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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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Daniele Nicolodi <nicolodi@science.unitn.it>
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1 % IIRINIT defines the initial state of an IIR filter.
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2 %
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Daniele Nicolodi <nicolodi@science.unitn.it>
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3 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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4 %
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Daniele Nicolodi <nicolodi@science.unitn.it>
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5 % DESCRIPTION
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6 %
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Daniele Nicolodi <nicolodi@science.unitn.it>
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7 % iirinit define initial states for an IIR filter finding for the
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Daniele Nicolodi <nicolodi@science.unitn.it>
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8 % steady state solution of the state quations in state-space
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Daniele Nicolodi <nicolodi@science.unitn.it>
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9 % representation.
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10 %
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11 % CALL:
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12 %
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13 % zi = iirinit(a,b)
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14 %
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15 % INPUT:
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16 %
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17 % a coefficients vector for the numerator
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18 % b coefficients vector for the denominator
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19 %
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20 %
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21 % OUTPUT:
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22 %
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23 % zi vector of filter initial states
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24 %
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25 % NOTE:
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26 %
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27 % zi has to be multiplied by the first value of the time series to be
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Daniele Nicolodi <nicolodi@science.unitn.it>
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28 % filtered and then can be passed to filter as initial conditions. e.g.
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29 % [Y,Zf] = FILTER(a,b,X,zi*X(1))
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30 %
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Daniele Nicolodi <nicolodi@science.unitn.it>
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31 % REFERENCES:
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32 %
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33 % [1] Autar K Kaw, Introduction to Matrix Algebra,
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34 % http://autarkaw.com/books/matrixalgebra/index.html,
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35 %
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36 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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37 % VERSION: $Id: iirinit.m,v 1.3 2008/12/19 14:44:08 luigi Exp $
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38 %
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Daniele Nicolodi <nicolodi@science.unitn.it>
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39 % HISTORY: 08-10-2008 L Ferraioli
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Daniele Nicolodi <nicolodi@science.unitn.it>
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40 % Creation
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41 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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42
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43 function zi = iirinit(a,b)
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44
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45 na = length(a); % a is numerator
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46 nb = length(b); % b is denominator
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47 nfilt = max(nb,na);
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48
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49 % Whant to deal with columns
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50 if size(a,2)>1
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51 a = a.';
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52 end
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53 if size(b,2)>1
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54 b = b.';
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55 end
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56
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57 if nb < nfilt % zero padding if necessary
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58 b = [b; zeros(nfilt-nb,1)];
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59 end
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60 if na < nfilt % zero padding if necessary
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61 a = [a; zeros(nfilt-na,1)];
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62 end
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63
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64 A = eye(nfilt-1) - [-b(2:end,1) [eye(nfilt-2);zeros(1,nfilt-2)]];
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65 B = a(2:end,1) - b(2:end,1).*a(1);
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66
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67 % Checking for the conditioning of A.
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68 % cond(A)*eps gives the value of the possible relative error in the
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69 % solution vector. E.g. if cond(A)*eps < 1e-3 the solution can be
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70 % considered accurate to the third significant digit [1]
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71 knum = cond(A)*eps('double');
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72 if knum>1e-3
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73 warning('MATLAB:illcondsysmatrix','Condition number of the system matrix is larger than 1e-3/eps. Filter initial state will be set to zero.')
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74 zi = zeros(max(na,nb)-1,1);
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75 else
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76 zi = A\B;
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77 end
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78
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79 nfi = isinf(zi);
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80 zi(nfi) = 0;
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81
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82 nnn = isnan(zi);
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83 zi(nnn) = 0;
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84
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85 end
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86
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