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Update utils.jquery * * * Update utils.jmysql.getsinfo
author Daniele Nicolodi <nicolodi@science.unitn.it>
date Mon, 05 Dec 2011 16:20:06 +0100
parents f0afece42f48
children
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1 <!--
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2 <p>
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3 <ul>
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4 <li><a href="#description">Description</a></li>
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5 <li><a href="#call">Call</a></li>
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6 <li><a href="#inputs">Inputs</a></li>
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7 <li><a href="#outputs">Outputs</a></li>
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8 <li><a href="#algorithm">Algorithm</a></li>
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9 <li><a href="#parameters">Parameters</a></li>
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10 </ul>
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11 </p>
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12 -->
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13 <h2><a name="description">Description</a></h2>
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14
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15 <p>
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16 whiten2D whitens cross-correlated time-series. Whitening filters are constructed
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17 by a fitting procedure to the corss-spectrum models provided.
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18 Note: The function assumes that the input model corresponds
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19 to the one-sided csd of the data to be whitened.
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20 </p>
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21
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22 <h2><a name="call">Call</a></h2>
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23 <div class="fragment">
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24 <pre>
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25 b = whiten2D(a, pl)
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26 [b1,b2] = whiten2D(a1, a2, pl)
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27 [b1,b2,...,bn] = whiten2D(a1,a2,...,an, pl);
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28 </pre>
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29 </div>
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30 <p>
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31 <ul>
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32 <li> Note1: input AOs must come in couples.
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33 <li> Note2: this method cannot be used as a modifier, the
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34 call <tt> a.whiten2D(pl) </tt> is forbidden.
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35 </ul>
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36 </p>
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37
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38
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39 <h2><a name="inputs">Inputs</a></h2>
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40
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41 <p>
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42 <ul>
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43 <li> a is at least a couple of time series analysis objects
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44 <li> pl is a parameter list, see the list of accepted parameters below
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45 </ul>
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46 </p>
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47
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48
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49 <h2><a name="outputs">Outputs</a></h2>
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50 <p>
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51 <ul>
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52 <li> b is at least a couple of "whitened" time-series AOs. The whitening
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53 filters used are stored in the objects procinfo field as.
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54 <ul>
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55 <li> b(1): 'Filt11' and 'Filt12'
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56 <li> b(2): 'Filt21' and 'Filt22'
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57 </ul>
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58 </ul>
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59 </p>
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60
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61
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62 <h2><a name="algorithm">Algorithm</a></h2>
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63
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64 <p>
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65 <ol>
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66 <li> Fit a set of partial fraction z-domain filters using
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67 utils.math.psd2wf
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68 <li> Convert to bank of mIIR filters
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69 <li> Filter time-series in parallel
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70 The filtering process is: <br/>
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71 b(1) = Filt11(a(1)) + Filt12(a(2)) <br/>
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72 b(2) = Filt21(a(1)) + Filt22(a(2))
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73 </ol>
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74 </p>
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75
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76
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77
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78 <h2><a name="parameters">Parameters</a></h2>
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79
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80 <p>
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81 <ul>
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82 <li> 'csd11' - a frequency-series AO describing the model csd11
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83 <li> 'csd12' - a frequency-series AO describing the model csd12
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84 <li> 'csd21' - a frequency-series AO describing the model csd21
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85 <li> 'csd22' - a frequency-series AO describing the model csd22
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86 <li> 'MaxIter' - Maximum number of iterations in fit routine
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87 [default: 30]
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88 <li> 'PoleType' - Choose the pole type for fitting:
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89 <ul>
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90 <li> 1 - use real starting poles.
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91 <li> 2 - generates complex conjugate poles of the
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92 type a.*exp(theta*pi*j)
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93 with theta = linspace(0,pi,N/2+1).
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94 <li> 3 - generates complex conjugate poles of the type
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95 a.*exp(theta*pi*j)
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96 with theta = linspace(0,pi,N/2+2) [default].
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97 </ul>
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98 </li>
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99 <li> 'MinOrder' - Minimum order to fit with. [default: 2].
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100 <li> 'MaxOrder' - Maximum order to fit with. [default: 25]
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101 <li> 'Weights' - choose weighting for the fit: [default: 2]
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102 <ul>
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103 <li> 1 - equal weights for each point.
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104 <li> 2 - weight with 1/abs(model).
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105 <li> 3 - weight with 1/abs(model).^2.
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106 <li> 4 - weight with inverse of the square mean spread of the model.
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107 </ul>
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108 </li>
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109 <li> 'Plot' - plot results of each fitting step. [default: false]
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110 <li> 'Disp' - Display the progress of the fitting iteration.
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111 [default: false]
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112 <li> 'FitTolerance' - Log Residuals difference check if the minimum
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113 of the logarithmic difference between data and
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114 residuals is larger than a specified value.
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115 ie. if the conditioning value is 2, the
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116 function ensures that the difference between
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117 data and residuals is at lest 2 order of
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118 magnitude lower than data itsleves. [default: 2].
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119 <li> 'RMSEVar' - Root Mean Squared Error Variation - Check if the
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120 variation of the RMS error is smaller than 10^(-b),
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121 where b is the value given to the variable. This
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122 option is useful for finding the minimum of Chi
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123 squared. [default: 7].
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124 <li> 'UseSym' - Use symbolic calculation in eigendecomposition. [default: 0]
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125 <ul>
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126 <li> 0 - perform double-precision calculation in the
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127 eigendecomposition procedure to identify 2dim
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128 systems and for poles stabilization
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129 <li> 1 - uses symbolic math toolbox variable precision
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130 arithmetic in the eigendecomposition for 2dim
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131 system identification and double-precison for
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132 poles stabilization
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133 <li> 2 - uses symbolic math toolbox variable precision
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134 arithmetic in the eigendecomposition for 2dim
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135 system identification and for poles
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136 stabilization
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137 </ul>
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138 </li>
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139 </ul>
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140 </p>
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141
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