016;
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−-2.80420398962379e-017;
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−9.21305973049041e-013 - 8.24686706827269e-014i;
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−9.21305973049041e-013 + 8.24686706827269e-014i;
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−5.10730060739905e-010 - 3.76571756625722e-011i;
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−5.10730060739905e-010 + 3.76571756625722e-011i;
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−3.45893698149735e-009;
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−3.98139182134446e-014 - 8.25503935419059e-014i;
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−3.98139182134446e-014 + 8.25503935419059e-014i;
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−-1.40595719147164e-011];
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−[mRes,idx] = sort(mRes);
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−
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−mPoles = [0.843464045655194 - 0.0959986292915475i;
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−0.843464045655194 + 0.0959986292915475i;
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−0.953187595424927 - 0.0190043625473383i;
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−0.953187595424927 + 0.0190043625473383i;
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−0.967176277937188;
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−0.995012027005247 - 0.00268322602801729i;
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−0.995012027005247 + 0.00268322602801729i;
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−0.996564761885673;
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−0.999999366165445;
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−0.999981722418555;
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−0.999921882627659;
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−0.999624431675213 - 0.000813407848742761i;
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−0.999624431675213 + 0.000813407848742761i;
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−0.997312006278751 - 0.00265611346834941i;
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−0.997312006278751 + 0.00265611346834941i;
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−0.990516544257531;
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−0.477796923118318 - 0.311064085401834i;
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−0.477796923118318 + 0.311064085401834i;
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−0];
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−mPoles = mPoles(idx);
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−
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−% Check the relative difference
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−(mRes-fRes)./abs(mRes)
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−(mPoles-fPoles)./abs(mPoles)
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−% Results are accurate to the 7th decimal digit
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−