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author Daniele Nicolodi <nicolodi@science.unitn.it>
date Mon, 05 Dec 2011 18:04:34 +0100
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1 <!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN"
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2 "http://www.w3.org/TR/1999/REC-html401-19991224/loose.dtd">
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3
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4 <html lang="en">
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5 <head>
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6 <meta name="generator" content=
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7 "HTML Tidy for Mac OS X (vers 1st December 2004), see www.w3.org">
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8 <meta http-equiv="Content-Type" content=
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9 "text/html; charset=us-ascii">
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10
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11 <title>Whitening noise (LTPDA Toolbox)</title>
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12 <link rel="stylesheet" href="docstyle.css" type="text/css">
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13 <meta name="generator" content="DocBook XSL Stylesheets V1.52.2">
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14 <meta name="description" content=
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15 "Presents an overview of the features, system requirements, and starting the toolbox.">
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16 </head>
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17
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18 <body>
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19 <a name="top_of_page" id="top_of_page"></a>
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20
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21 <p style="font-size:1px;">&nbsp;</p>
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22
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23 <table class="nav" summary="Navigation aid" border="0" width=
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24 "100%" cellpadding="0" cellspacing="0">
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25 <tr>
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26 <td valign="baseline"><b>LTPDA Toolbox</b></td><td><a href="../helptoc.html">contents</a></td>
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27
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28 <td valign="baseline" align="right"><a href=
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29 "ltpda_training_topic_2_5.html"><img src="b_prev.gif" border="0" align=
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30 "bottom" alt="Remove trends from a time-series AO"></a>&nbsp;&nbsp;&nbsp;<a href=
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31 "ltpda_training_topic_2_7.html"><img src="b_next.gif" border="0" align=
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32 "bottom" alt="Select and find data from an AO"></a></td>
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33 </tr>
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34 </table>
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35
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36 <h1 class="title"><a name="f3-12899" id="f3-12899"></a>Whitening noise</h1>
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37 <hr>
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38
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39 <p>
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40 <p>
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41 The LTPDA toolbox offers various ways in which you could whiten data. Perhaps you know the whitening
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42 filter you want to use, in which case you can build the filter and filter the data. Alternatively, you
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43 may have a model for the spectral content of the data, in which case you can use the method <tt>ao/whiten1D</tt>
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44 if you are dealing with single, uncorrelated data streams, or <tt>ao/whiten2D</tt> if you have a pair of
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45 correlated data streams. You can also use <tt>ao/whiten1D</tt> in the case where you don't have a model for
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46 the spectral content of the data. In this case, the method
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47 calculates the spectrum of the data, re-bins the spectrum so to
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48 reduce the individual points fluctuations, and fits a model
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49 of the spectrum as a series of partial fractions z-domain filters.
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50 </p>
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51 <p>
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52 The whitening algorithms are highly configurable and accept a large number of parameters. The main ones that
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53 we will change from the defaults in the following examples are
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54 <table cellspacing="0" class="body" cellpadding="2" border="0" width="80%">
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55 <colgroup>
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56 <col width="25%"/>
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57 <col width="75%"/>
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58 </colgroup>
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59 <thead>
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60 <tr valign="top">
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61 <th class="categorylist">Key</th>
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62 <th class="categorylist">Description</th>
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63 </tr>
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64 </thead>
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65 <tbody>
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66 <!-- Key 'Plot' -->
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67 <tr valign="top">
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68 <td bgcolor="#f3f4f5">
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69 <p><tt>PLOT</tt></p>
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70 </td>
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71 <td bgcolor="#f3f4f5">
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72 <p>Plot the result of the fitting as it proceeds.</p>
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73 </td>
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74 </tr>
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75 <!-- Key 'MAXORDER' -->
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76 <tr valign="top">
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77 <td bgcolor="#f3f4f5">
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78 <p><tt>MAXORDER</tt></p>
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79 </td>
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80 <td bgcolor="#f3f4f5">
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81 <p>Specify the maximum allowed model order that can be fit.</p>
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82 </td>
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83 </tr>
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84 <!-- Key 'weights' -->
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85 <tr valign="top">
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86 <td bgcolor="#f3f4f5">
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87 <p><tt>WEIGHTS</tt></p>
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88 </td>
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89 <td bgcolor="#f3f4f5">
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90 <p>Choose the way the data is weighted in the fitting procedure.</p>
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91 </td>
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92 </tr>
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93 <!-- Key 'RMSVAR' -->
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94 <tr valign="top">
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95 <td bgcolor="#f3f4f5">
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96 <p><tt>RMSVAR</tt></p>
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97 </td>
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98 <td bgcolor="#f3f4f5">
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99 <p>Check if the variation of the RMS error is smaller than 10^(-b),
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100 where b is the value given in the plist.</p>
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101 </td>
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102 </tr>
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103 </tbody>
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104 </table>
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105 </p>
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106 <p>
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107 We will start by whitening some data using this last method, i.e., allowing <tt>whiten1D</tt> to determine
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108 the whitening filter from the data itself.
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109 </p>
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110 <p>
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111 The data we will whiten can be found in your data packet in the 'topic2' sub-directory.
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112 </p>
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113 <p>
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114 We start by loading the mat file:
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115 </p>
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116 <div class="fragment"><pre>
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117 a = ao(<span class="string">'topic2/whiten.mat'</span>);
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118 </pre>
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119 </div>
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120 <p>
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121 The AO stored in the variable <tt>a</tt> is a coloured noise time-series.
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122 Let's have a look at this times series using <tt>iplot</tt>.
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123 </p>
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124 <div class="fragment"><pre>
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125 >> iplot(a);
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126 </pre></div>
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127 <p>The result should be similar to: </p>
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128 <img src="images/ltpda_training_1/topic2/coloured.png" alt="coloured" border="1">
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129 <p>
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130 Before we can whiten the data, we have to define the parameter list for the whitening tool:
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131 </p>
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132 <div class="fragment"><pre>
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133 pl = plist(...
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134 <span class="string">'Plot'</span>, true, ...
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135 <span class="string">'MaxOrder'</span>, 9, ...
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136 <span class="string">'Weights'</span>, 2);</pre>
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137 </div>
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138 <p>
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139 Now we can call the whitening function <tt>whiten1D</tt> with our input AO, <tt>a</tt> and the
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140 parameter list <tt>pl</tt>:
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141 </p>
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142 <div class="fragment"><pre> >> aw = whiten1D(a,pl); </pre></div>
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143 <p>
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144 To compare the whitened data with the coloured noise we compute the power spectrum (for details see <a
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145 href="ltpda_training_topic_3_2.html"><tt>Power spectral density estimation</tt></a>):
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146 </p>
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147 <div class="fragment"><pre>
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148 awxx = aw.lpsd;
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149 axx = a.lpsd;
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150 </pre></div>
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151 <p>
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152 and finally plot our result in the frequency domain; in particular we plot the whitened data (<tt>awxx</tt>) compared to the coloured noise that was our input (<tt>axx</tt>).
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153 </p>
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154 </pre> </div>
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155 <div class="fragment"><pre>
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156 iplot(axx, awxx);
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157 </pre>
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158 </div>
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159 <img src="images/ltpda_training_1/topic2/whiten.png" alt="white" border="1">
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160
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161 </p>
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162
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163 <br>
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164 <br>
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165 <table class="nav" summary="Navigation aid" border="0" width=
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166 "100%" cellpadding="0" cellspacing="0">
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167 <tr valign="top">
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168 <td align="left" width="20"><a href="ltpda_training_topic_2_5.html"><img src=
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169 "b_prev.gif" border="0" align="bottom" alt=
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170 "Remove trends from a time-series AO"></a>&nbsp;</td>
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171
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172 <td align="left">Remove trends from a time-series AO</td>
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173
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174 <td>&nbsp;</td>
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175
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176 <td align="right">Select and find data from an AO</td>
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177
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178 <td align="right" width="20"><a href=
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179 "ltpda_training_topic_2_7.html"><img src="b_next.gif" border="0" align=
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180 "bottom" alt="Select and find data from an AO"></a></td>
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181 </tr>
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182 </table><br>
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183
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184 <p class="copy">&copy;LTP Team</p>
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185 </body>
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186 </html>