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Fix. Default password should be [] not an empty string
author Daniele Nicolodi <nicolodi@science.unitn.it>
date Wed, 07 Dec 2011 17:29:47 +0100
parents f0afece42f48
children
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Daniele Nicolodi <nicolodi@science.unitn.it>
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1
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2 <p>
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3 <ul>
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Daniele Nicolodi <nicolodi@science.unitn.it>
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4 <li><a href="#description">Description</a></li>
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Daniele Nicolodi <nicolodi@science.unitn.it>
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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 <li><a href="#example">Example</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 noisegen1D is a coloring tool allowing the generation of colored noise from withe noise with a given spectrum.
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Daniele Nicolodi <nicolodi@science.unitn.it>
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18 The function constructs a coloring filter through a fitting procedure to the model provided.
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Daniele Nicolodi <nicolodi@science.unitn.it>
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19 If no model is provided an error is prompted. The colored noise provided has one-sided psd
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20 corresponding to the input model.
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21 </p>
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22
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23 <h2><a name="call">Call</a></h2>
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24 <div class="fragment">
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25 <pre>
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26 b = noisegen1D(a, pl);
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27 [b1,b2,...,bn] = noisegen1D(a1,a2,...,an, pl);
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28 </pre>
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29 </div>
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30
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31 <h2><a name="inputs">Inputs</a></h2>
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32
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33 <p>
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34 <ul>
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Daniele Nicolodi <nicolodi@science.unitn.it>
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35 <li> a - is a tsdata analysis object or a vector of tsdata analysis objects
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Daniele Nicolodi <nicolodi@science.unitn.it>
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36 <li> pl - is a plist with the input parameters. See the list of function parameters below
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Daniele Nicolodi <nicolodi@science.unitn.it>
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37 </ul>
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38 </p>
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39
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40 <h2><a name="outputs">Outputs</a></h2>
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41
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42 <p>
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43 <ul>
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44 <li> b - Colored time-series AOs. The coloring filters used
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45 are stored in the objects procinfo field under the
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Daniele Nicolodi <nicolodi@science.unitn.it>
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46 parameter 'Filt'.
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47 </ul>
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48 </p>
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49
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50 <h2><a name="algorithm">Algorithm</a></h2>
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51
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52 <p>
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53 <ol>
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Daniele Nicolodi <nicolodi@science.unitn.it>
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54 <li> Fit a set of partial fraction z-domain filters using utils.math.psd2tf.
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55 <li> Convert to array of MIIR filters.
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Daniele Nicolodi <nicolodi@science.unitn.it>
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56 <li> Filter time-series in parallel.
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57 </ol>
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58 </p>
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59
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60 <h2><a name="parameters">Parameters</a></h2>
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61 <p>
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62 <ul>
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Daniele Nicolodi <nicolodi@science.unitn.it>
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63 <li> 'Model' - a frequency-series AO describing the model psd.
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64 <li> 'MaxIter' - Maximum number of iterations in fit routine
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65 [default: 30]
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66 <li> 'PoleType' - Choose the pole type for fitting:
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67 <ul>
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68 <li> 1 - use real starting poles.
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69 <li> 2 - generates complex conjugate poles of the
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Daniele Nicolodi <nicolodi@science.unitn.it>
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70 type a.*exp(theta*pi*j)
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Daniele Nicolodi <nicolodi@science.unitn.it>
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71 with theta = linspace(0,pi,N/2+1).
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72 <li> 3 - generates complex conjugate poles of the type
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73 a.*exp(theta*pi*j)
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Daniele Nicolodi <nicolodi@science.unitn.it>
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74 with theta = linspace(0,pi,N/2+2) [default].
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Daniele Nicolodi <nicolodi@science.unitn.it>
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75 </ul>
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76 </li>
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77 <li> 'MinOrder' - Minimum order to fit with. [default: 2].
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78 <li> 'MaxOrder' - Maximum order to fit with. [default: 25]
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79 <li> 'Weights' - choose weighting for the fit: [default: 2]
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80 <ul>
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81 <li> 1 - equal weights for each point.
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82 <li> 2 - weight with 1/abs(model).
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83 <li> 3 - weight with 1/abs(model).^2.
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84 <li> 4 - weight with inverse of the square mean spread of the model.
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85 </ul>
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86 </li>
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87 <li> 'Plot' - plot results of each fitting step. [default: false]
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88 <li> 'Disp' - Display the progress of the fitting iteration.
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89 [default: false]
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90 <li> 'FitTolerance' - Log Residuals difference - Check if the minimum
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Daniele Nicolodi <nicolodi@science.unitn.it>
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91 of the logarithmic difference between data and
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Daniele Nicolodi <nicolodi@science.unitn.it>
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92 residuals is larger than a specified value.
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93 ie. if the conditioning value is 2, the
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94 function ensures that the difference between
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95 data and residuals is at lest 2 order of
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96 magnitude lower than data itsleves. [Default: 2].
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97 <li> 'RMSEVar' - Root Mean Squared Error Variation - Check if the
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98 variation of the RMS error is smaller than 10^(-b),
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Daniele Nicolodi <nicolodi@science.unitn.it>
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99 where b is the value given to the variable. This
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100 option is useful for finding the minimum of Chi
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Daniele Nicolodi <nicolodi@science.unitn.it>
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101 squared. [default: 7].
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102 </ul>
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103 </p>
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104
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105 <h2><a name="example">Example</a></h2>
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106
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107 <div class="fragment">
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108 <pre>
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109 %% Noise generation from fsdata model object %%%%%%%%%%%%%%%%%%%%%%%%%%%
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110
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111 % Description:
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Daniele Nicolodi <nicolodi@science.unitn.it>
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112 % 1) Generate a fsdata object to be used as psd model
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Daniele Nicolodi <nicolodi@science.unitn.it>
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113 % 2) Generate a random series of data (white)
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Daniele Nicolodi <nicolodi@science.unitn.it>
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114 % 3) Generate colored noise with noisegen1D
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115 % 4) calculated psd of generated data
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116 % 5) check result by plotting
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117
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118 % 1)
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119 fs = 10; % sampling frequency
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120 pl_mod1 = plist('fsfcn', '0.01./(0.01+f)', 'f1', 1e-6, 'f2', 5, 'nf', 100);
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121 mod1 = ao(pl_mod1); % fsdata model object
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122
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123 % 2)
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124 % generating white noise
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125 a1 = ao(plist('tsfcn', 'randn(size(t))', 'fs', fs, 'nsecs', 1000));
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126
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127 % 3) Noise generation
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128
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129 pl1 = plist(...
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130 'model', mod1, ...
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131 'MaxIter', 30, ...
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Daniele Nicolodi <nicolodi@science.unitn.it>
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132 'PoleType', 2, ...
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133 'MinOrder', 10, ...
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134 'MaxOrder', 20, ...
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Daniele Nicolodi <nicolodi@science.unitn.it>
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135 'Weights', 2, ...
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136 'Plot', false,...
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Daniele Nicolodi <nicolodi@science.unitn.it>
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137 'Disp', false,...
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Daniele Nicolodi <nicolodi@science.unitn.it>
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138 'RMSEVar', 5,...
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Daniele Nicolodi <nicolodi@science.unitn.it>
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139 'FitTolerance', 2);
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140
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141 ac1 = noisegen1D(a1, pl1);
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142
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143 % 4)
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144 acxx1 = ac1.psd;
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145 % 5)
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146 iplot(acxx1, mod1);
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147 </pre>
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148 </div>
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149
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150 <p>
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151 <div align="center">
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152 <IMG src="images/ng1D_1.png" width="800" height="600" align="center" border="0">
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153 </div>
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154 </p>
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155
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163
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
164
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
165