Mercurial > hg > ltpda

annotate m-toolbox/classes/+utils/@math/pfallpsyms.m @ 24:056f8e1e995e database-connection-manager

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author Daniele Nicolodi <nicolodi@science.unitn.it>
date Mon, 05 Dec 2011 16:20:06 +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 %
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Daniele Nicolodi <nicolodi@science.unitn.it>
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2 % DESCRIPTION:
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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 % All pass filtering in order to stabilize transfer function poles and
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Daniele Nicolodi <nicolodi@science.unitn.it>
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5 % zeros. It inputs a partial fraction expanded continuous model and
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Daniele Nicolodi <nicolodi@science.unitn.it>
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6 % outputs a pole-zero minimum phase system
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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>
parents:
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8 % CALL:
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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9 %
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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10 % [nr,np,nd,resp] = pfallpsyms(r,p,d,f)
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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 % INPUTS:
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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>
parents:
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14 % r: are residues
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Daniele Nicolodi <nicolodi@science.unitn.it>
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15 % p: are poles
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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16 % d: is direct term
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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17 % f: is the frequancies vector in (Hz)
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Daniele Nicolodi <nicolodi@science.unitn.it>
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18 % fs: is the sampling frequency in (Hz)
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Daniele Nicolodi <nicolodi@science.unitn.it>
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19 %
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Daniele Nicolodi <nicolodi@science.unitn.it>
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20 % OUTPUTS:
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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21 %
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Daniele Nicolodi <nicolodi@science.unitn.it>
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22 % resp: is the minimum phase frequency response
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Daniele Nicolodi <nicolodi@science.unitn.it>
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23 % np: are the new stable poles
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Daniele Nicolodi <nicolodi@science.unitn.it>
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24 % nz: are the new stable zeros
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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 % NOTE:
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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27 %
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Daniele Nicolodi <nicolodi@science.unitn.it>
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28 % This function make use of symbolic math toolbox functions
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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 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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31 % VERSION: '$Id: pfallpsyms.m,v 1.3 2008/11/10 15:40:11 luigi Exp $';
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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>
parents:
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33 % HISTORY: 12-09-2008 L Ferraioli
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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34 % Creation
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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>
parents:
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36 function [nr,np,nd,nmresp] = pfallpsyms(r,p,d,f)
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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37
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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38 % Reshaping
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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39 [a,b] = size(r);
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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40 if a<b
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Daniele Nicolodi <nicolodi@science.unitn.it>
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41 r = r.'; % reshape as a column vector
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Daniele Nicolodi <nicolodi@science.unitn.it>
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42 end
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Daniele Nicolodi <nicolodi@science.unitn.it>
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43
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Daniele Nicolodi <nicolodi@science.unitn.it>
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44 [a,b] = size(p);
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Daniele Nicolodi <nicolodi@science.unitn.it>
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45 if a<b
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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46 p = p.'; % reshape as a column vector
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Daniele Nicolodi <nicolodi@science.unitn.it>
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47 end
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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 [a,b] = size(f);
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Daniele Nicolodi <nicolodi@science.unitn.it>
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50 if a<b
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Daniele Nicolodi <nicolodi@science.unitn.it>
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51 f = f.'; % reshape as a column vector
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Daniele Nicolodi <nicolodi@science.unitn.it>
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52 end
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Daniele Nicolodi <nicolodi@science.unitn.it>
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53
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Daniele Nicolodi <nicolodi@science.unitn.it>
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54 [a,b] = size(d);
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Daniele Nicolodi <nicolodi@science.unitn.it>
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55 if a ~= b
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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56 disp(' Function can handle only single constant direct terms. Only first term will be considered! ')
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Daniele Nicolodi <nicolodi@science.unitn.it>
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57 d = d(1);
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Daniele Nicolodi <nicolodi@science.unitn.it>
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58 end
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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59
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Daniele Nicolodi <nicolodi@science.unitn.it>
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60 if isempty(d)
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Daniele Nicolodi <nicolodi@science.unitn.it>
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61 d = 0;
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Daniele Nicolodi <nicolodi@science.unitn.it>
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62 end
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Daniele Nicolodi <nicolodi@science.unitn.it>
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63
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Daniele Nicolodi <nicolodi@science.unitn.it>
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64 % digits(100)
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Daniele Nicolodi <nicolodi@science.unitn.it>
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65 % Defining inputs as symbolic variable
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Daniele Nicolodi <nicolodi@science.unitn.it>
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66 r = sym(r,'f');
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Daniele Nicolodi <nicolodi@science.unitn.it>
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67 p = sym(p,'f');
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Daniele Nicolodi <nicolodi@science.unitn.it>
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68 d = sym(d,'f');
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Daniele Nicolodi <nicolodi@science.unitn.it>
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69 f = sym(f,'f');
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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70 syms z
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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71
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Daniele Nicolodi <nicolodi@science.unitn.it>
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72 % Function gain coefficient
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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73 if double(d) == 0
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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74 k = sum(r);
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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75 else
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Daniele Nicolodi <nicolodi@science.unitn.it>
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76 k = d;
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Daniele Nicolodi <nicolodi@science.unitn.it>
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77 end
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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 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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Daniele Nicolodi <nicolodi@science.unitn.it>
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80 f = sym(f,'f');
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Daniele Nicolodi <nicolodi@science.unitn.it>
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81 syms z
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Daniele Nicolodi <nicolodi@science.unitn.it>
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82 p = sym(p,'f');
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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83
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Daniele Nicolodi <nicolodi@science.unitn.it>
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84 % stabilize poles
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Daniele Nicolodi <nicolodi@science.unitn.it>
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85 sp = p;
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Daniele Nicolodi <nicolodi@science.unitn.it>
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86 unst = abs(double(sp)) > 1;
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Daniele Nicolodi <nicolodi@science.unitn.it>
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87 sp(unst) = 1./conj(sp(unst));
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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88 skp = prod(1./conj(p(unst)));
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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89
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Daniele Nicolodi <nicolodi@science.unitn.it>
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90 [Na,Nb] = size(r);
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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91
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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92 for nn = 1:Nb
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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93
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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94 % digits(100)
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Daniele Nicolodi <nicolodi@science.unitn.it>
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95 % Defining inputs as symbolic variable
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Daniele Nicolodi <nicolodi@science.unitn.it>
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96 rt = sym(r(:,nn),'f');
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Daniele Nicolodi <nicolodi@science.unitn.it>
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97 % p = sym(p,'f');
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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98 dt = sym(d(1,nn),'f');
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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99 % f = sym(f,'f');
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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100 % fs = sym(fs,'f');
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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101 % syms z
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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 % Function gain coefficient
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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104 if double(d) == 0
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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105 k = sum(r);
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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106 else
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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107 k = d;
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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108 end
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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109
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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110 Np = length(p);
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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111
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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112 % Defining the symbolic transfer function
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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113 vter = rt./(z-p);
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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114 vter = [vter; dt];
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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115 Mter = diag(vter);
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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116 H = trace(Mter);
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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117
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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118 % Factorizing the transfer function
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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119 HH = factor(H);
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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 % Extracting numerator and denominator
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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122 [N,D] = numden(HH);
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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123
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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124 % Symbolci calculation of function zeros
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Daniele Nicolodi <nicolodi@science.unitn.it>
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125 cN = coeffs(expand(N),z);
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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126 n = length(cN);
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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127 cN2 = -1.*cN(2:end)./cN(1);
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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128 A = sym(diag(ones(1,n-2),-1));
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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129 A(1,:) = cN2;
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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130 zrs = eig(A);
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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131 % if double(d) == 0
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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132 % zrs = [zrs; sym(0,'f')];
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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133 % end
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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134
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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135 if isempty(skp)
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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136 skp = sym(1,'f');
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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137 end
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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138 if isempty(k)
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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139 k = sym(1,'f');
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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140 end
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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141
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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142 % Calculating new gain
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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143 % sk = real(k*skz*skp);
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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144 sk = real(k*skp);
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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145
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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146 HHHn = sym(1,'f');
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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147
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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148 for ii = 1:length(zrs)
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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149 HHHn = HHHn.*(z-zrs(ii));
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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150 end
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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151 for jj = 1:Np
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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152 tsp = sp;
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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153 tsp(jj) = [];
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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154 tHHHd = sym(1,'f');
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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155 for kk = 1:Np-1
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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156 tHHHd = tHHHd.*(z-tsp(kk));
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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157 end
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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158 HHHd(jj,1) = tHHHd;
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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159
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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160 end
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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161
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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162 for jj = 1:Np
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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163 sr(jj,1) = subs(sk*HHHn/(z*HHHd(jj,1)),z,sp(jj));
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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164 end
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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165
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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166 np = double(sp);
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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167 for kk = 1:Np
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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168 if imag(np(kk)) == 0
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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169 sr(kk) = real(sr(kk));
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170 end
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171 end
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172
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173 nr(:,nn) = double(sr);
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174 nd(:,nn) = double(dt);
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175
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176 % Model evaluation
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177 pfparams.type = 'cont';
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178 pfparams.freq = f;
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179 pfparams.res = nr(:,nn);
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180 pfparams.pol = np;
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181 pfparams.dterm = nd(:,nn);
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182 pfr = utils.math.pfresp(pfparams);
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183 resp = pfr.resp;
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184
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185 ratio = mean(abs(mresp(:,nn))./abs(resp));
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Daniele Nicolodi <nicolodi@science.unitn.it>
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186 resp = resp.*ratio;
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187 nr(:,nn) = nr(:,nn).*ratio;
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188 nd(:,nn) = nd(:,nn).*ratio;
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189 nmresp(:,nn) = resp;
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190
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191 end