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Update ao_model_retrieve_in_timespan
author Daniele Nicolodi <nicolodi@science.unitn.it>
date Mon, 05 Dec 2011 16:20:06 +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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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 <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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17 whiten1D whitens input time-series. Whitening filter is constructed
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Daniele Nicolodi <nicolodi@science.unitn.it>
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18 by a fitting procedure to the model provided. If no model is provided, a
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19 fit is made to a log-spectral-density estimate of the
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20 time-series (made using lpsd).
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21 Note: The function assumes that the input model corresponds
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22 to the one-sided psd of the data to be whitened.
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23 </p>
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24
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25 <h2><a name="call">Call</a></h2>
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26 <div class="fragment">
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27 <pre>
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28 <br>
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29 b = whiten1D(a, pl)
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30 [b1,b2,...,bn] = whiten1D(a1,a2,...,an, pl);
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31 </pre>
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32 </div>
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33
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34 <h2><a name="inputs">Inputs</a></h2>
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35
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36 <p>
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37 <ul>
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Daniele Nicolodi <nicolodi@science.unitn.it>
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38 <li> a - is a tsdata analysis object or a vector of tsdata analysis objects
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39 <li> pl - is a plist with the input parameters. See the list of function parameters below
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40 </ul>
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41 </p>
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42
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43 <h2><a name="outputs">Outputs</a></h2>
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44
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45 <p>
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46 <ul>
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47 <li> b "whitened" time-series AOs. The whitening filters used
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48 are stored in the objects procinfo field under the
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49 parameter 'Filt'.
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50 </ul>
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51 </p>
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52
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53 <h2><a name="algorithm">Algorithm</a></h2>
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54
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55 <p>
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56 <ol>
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Daniele Nicolodi <nicolodi@science.unitn.it>
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57 <li> If no model provided, make lpsd of time-series and take it
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58 as a model for the data power spectral density
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59 <li> Fit a set of partial fraction z-domain filters using
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60 utils.math.psd2wf. The fit is automatically stopped when
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61 the accuracy tolerance is reached.
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62 <li> Convert to bank of MIIR filters.
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63 <li> Filter time-series in parallel
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64 </ol>
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65 </p>
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66 <p>
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67 Accuracy tolerance criteria
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68 <ul>
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69 <li> No model provided <br/>
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70 In such a case the algorithm try to extract a smooth model
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71 from lpsd noisy data. Fit residuals spectral flatness is
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72 compared with the 'FitTolerance' parameter. Fit is stopped
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73 when residuals spectral flatness is larger than the
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74 'FitTolerance' parameter. Admitted values are 0 < tol < 1.
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75 Recommended values are 0.5 < tol < 0.7. If out of range values
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76 are provided the parameter is set to 0.5.
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77 <li> Model provided <br/>
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78 In such a case the algorithm try to exactly fit the input
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79 model whitin the accuracy reported in 'FitTolerance'. Check
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80 if the minimum of the logarithmic difference between data
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81 and residuals is larger than a specified value.
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82 Admitted values are tol>0. Recommended values are
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83 0.5 < tol < 2. if the conditioning value is 2, the function
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84 ensures that the difference between data and residuals is
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85 at lest 2 order of magnitude lower than data itsleves. If a
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86 negative value is provided the tolerance is set to 1.
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87 </ul>
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88 </p>
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89
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90
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91 <h2><a name="parameters">Parameters</a></h2>
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92 <p>
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93 <ul>
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94 <li> 'Model' - a frequency-series AO describing the model
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95 response to build the filter from. [default: lpsd
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96 of time-series].
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97 <li> 'MaxIter' - Maximum number of iterations in fit routine
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98 [default: 30]
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99 <li> 'PoleType' - Choose the pole type for fitting:
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100 <ul>
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101 <li> 1 - use real starting poles.
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102 <li> 2 - generates complex conjugate poles of the
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103 type a.*exp(theta*pi*j)
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104 with theta = linspace(0,pi,N/2+1).
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105 <li> 3 - generates complex conjugate poles of the type
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106 a.*exp(theta*pi*j)
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107 with theta = linspace(0,pi,N/2+2) [default].
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108 </ul>
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109 </li>
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110 <li> 'MinOrder' - Minimum order to fit with. [default: 2].
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111 <li> 'MaxOrder' - Maximum order to fit with. [default: 25]
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112 <li> 'Weights' - choose weighting for the fit: [default: 2]
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113 <ul>
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114 <li> 1 - equal weights for each point.
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115 <li> 2 - weight with 1/abs(model).
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116 <li> 3 - weight with 1/abs(model).^2.
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117 <li> 4 - weight with inverse of the square mean spread of the model.
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118 </ul>
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119 </li>
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120 <li> 'Plot' - plot results of each fitting step. [default: false]
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121 <li> 'Disp' - Display the progress of the fitting iteration.
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122 [default: false]
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123 <li> 'FitTolerance' - Stopping fit tolerance condition. Be sure to
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Daniele Nicolodi <nicolodi@science.unitn.it>
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124 read the algorithm description to provide the
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125 correct value. [default: 0.6]
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126 <li> 'RMSEVar' - Root Mean Squared Error Variation - Check if the
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127 variation of the RMS error is smaller than 10^(-b),
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128 where b is the value given to the variable. This
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129 option is useful for finding the minimum of Chi
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130 squared. [default: 7].
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131 </ul>
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132 parameters passed to lpsd()
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133 <ul>
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134 <li> 'Jdes' - The number of points in the power spectrum.
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135 [default: help lpsd].
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136 <li> 'Win' - Spectral window used in spectral estimation.
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137 [default: help lpsd].
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Daniele Nicolodi <nicolodi@science.unitn.it>
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138 <li> 'Order' - order of segment detrending: [default: help lpsd]
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139 <ul>
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140 <li> -1 - no detrending
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141 <li> 0 - subtract mean
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142 <li> 1 - subtract linear fit
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143 <li> N - subtract fit of polynomial, order N
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144 </ul>
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145 </ul>
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146 </p>
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147
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148 <h2><a name="example">Example</a></h2>
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149
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150 <div class="fragment">
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151 <br>
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152 <pre>
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153 <span class="comment">% Generate white noise</span>
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154 fs = 1;
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155 a = ao(plist( <span class="string">'tsfcn'</span>, <span class="string">'randn(size(t))'</span>, <span class="string">'fs'</span>, fs, <span class="string">'nsecs'</span>, 10000, <span class="string">'yunits'</span>, <span class="string">'m'</span>, <span class="string">'name'</span>, <span class="string">'input'</span>));
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156
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157 <span class="comment">% filter </span>
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158 pzm = pzmodel(1e-2, {0.01}, {0.1});
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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159 ft = miir(pzm,plist( <span class="string">'fs'</span>,fs));
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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160
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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161 <span class="comment">% coloring white noise </span>
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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162 af = filter(a, ft);
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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163
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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164 <span class="comment">% Whitening colored noise</span>
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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165 pl = plist(...
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
166 <span class="string">'model'</span>, [], ...
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
167 <span class="string">'MaxIter'</span>, 30, ...
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
168 <span class="string">'PoleType'</span>, 2, ...
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
169 <span class="string">'MinOrder'</span>, 2, ...
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
170 <span class="string">'MaxOrder'</span>, 9, ...
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
171 <span class="string">'Weights'</span>, 2, ...
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
172 <span class="string">'Plot'</span>, false,...
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
173 <span class="string">'Disp'</span>, false,...
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
174 <span class="string">'RMSEVar'</span>, 3,...
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
175 <span class="string">'FitTolerance'</span>, 0.6); <span class="comment">% tolerancee on fit residuals spectral flatness</span>
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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176
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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177 aw = whiten1D(af,pl);
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
178
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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179 <span class="comment">% Calculate psd of colored and whitened data </span>
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
180 afxx = af.psd;
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
181 awxx = aw.psd;
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
182
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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183 <span class="comment">% plotting </span>
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
184 iplot(afxx,awxx)
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
185 </pre>
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
186 </div>
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
187 <br>
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
188 <br>
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
189 <p>
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
190 <div align="center">
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
191 <IMG src="images/whiten1D_1.png" align="center" border="0">
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
192 </div>
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
193 </p>
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
194
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
195
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
196
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
197
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
198
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
199
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
200
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
201
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
202
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
203
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
204