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author | Daniele Nicolodi <nicolodi@science.unitn.it> |
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date | Mon, 05 Dec 2011 16:20:06 +0100 |
parents | f0afece42f48 |
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% Training session Topic 5 exercise 02 % % System identification in z-domain 2 % % 1) Load fsdata object from file % 2) Fit loaded TF data with zDomainFit and fixed order % 3) Compare results % % L FERRAIOLI 22-02-09 % % $Id: TrainigSession_T5_Ex02.m,v 1.3 2009/02/25 18:18:45 luigi Exp $ % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% 1) load fsdata % load AO from file rfilt = ao(plist('filename', 'topic5\T5_Ex02_rfilt.xml')); iplot(rfilt) %% 2) Fitting TF - fixed model order % Loaded fsdata are the response of an order 19 partial fractioned filter. % We now try to fitting the loaded filter response with zDomainFit with a % fixed model order. % We set Autosearch to off, in this case the function do not perform % accuracy test but simply run how far maximum number of iteration is % reached. Model order is fixed by minorder parameter. plfit1 = plist('FS',10,... % Sampling frequency for the model filters 'AutoSearch','off',... % Automatically search for a good model 'StartPolesOpt','c1',... % Define the properties of the starting poles - complex distributed in the unitary circle 'maxiter',30,... % maximum number of iteration per model order 'minorder',19,... % fixed model order 'weightparam','abs',... % assign weights as 1./abs(data) 'Plot','on',... % set the plot on or off 'ForceStability','on',... % force to output a stable ploes model 'CheckProgress','off'); % display fitting progress on the command window % Do the fit fobj = zDomainFit(rfilt,plfit1); % setting input and output units for fitted model %% 3) Compare results % Extracting residues and poles from fit results fRes = zeros(numel(fobj),1); % fit residue vector initialization fPoles = zeros(numel(fobj),1); % fit poles vector initialization % extracting data from fitted filters for ii = 1:numel(fobj) fRes(ii,1) = fobj(ii).a(1); fPoles(ii,1) = -1*fobj(ii).b(2); end [fRes,idx] = sort(fRes); fPoles = fPoles(idx); % starting model residues and poles mRes = [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]; [mRes,idx] = sort(mRes); mPoles = [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]; mPoles = mPoles(idx); % Check the relative difference (mRes-fRes)./abs(mRes) (mPoles-fPoles)./abs(mPoles) % Results are accurate to the 7th decimal digit