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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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1
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2
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3 <p>
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4 <ul>
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Daniele Nicolodi <nicolodi@science.unitn.it>
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5 <li><a href="#description">Description</a></li>
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6 <li><a href="#call">Call</a></li>
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7 <li><a href="#inputs">Inputs</a></li>
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8 <li><a href="#outputs">Outputs</a></li>
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9 <li><a href="#algorithm">Algorithm</a></li>
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10 <li><a href="#parameters">Parameters</a></li>
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11 </ul>
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12 </p>
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13
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14 <h2><a name="description">Description</a></h2>
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15
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16 <p>
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Daniele Nicolodi <nicolodi@science.unitn.it>
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17 noisegen2D generates colored noise from withe noise with a
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18 given cross spectrum. The coloring filter is constructed by a fitting procedure to the
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19 models provided. If no model is provided an error is
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20 prompted. The cross-spectral matrix is assumed to be
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21 frequency by frequency of the type:
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22 </p>
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23 <div class="fragment"><pre>
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24
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25 / csd11(f) csd12(f) \
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26 CSD(f) = | |
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27 \ csd21(f) csd22(f) /
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28
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29 </pre></div>
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30 <p>
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31 Note: The function output colored noise data with one-sided
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32 cross spectral density corresponding to the model provided.
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33 </p>
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34
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35 <h2><a name="call">Call</a></h2>
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36 <div class="fragment">
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37 <pre>
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38 b = noisegen2D(a, pl)
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39 [b1,b2] = noisegen2D(a1, a2, pl)
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40 [b1,b2,...,bn] = noisegen2D(a1,a2,...,an, pl);
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41 </pre>
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42 </div>
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43 <p>
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44 <ul>
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Daniele Nicolodi <nicolodi@science.unitn.it>
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45 <li> Note1: input AOs must come in couples.
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46 <li> Note2: this method cannot be used as a modifier, the
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47 call <tt> a.noisegen2D(pl) </tt> is forbidden.
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48 </ul>
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49 </p>
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50
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51
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52 <h2><a name="inputs">Inputs</a></h2>
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53
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54 <p>
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55 <ul>
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Daniele Nicolodi <nicolodi@science.unitn.it>
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56 <li> a is at least a couple of time series analysis objects
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Daniele Nicolodi <nicolodi@science.unitn.it>
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57 <li> pl is a parameter list, see the list of accepted parameters below
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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="outputs">Outputs</a></h2>
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63 <p>
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64 <ul>
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65 <li> b are a couple of colored time-series AOs. The coloring
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66 filters used are stored in the objects procinfo field under
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67 the parameters:
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68 <ul>
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69 <li> b(1): 'Filt11' and 'Filt12'
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70 <li> b(2): 'Filt21' and 'Filt22'
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71 </ul>
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72 </ul>
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73 </p>
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74
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75
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76 <h2><a name="algorithm">Algorithm</a></h2>
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77
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78 <p>
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79 <ol>
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80 <li> Fit a set of partial fraction z-domain filters using
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81 utils.math.psd2tf
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82 <li> Convert to bank of mIIR filters
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83 <li> Filter time-series in parallel
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84 The filtering process is: <br/>
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85 b(1) = Filt11(a(1)) + Filt12(a(2)) <br/>
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86 b(2) = Filt21(a(1)) + Filt22(a(2))
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87 </ol>
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88 </p>
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89
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90
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91
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92 <h2><a name="parameters">Parameters</a></h2>
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93
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94 <p>
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95 <ul>
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96 <li> 'csd11' - a frequency-series AO describing the model csd11
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Daniele Nicolodi <nicolodi@science.unitn.it>
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97 <li> 'csd12' - a frequency-series AO describing the model csd12
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98 <li> 'csd21' - a frequency-series AO describing the model csd21
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99 <li> 'csd22' - a frequency-series AO describing the model csd22
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100 <li> 'MaxIter' - Maximum number of iterations in fit routine
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101 [default: 30]
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102 <li> 'PoleType' - Choose the pole type for fitting:
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103 <ul>
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104 <li> 1 - use real starting poles.
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105 <li> 2 - generates complex conjugate poles of the
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106 type a.*exp(theta*pi*j)
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107 with theta = linspace(0,pi,N/2+1).
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108 <li> 3 - generates complex conjugate poles of the type
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109 a.*exp(theta*pi*j)
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110 with theta = linspace(0,pi,N/2+2) [default].
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111 </ul>
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112 </li>
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113 <li> 'MinOrder' - Minimum order to fit with. [default: 2].
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114 <li> 'MaxOrder' - Maximum order to fit with. [default: 25]
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115 <li> 'Weights' - choose weighting for the fit: [default: 2]
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116 <ul>
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117 <li> 1 - equal weights for each point.
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118 <li> 2 - weight with 1/abs(model).
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119 <li> 3 - weight with 1/abs(model).^2.
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120 <li> 4 - weight with inverse of the square mean spread of the model.
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121 </ul>
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122 </li>
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123 <li> 'Plot' - plot results of each fitting step. [default: false]
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124 <li> 'Disp' - Display the progress of the fitting iteration.
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125 [default: false]
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126 <li> 'FitTolerance' - Log Residuals difference check if the minimum
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127 of the logarithmic difference between data and
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128 residuals is larger than a specified value.
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129 ie. if the conditioning value is 2, the
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130 function ensures that the difference between
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131 data and residuals is at lest 2 order of
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132 magnitude lower than data itsleves. [default: 2].
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133 <li> 'RMSEVar' - Root Mean Squared Error Variation - Check if the
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134 variation of the RMS error is smaller than 10^(-b),
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135 where b is the value given to the variable. This
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136 option is useful for finding the minimum of Chi
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Daniele Nicolodi <nicolodi@science.unitn.it>
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137 squared. [default: 7].
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Daniele Nicolodi <nicolodi@science.unitn.it>
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138 <li> 'UseSym' - Use symbolic calculation in eigendecomposition. [default: 0]
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139 <ul>
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140 <li> 0 - perform double-precision calculation in the
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Daniele Nicolodi <nicolodi@science.unitn.it>
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141 eigendecomposition procedure to identify 2dim
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142 systems and for poles stabilization
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Daniele Nicolodi <nicolodi@science.unitn.it>
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143 <li> 1 - uses symbolic math toolbox variable precision
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Daniele Nicolodi <nicolodi@science.unitn.it>
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144 arithmetic in the eigendecomposition for 2dim
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Daniele Nicolodi <nicolodi@science.unitn.it>
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145 system identification and double-precison for
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Daniele Nicolodi <nicolodi@science.unitn.it>
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146 poles stabilization
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Daniele Nicolodi <nicolodi@science.unitn.it>
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147 <li> 2 - uses symbolic math toolbox variable precision
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Daniele Nicolodi <nicolodi@science.unitn.it>
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148 arithmetic in the eigendecomposition for 2dim
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Daniele Nicolodi <nicolodi@science.unitn.it>
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149 system identification and for poles
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150 stabilization
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151 </ul>
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152 </li>
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153 </ul>
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154 </p>