Mercurial > hg > ltpda

annotate m-toolbox/classes/+utils/@math/eigpsd.m @ 0:f0afece42f48

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Import.
author Daniele Nicolodi <nicolodi@science.unitn.it>
date Wed, 23 Nov 2011 19:22:13 +0100
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0
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Daniele Nicolodi <nicolodi@science.unitn.it>
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1 % EIGPSD calculates TFs from 2D cross-correlated spectra.
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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>
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4 % DESCRIPTION:
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Daniele Nicolodi <nicolodi@science.unitn.it>
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5 %
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Daniele Nicolodi <nicolodi@science.unitn.it>
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6 % Calculates TFs or WFs from 2dim cross correlated spectra
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Daniele Nicolodi <nicolodi@science.unitn.it>
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7 %
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Daniele Nicolodi <nicolodi@science.unitn.it>
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8 % CALL: [h11,h12,h21,h22] = eigpsd(psd1,csd,psd2,varargin)
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Daniele Nicolodi <nicolodi@science.unitn.it>
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9 %
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Daniele Nicolodi <nicolodi@science.unitn.it>
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10 % INPUT:
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Daniele Nicolodi <nicolodi@science.unitn.it>
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11 %
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Daniele Nicolodi <nicolodi@science.unitn.it>
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12 % psd1 is the first power spectral density
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Daniele Nicolodi <nicolodi@science.unitn.it>
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13 % csd is the cross spectrum
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Daniele Nicolodi <nicolodi@science.unitn.it>
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14 % psd2 is the second power spectral density
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Daniele Nicolodi <nicolodi@science.unitn.it>
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15 % Input also the parameters specifying calculation options
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Daniele Nicolodi <nicolodi@science.unitn.it>
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16 % 'USESYM' define the calculation method, allowed values are 0
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Daniele Nicolodi <nicolodi@science.unitn.it>
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17 % (double precision arithmetic) and 1 (symbolic toolbox variable
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Daniele Nicolodi <nicolodi@science.unitn.it>
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18 % precision arithmetic)
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Daniele Nicolodi <nicolodi@science.unitn.it>
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19 % 'DIG' define the digits used in VPA calculation
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Daniele Nicolodi <nicolodi@science.unitn.it>
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20 % 'OTP' define the output type. Allowed values are 'TF' output the
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Daniele Nicolodi <nicolodi@science.unitn.it>
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21 % transfer functions or 'WF' output the whitening filters frequency
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Daniele Nicolodi <nicolodi@science.unitn.it>
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22 % responses
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Daniele Nicolodi <nicolodi@science.unitn.it>
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23 %
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Daniele Nicolodi <nicolodi@science.unitn.it>
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24 % OUTPUT:
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Daniele Nicolodi <nicolodi@science.unitn.it>
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25 %
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Daniele Nicolodi <nicolodi@science.unitn.it>
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26 % h11, h12, h21 and h22 are the four innovation TFs frequency responses
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Daniele Nicolodi <nicolodi@science.unitn.it>
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27 % or the four whitening filters frequency responses
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Daniele Nicolodi <nicolodi@science.unitn.it>
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28 %
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Daniele Nicolodi <nicolodi@science.unitn.it>
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29 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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Daniele Nicolodi <nicolodi@science.unitn.it>
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30 % HISTORY: 02-10-2008 L Ferraioli
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Daniele Nicolodi <nicolodi@science.unitn.it>
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31 % Creation
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Daniele Nicolodi <nicolodi@science.unitn.it>
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32 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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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 % VERSION: $Id: eigpsd.m,v 1.3 2008/10/24 14:40:20 luigi Exp $
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Daniele Nicolodi <nicolodi@science.unitn.it>
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35 %
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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 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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Daniele Nicolodi <nicolodi@science.unitn.it>
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38 function [h11,h12,h21,h22] = eigpsd(psd1,csd,psd2,varargin)
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39
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Daniele Nicolodi <nicolodi@science.unitn.it>
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40 % Init
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Daniele Nicolodi <nicolodi@science.unitn.it>
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41
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Daniele Nicolodi <nicolodi@science.unitn.it>
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42 S11 = psd1;
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Daniele Nicolodi <nicolodi@science.unitn.it>
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43 S22 = psd2;
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Daniele Nicolodi <nicolodi@science.unitn.it>
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44 S12 = csd;
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Daniele Nicolodi <nicolodi@science.unitn.it>
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45 S21 = conj(S12);
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Daniele Nicolodi <nicolodi@science.unitn.it>
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46
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Daniele Nicolodi <nicolodi@science.unitn.it>
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47 npts = length(S11);
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Daniele Nicolodi <nicolodi@science.unitn.it>
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48
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Daniele Nicolodi <nicolodi@science.unitn.it>
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49 % Finding parameters
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Daniele Nicolodi <nicolodi@science.unitn.it>
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50
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Daniele Nicolodi <nicolodi@science.unitn.it>
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51 % default
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Daniele Nicolodi <nicolodi@science.unitn.it>
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52 usesym = 1;
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Daniele Nicolodi <nicolodi@science.unitn.it>
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53 dig = 50;
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Daniele Nicolodi <nicolodi@science.unitn.it>
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54 otp = 'TF';
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Daniele Nicolodi <nicolodi@science.unitn.it>
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55
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Daniele Nicolodi <nicolodi@science.unitn.it>
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56 if ~isempty(varargin)
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Daniele Nicolodi <nicolodi@science.unitn.it>
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57 for j=1:length(varargin)
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Daniele Nicolodi <nicolodi@science.unitn.it>
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58 if strcmp(varargin{j},'USESYM')
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Daniele Nicolodi <nicolodi@science.unitn.it>
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59 usesym = varargin{j+1};
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Daniele Nicolodi <nicolodi@science.unitn.it>
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60 end
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Daniele Nicolodi <nicolodi@science.unitn.it>
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61 if strcmp(varargin{j},'DIG')
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Daniele Nicolodi <nicolodi@science.unitn.it>
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62 dig = varargin{j+1};
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63 end
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Daniele Nicolodi <nicolodi@science.unitn.it>
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64 if strcmp(varargin{j},'OTP')
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Daniele Nicolodi <nicolodi@science.unitn.it>
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65 otp = varargin{j+1};
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Daniele Nicolodi <nicolodi@science.unitn.it>
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66 end
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Daniele Nicolodi <nicolodi@science.unitn.it>
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67 end
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68 end
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69
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Daniele Nicolodi <nicolodi@science.unitn.it>
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70 % Defining calculation method
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Daniele Nicolodi <nicolodi@science.unitn.it>
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71 if usesym == 1
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Daniele Nicolodi <nicolodi@science.unitn.it>
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72 method = 'VPA';
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Daniele Nicolodi <nicolodi@science.unitn.it>
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73 else
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Daniele Nicolodi <nicolodi@science.unitn.it>
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74 method = 'NUM';
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Daniele Nicolodi <nicolodi@science.unitn.it>
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75 end
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76
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Daniele Nicolodi <nicolodi@science.unitn.it>
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77 % Finding suppressio
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Daniele Nicolodi <nicolodi@science.unitn.it>
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78
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Daniele Nicolodi <nicolodi@science.unitn.it>
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79 k = min(sqrt(S11./S22));
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Daniele Nicolodi <nicolodi@science.unitn.it>
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80 if k>=1
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Daniele Nicolodi <nicolodi@science.unitn.it>
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81 suppr = floor(k);
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Daniele Nicolodi <nicolodi@science.unitn.it>
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82 else
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Daniele Nicolodi <nicolodi@science.unitn.it>
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83 n=0;
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Daniele Nicolodi <nicolodi@science.unitn.it>
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84 while k<1
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Daniele Nicolodi <nicolodi@science.unitn.it>
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85 k=k*10;
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Daniele Nicolodi <nicolodi@science.unitn.it>
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86 n=n+1;
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Daniele Nicolodi <nicolodi@science.unitn.it>
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87 end
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Daniele Nicolodi <nicolodi@science.unitn.it>
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88 k = floor(k);
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Daniele Nicolodi <nicolodi@science.unitn.it>
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89 suppr = k*10^(-n);
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Daniele Nicolodi <nicolodi@science.unitn.it>
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90 end
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Daniele Nicolodi <nicolodi@science.unitn.it>
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91
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Daniele Nicolodi <nicolodi@science.unitn.it>
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92 supmat = [1 0;0 suppr];
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Daniele Nicolodi <nicolodi@science.unitn.it>
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93 isupmat = [1 0;0 1/suppr];
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Daniele Nicolodi <nicolodi@science.unitn.it>
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94
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Daniele Nicolodi <nicolodi@science.unitn.it>
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95 % Core Calculation
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Daniele Nicolodi <nicolodi@science.unitn.it>
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96
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Daniele Nicolodi <nicolodi@science.unitn.it>
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97 switch method
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Daniele Nicolodi <nicolodi@science.unitn.it>
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98 case 'NUM'
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Daniele Nicolodi <nicolodi@science.unitn.it>
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99
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Daniele Nicolodi <nicolodi@science.unitn.it>
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100 % initializing output data
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Daniele Nicolodi <nicolodi@science.unitn.it>
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101 h11 = ones(npts,1);
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Daniele Nicolodi <nicolodi@science.unitn.it>
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102 h12 = ones(npts,1);
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Daniele Nicolodi <nicolodi@science.unitn.it>
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103 h21 = ones(npts,1);
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Daniele Nicolodi <nicolodi@science.unitn.it>
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104 h22 = ones(npts,1);
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Daniele Nicolodi <nicolodi@science.unitn.it>
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105
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Daniele Nicolodi <nicolodi@science.unitn.it>
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106 for phi = 1:npts
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Daniele Nicolodi <nicolodi@science.unitn.it>
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107
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Daniele Nicolodi <nicolodi@science.unitn.it>
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108 % Appliing suppression
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Daniele Nicolodi <nicolodi@science.unitn.it>
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109 PP = supmat*[S11(phi) S12(phi);S21(phi) S22(phi)]*supmat;
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Daniele Nicolodi <nicolodi@science.unitn.it>
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110
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Daniele Nicolodi <nicolodi@science.unitn.it>
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111 % Calculate eignevalues Matrix Lp
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Daniele Nicolodi <nicolodi@science.unitn.it>
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112 k = (4*PP(1,2)*PP(2,1))/((PP(1,1)-PP(2,2))^2);
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113
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Daniele Nicolodi <nicolodi@science.unitn.it>
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114 Lp1 = (PP(1,1)+PP(2,2)+(PP(1,1)-PP(2,2))*sqrt(1+k))/2;
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Daniele Nicolodi <nicolodi@science.unitn.it>
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115 Lp2 = (PP(1,1)+PP(2,2)-(PP(1,1)-PP(2,2))*sqrt(1+k))/2;
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Daniele Nicolodi <nicolodi@science.unitn.it>
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116
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Daniele Nicolodi <nicolodi@science.unitn.it>
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117 % Calculate eigenvectors Matrix Vp, eigenvectors are on the columns
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Daniele Nicolodi <nicolodi@science.unitn.it>
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118 Vp1 = (-1/sqrt(1+(k/((1+sqrt(1+k))^2))))*[1;2*PP(2,1)/((PP(1,1)-PP(2,2))*(1+sqrt(1+k)))];
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Daniele Nicolodi <nicolodi@science.unitn.it>
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119 Vp2 = (1/sqrt(1+(((1-sqrt(1+k))^2)/k)))*[(PP(1,1)-PP(2,2))*(1-sqrt(1+k))/(2*PP(2,1));1];
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Daniele Nicolodi <nicolodi@science.unitn.it>
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120
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Daniele Nicolodi <nicolodi@science.unitn.it>
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121 % Definition of the transfer functions
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Daniele Nicolodi <nicolodi@science.unitn.it>
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122 switch otp
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Daniele Nicolodi <nicolodi@science.unitn.it>
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123 case 'TF'
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Daniele Nicolodi <nicolodi@science.unitn.it>
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124 HH = isupmat*[conj(Vp1) conj(Vp2)]*[sqrt(Lp1) 0;0 sqrt(Lp2)];
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Daniele Nicolodi <nicolodi@science.unitn.it>
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125 case 'WF'
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Daniele Nicolodi <nicolodi@science.unitn.it>
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126 HH = [1/sqrt(Lp1) 0;0 1/sqrt(Lp2)]*inv([conj(Vp1) conj(Vp2)])*supmat;
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Daniele Nicolodi <nicolodi@science.unitn.it>
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127 end
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Daniele Nicolodi <nicolodi@science.unitn.it>
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128
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Daniele Nicolodi <nicolodi@science.unitn.it>
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129 h11(phi,1) = HH(1,1);
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Daniele Nicolodi <nicolodi@science.unitn.it>
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130 h12(phi,1) = HH(1,2);
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Daniele Nicolodi <nicolodi@science.unitn.it>
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131 h21(phi,1) = HH(2,1);
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Daniele Nicolodi <nicolodi@science.unitn.it>
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132 h22(phi,1) = HH(2,2);
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Daniele Nicolodi <nicolodi@science.unitn.it>
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133
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Daniele Nicolodi <nicolodi@science.unitn.it>
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134 end
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Daniele Nicolodi <nicolodi@science.unitn.it>
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135
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Daniele Nicolodi <nicolodi@science.unitn.it>
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136 case 'VPA'
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Daniele Nicolodi <nicolodi@science.unitn.it>
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137 % Define the numerical precision
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Daniele Nicolodi <nicolodi@science.unitn.it>
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138 digits(dig)
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Daniele Nicolodi <nicolodi@science.unitn.it>
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139
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Daniele Nicolodi <nicolodi@science.unitn.it>
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140 % initializing output data
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Daniele Nicolodi <nicolodi@science.unitn.it>
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141 h11 = vpa(ones(npts,1));
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Daniele Nicolodi <nicolodi@science.unitn.it>
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142 h12 = vpa(ones(npts,1));
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Daniele Nicolodi <nicolodi@science.unitn.it>
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143 h21 = vpa(ones(npts,1));
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Daniele Nicolodi <nicolodi@science.unitn.it>
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144 h22 = vpa(ones(npts,1));
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Daniele Nicolodi <nicolodi@science.unitn.it>
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145
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Daniele Nicolodi <nicolodi@science.unitn.it>
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146 SS11 = vpa(S11);
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Daniele Nicolodi <nicolodi@science.unitn.it>
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147 SS12 = vpa(S12);
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Daniele Nicolodi <nicolodi@science.unitn.it>
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148 SS21 = vpa(S21);
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Daniele Nicolodi <nicolodi@science.unitn.it>
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149 SS22 = vpa(S22);
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Daniele Nicolodi <nicolodi@science.unitn.it>
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150
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Daniele Nicolodi <nicolodi@science.unitn.it>
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151 for phi = 1:npts
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Daniele Nicolodi <nicolodi@science.unitn.it>
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152
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Daniele Nicolodi <nicolodi@science.unitn.it>
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153 % Appliing suppression
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Daniele Nicolodi <nicolodi@science.unitn.it>
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154 PP = supmat*[SS11(phi) SS12(phi);SS21(phi) SS22(phi)]*supmat;
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Daniele Nicolodi <nicolodi@science.unitn.it>
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155
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Daniele Nicolodi <nicolodi@science.unitn.it>
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156 % Calculate eignevalues Matrix Lp
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Daniele Nicolodi <nicolodi@science.unitn.it>
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157 k = (4*PP(1,2)*PP(2,1))/((PP(1,1)-PP(2,2))^2);
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Daniele Nicolodi <nicolodi@science.unitn.it>
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158
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Daniele Nicolodi <nicolodi@science.unitn.it>
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159 Lp1 = (PP(1,1)+PP(2,2)+(PP(1,1)-PP(2,2))*sqrt(1+k))/2;
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Daniele Nicolodi <nicolodi@science.unitn.it>
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160 Lp2 = (PP(1,1)+PP(2,2)-(PP(1,1)-PP(2,2))*sqrt(1+k))/2;
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Daniele Nicolodi <nicolodi@science.unitn.it>
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161
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Daniele Nicolodi <nicolodi@science.unitn.it>
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162 % Calculate eigenvectors Matrix Vp, eigenvectors are on the columns
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163 Vp1 = (-1/sqrt(1+(k/((1+sqrt(1+k))^2))))*[1;2*PP(2,1)/((PP(1,1)-PP(2,2))*(1+sqrt(1+k)))];
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164 Vp2 = (1/sqrt(1+(((1-sqrt(1+k))^2)/k)))*[(PP(1,1)-PP(2,2))*(1-sqrt(1+k))/(2*PP(2,1));1];
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165
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Daniele Nicolodi <nicolodi@science.unitn.it>
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166 % Definition of the transfer functions
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Daniele Nicolodi <nicolodi@science.unitn.it>
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167 switch otp
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Daniele Nicolodi <nicolodi@science.unitn.it>
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168 case 'TF'
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Daniele Nicolodi <nicolodi@science.unitn.it>
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169 HH = isupmat*[conj(Vp1) conj(Vp2)]*[sqrt(Lp1) 0;0 sqrt(Lp2)];
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Daniele Nicolodi <nicolodi@science.unitn.it>
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170 case 'WF'
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Daniele Nicolodi <nicolodi@science.unitn.it>
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171 HH = [1/sqrt(Lp1) 0;0 1/sqrt(Lp2)]*inv([conj(Vp1) conj(Vp2)])*supmat;
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Daniele Nicolodi <nicolodi@science.unitn.it>
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172 end
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Daniele Nicolodi <nicolodi@science.unitn.it>
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173
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Daniele Nicolodi <nicolodi@science.unitn.it>
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174 h11(phi,1) = HH(1,1);
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Daniele Nicolodi <nicolodi@science.unitn.it>
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175 h12(phi,1) = HH(1,2);
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Daniele Nicolodi <nicolodi@science.unitn.it>
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176 h21(phi,1) = HH(2,1);
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Daniele Nicolodi <nicolodi@science.unitn.it>
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177 h22(phi,1) = HH(2,2);
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178
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Daniele Nicolodi <nicolodi@science.unitn.it>
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179 end
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Daniele Nicolodi <nicolodi@science.unitn.it>
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180 h11 = double(h11);
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Daniele Nicolodi <nicolodi@science.unitn.it>
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181 h12 = double(h12);
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Daniele Nicolodi <nicolodi@science.unitn.it>
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182 h21 = double(h21);
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Daniele Nicolodi <nicolodi@science.unitn.it>
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183 h22 = double(h22);
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Daniele Nicolodi <nicolodi@science.unitn.it>
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184 end