Mercurial > hg > ltpda

annotate m-toolbox/classes/@matrix/MultiChannelNoise.m @ 52:daf4eab1a51e database-connection-manager tip

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Fix. Default password should be [] not an empty string
author Daniele Nicolodi <nicolodi@science.unitn.it>
date Wed, 07 Dec 2011 17:29:47 +0100
parents f0afece42f48
children
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rev   line source
0
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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1 % MULTICHANNELNOISE
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Daniele Nicolodi <nicolodi@science.unitn.it>
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2 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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Daniele Nicolodi <nicolodi@science.unitn.it>
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3 %
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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4 % FUNCTION: MultiChannelNoise
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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5 %
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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6 % DESCRIPTION:
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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7 %
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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8 %
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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9 % CALL: a = MultiChannelNoise(a, pl)
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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10 %
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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11 % PARAMETER:
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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12 % pl: plist containing Nsecs, fs
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Daniele Nicolodi <nicolodi@science.unitn.it>
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13 %
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Daniele Nicolodi <nicolodi@science.unitn.it>
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14 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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15 function a = MultiChannelNoise(a, pli)
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Daniele Nicolodi <nicolodi@science.unitn.it>
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16
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Daniele Nicolodi <nicolodi@science.unitn.it>
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17 VERSION = '$Id: MultiChannelNoise.m,v 1.10 2010/10/29 16:09:13 ingo Exp $';
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Daniele Nicolodi <nicolodi@science.unitn.it>
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18
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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19 % get AO info
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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20 iobj = matrix.getInfo('matrix', 'Multichannel Noise');
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Daniele Nicolodi <nicolodi@science.unitn.it>
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21
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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22 % Set the method version string in the minfo object
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Daniele Nicolodi <nicolodi@science.unitn.it>
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23 iobj.setMversion([VERSION '-->' iobj.mversion]);
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Daniele Nicolodi <nicolodi@science.unitn.it>
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24
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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25 % Add default values
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Daniele Nicolodi <nicolodi@science.unitn.it>
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26 pl = parse(pli, iobj.plists);
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Daniele Nicolodi <nicolodi@science.unitn.it>
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27
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Daniele Nicolodi <nicolodi@science.unitn.it>
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28 % Get parameters and set params for fit
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Daniele Nicolodi <nicolodi@science.unitn.it>
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29 Nsecs = find(pl, 'nsecs');
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Daniele Nicolodi <nicolodi@science.unitn.it>
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30 fs = find(pl, 'fs');
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Daniele Nicolodi <nicolodi@science.unitn.it>
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31 filter = find(pl, 'model');
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Daniele Nicolodi <nicolodi@science.unitn.it>
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32 yunit = find(pl, 'yunits');
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Daniele Nicolodi <nicolodi@science.unitn.it>
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33
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Daniele Nicolodi <nicolodi@science.unitn.it>
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34 % total number of data in the series
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Daniele Nicolodi <nicolodi@science.unitn.it>
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35 Ntot = round(Nsecs*fs);
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Daniele Nicolodi <nicolodi@science.unitn.it>
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36
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Daniele Nicolodi <nicolodi@science.unitn.it>
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37 % chose case for input filter
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Daniele Nicolodi <nicolodi@science.unitn.it>
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38 if isa(filter,'matrix') && isa(filter.objs(1),'filterbank')
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Daniele Nicolodi <nicolodi@science.unitn.it>
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39 % discrete system
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Daniele Nicolodi <nicolodi@science.unitn.it>
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40 sys = 'z';
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Daniele Nicolodi <nicolodi@science.unitn.it>
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41 mfil = filter.objs;
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Daniele Nicolodi <nicolodi@science.unitn.it>
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42 [nn,mm] = size(mfil);
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Daniele Nicolodi <nicolodi@science.unitn.it>
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43 if nn~=mm
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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44 error('!!! Filter matrix must be square')
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Daniele Nicolodi <nicolodi@science.unitn.it>
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45 end
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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46 elseif isa(filter,'matrix') && isa(filter.objs(1),'parfrac')
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Daniele Nicolodi <nicolodi@science.unitn.it>
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47 % continuous system
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Daniele Nicolodi <nicolodi@science.unitn.it>
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48 sys = 's';
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Daniele Nicolodi <nicolodi@science.unitn.it>
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49 mfil = filter.objs;
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Daniele Nicolodi <nicolodi@science.unitn.it>
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50 [nn,mm] = size(mfil);
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Daniele Nicolodi <nicolodi@science.unitn.it>
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51 if nn~=mm
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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52 error('!!! Filter matrix must be square')
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Daniele Nicolodi <nicolodi@science.unitn.it>
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53 end
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Daniele Nicolodi <nicolodi@science.unitn.it>
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54 else
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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55 error('!!! Input filter must be a ''matrix'' of ''filterbank'' or ''parfrac'' objects.')
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Daniele Nicolodi <nicolodi@science.unitn.it>
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56 end
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Daniele Nicolodi <nicolodi@science.unitn.it>
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57
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Daniele Nicolodi <nicolodi@science.unitn.it>
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58 % init output
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Daniele Nicolodi <nicolodi@science.unitn.it>
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59 out(nn,1) = ao;
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Daniele Nicolodi <nicolodi@science.unitn.it>
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60
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Daniele Nicolodi <nicolodi@science.unitn.it>
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61 % switch between input filter type
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Daniele Nicolodi <nicolodi@science.unitn.it>
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62 switch sys
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Daniele Nicolodi <nicolodi@science.unitn.it>
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63 case 'z' % discrete input filters
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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64
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Daniele Nicolodi <nicolodi@science.unitn.it>
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65 o = zeros(nn,Ntot);
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Daniele Nicolodi <nicolodi@science.unitn.it>
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66
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Daniele Nicolodi <nicolodi@science.unitn.it>
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67 for zz=1:nn % moving along system dimension
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Daniele Nicolodi <nicolodi@science.unitn.it>
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68
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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69 % extract residues and poles from input objects
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Daniele Nicolodi <nicolodi@science.unitn.it>
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70 % run over matrix dimensions
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Daniele Nicolodi <nicolodi@science.unitn.it>
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71 res = [];
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Daniele Nicolodi <nicolodi@science.unitn.it>
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72 pls = [];
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Daniele Nicolodi <nicolodi@science.unitn.it>
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73 filtsz = [];
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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74 for jj=1:nn % collect filters coefficients along the columns zz
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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75 bfil = mfil(jj,zz).filters;
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Daniele Nicolodi <nicolodi@science.unitn.it>
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76 filtsz = [filtsz; numel(bfil)];
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Daniele Nicolodi <nicolodi@science.unitn.it>
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77 for kk=1:numel(bfil)
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Daniele Nicolodi <nicolodi@science.unitn.it>
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78 num = bfil(kk).a;
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Daniele Nicolodi <nicolodi@science.unitn.it>
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79 den = bfil(kk).b;
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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80 res = [res; num(1)];
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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81 pls = [pls; -1*den(2)];
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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82 end
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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83 end
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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84
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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85 % rescaling residues to get the correct result for univariate psd
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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86 res = res.*sqrt(fs/2);
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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87
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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88 Nrs = numel(res);
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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89 % get covariance matrix
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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90 R = zeros(Nrs);
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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91 for aa=1:Nrs
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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92 for bb=1:Nrs
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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93 R(aa,bb) = (res(aa)*conj(res(bb)))/(1-pls(aa)*conj(pls(bb)));
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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94 end
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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95 end
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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96
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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97 % avoiding problems caused by roundoff errors
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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98 HH = triu(R,0); % get upper triangular part of R
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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99 HH1 = triu(R,1); % get upper triangular part of R above principal diagonal
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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100 HH2 = HH1'; % do transpose conjugate
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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101 R = HH + HH2; % reconstruct R in order to be really hermitian
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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102
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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103 % get singular value decomposition of R
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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104 [U,S,V] = svd(R,0);
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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105
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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106 % conversion matrix
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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107 A = V*sqrt(S);
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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108
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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109 % generate unitary variance gaussian random noise
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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110 %ns = randn(Nrs,Ntot);
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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111 ns = randn(Nrs,1);
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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112
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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113 % get correlated starting data points
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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114 cns = A*ns;
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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115
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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116 % need to correct for roundoff errors
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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117 % cleaning up results for numerical approximations
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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118 idx = imag(pls(:,1))==0;
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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119 cns(idx) = real(cns(idx));
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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120
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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121 % cleaning up results for numerical roundoff errors
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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122 % states associated to complex conjugate poles must be complex
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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123 % conjugate
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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124 idxi = imag(pls(:,1))~=0;
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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125 icns = cns(idxi);
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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126 for jj = 1:2:numel(icns)
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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127 icns(jj+1,1) = conj(icns(jj,1));
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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128 end
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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129 cns(idxi) = icns;
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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130
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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131 y = zeros(sum(filtsz),2);
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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132 rnoise = zeros(sum(filtsz),1);
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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133 rns = randn(1,Ntot);
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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134 %rns = utils.math.blwhitenoise(Ntot,fs,1/Nsecs,fs/2);
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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135 %rns = rns.'; % willing to work with raw
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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136
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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137 y(:,1) = cns;
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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138
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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139 % start recurrence
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
140 for xx = 2:Ntot+1
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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141 rnoise(:,1) = rns(xx-1);
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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142 y(:,2) = pls.*y(:,1) + res.*rnoise;
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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143 idxr = 0;
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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144 for kk=1:nn
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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145 o(kk,xx-1) = o(kk,xx-1) + sum(y(idxr+1:idxr+filtsz(kk),2));
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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146 idxr = idxr+filtsz(kk);
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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147 end
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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148 y(:,1) = y(:,2);
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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149 end
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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150
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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151 end
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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152
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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153 clear rns
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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154
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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155 % build output ao
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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156 for dd=1:nn
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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157 out(dd,1) = ao(tsdata(o(dd,:),fs));
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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158 out(dd,1).setYunits(unit(yunit));
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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159 end
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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160
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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161 a = matrix(out);
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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162
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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163 case 's' % continuous input filters
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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164
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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165 o = zeros(nn,Ntot);
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
166
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
167 T = 1/fs; % sampling period
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
168
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
169 for zz=1:nn % moving along system dimension
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
170
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
171 % extract residues and poles from input objects
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
172 % run over matrix dimensions
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
173 res = [];
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
174 pls = [];
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
175 filtsz = [];
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
176 for jj=1:nn % collect filters coefficients along the columns zz
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
177 bfil = mfil(jj,zz);
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
178 filtsz = [filtsz; numel(bfil.res)];
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
179 res = [res; bfil.res];
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
180 pls = [pls; bfil.poles];
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
181 end
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
182
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
183 % rescaling residues to get the correct result for univariate psd
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
184 res = res.*sqrt(fs/2);
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
185
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
186 Nrs = numel(res);
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
187
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
188 % get covariance matrix for innovation
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
189 Ri = zeros(Nrs);
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
190 for aa=1:Nrs
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
191 for bb=1:Nrs
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
192 Ri(aa,bb) = (res(aa)*conj(res(bb)))*(exp((pls(aa) + conj(pls(bb)))*T)-1)/(pls(aa) + conj(pls(bb)));
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
193 end
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
194 end
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
195
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
196 % avoiding problems caused by roundoff errors
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
197 HH = triu(Ri,0); % get upper triangular part of R
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
198 HH1 = triu(Ri,1); % get upper triangular part of R above principal diagonal
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
199 HH2 = HH1'; % do transpose conjugate
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
200 Ri = HH + HH2; % reconstruct R in order to be really hermitian
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
201
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
202 % get singular value decomposition of R
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
203 [Ui,Si,Vi] = svd(Ri,0);
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
204
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
205 % conversion matrix for innovation
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
206 Ai = Vi*sqrt(Si);
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
207
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
208 % get covariance matrix for initial state
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
209 Rx = zeros(Nrs);
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
210 for aa=1:Nrs
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
211 for bb=1:Nrs
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
212 Rx(aa,bb) = -1*(res(aa)*conj(res(bb)))/(pls(aa) + conj(pls(bb)));
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
213 end
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
214 end
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
215
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
216 % avoiding problems caused by roundoff errors
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
217 HH = triu(Rx,0); % get upper triangular part of R
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
218 HH1 = triu(Rx,1); % get upper triangular part of R above principal diagonal
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
219 HH2 = HH1'; % do transpose conjugate
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
220 Rx = HH + HH2; % reconstruct R in order to be really hermitian
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
221
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
222 % get singular value decomposition of R
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
223 [Ux,Sx,Vx] = svd(Rx,0);
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
224
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
225 % conversion matrix for initial state
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
226 Ax = Vx*sqrt(Sx);
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
227
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
228 % generate unitary variance gaussian random noise
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
229 %ns = randn(Nrs,Ntot);
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
230 ns = randn(Nrs,1);
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
231
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
232 % get correlated starting data points
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
233 cns = Ax*ns;
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
234
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
235 % need to correct for roundoff errors
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
236 % cleaning up results for numerical approximations
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
237 idx = imag(pls(:,1))==0;
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
238 cns(idx) = real(cns(idx));
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
239
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
240 % cleaning up results for numerical roundoff errors
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
241 % states associated to complex conjugate poles must be complex
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
242 % conjugate
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
243 idxi = imag(pls(:,1))~=0;
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
244 icns = cns(idxi);
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
245 for jj = 1:2:numel(icns)
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
246 icns(jj+1,1) = conj(icns(jj,1));
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
247 end
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
248 cns(idxi) = icns;
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
249
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
250 y = zeros(sum(filtsz),2);
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
251 rnoise = zeros(sum(filtsz),1);
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
252 rns = randn(1,Ntot);
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
253 %rns = utils.math.blwhitenoise(Ntot,fs,1/Nsecs,fs/2);
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
254 %rns = rns.'; % willing to work with raw
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
255
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
256 y(:,1) = cns;
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
257
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
258 % start recurrence
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
259 for xx = 2:Ntot+1
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
260 % innov = Ai*randn(sum(filtsz),1);
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
261 rnoise(:,1) = rns(xx-1);
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
262 innov = Ai*rnoise;
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
263 % need to correct for roundoff errors
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
264 % cleaning up results for numerical approximations
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
265 innov(idx) = real(innov(idx));
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
266
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
267 % cleaning up results for numerical roundoff errors
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
268 % states associated to complex conjugate poles must be complex
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
269 % conjugate
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
270 iinnov = innov(idxi);
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
271 for jj = 1:2:numel(iinnov)
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
272 iinnov(jj+1,1) = conj(iinnov(jj,1));
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
273 end
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
274 innov(idxi) = iinnov;
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
275
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
276 y(:,2) = diag(exp(pls.*T))*y(:,1) + innov;
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
277
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
278 idxr = 0;
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
279 for kk=1:nn
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
280 o(kk,xx-1) = o(kk,xx-1) + sum(y(idxr+1:idxr+filtsz(kk),2));
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
281 idxr = idxr+filtsz(kk);
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
282 end
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
283 y(:,1) = y(:,2);
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
284 end
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
285
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
286 end
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
287
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
288 % clear rns
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
289
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
290 % build output ao
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
291 for dd=1:nn
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
292 out(dd,1) = ao(tsdata(o(dd,:),fs));
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
293 out(dd,1).setYunits(unit(yunit));
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
294 end
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
295
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
296 a = matrix(out);
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
297
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
298 end
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
299
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
300
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
301 end
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
302
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
303