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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>Building a model (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;"> </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 "pzmodel.html"><img src="b_prev.gif" border="0" align=
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30 "bottom" alt="Pole/Zero representation"></a> <a href=
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31 "pzmodel_gui.html"><img src="b_next.gif" border="0" align=
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32 "bottom" alt="Model helper GUI"></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>Building a model</h1>
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37 <hr>
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38
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39 <p>
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40
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41 <p>
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42 Poles and zeros can be combined together to create a pole/zero model. In addition to a list of poles
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43 and zeros, a gain factor and a delay can be specified such that the resulting model is of the form:
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44 </p>
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45 <br>
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46 <div align="center">
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47 <img src="images/pzmodel_tf_eqn.png" alt="Pole/zero model TF" border="3">
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48 </div>
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49 <br>
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50 <p>
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51 The following sections introduce how to produce and use pole/zero models in the LTPDA environment.
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52 <ul>
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53 <li><a href="#direct">Direct form</a></li>
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54 <li><a href="#plist">Creating from a <tt>plist</tt></a></li>
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55 <li><a href="#resp">Computing the response of the model</a></li>
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56 </ul>
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57 </p>
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58
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59
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60 <h2><a name="direct">Direct form</a></h2>
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61
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62 The following code fragment creates a pole/zero model consisting of 2 poles and 2 zeros with a gain
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63 factor of 10 and a 10ms delay:
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64 <div class="fragment"><pre>
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65 >> pzm = pzmodel(10, {[1 2], 3}, {5, 10}, 0.01)
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66 ---- pzmodel 1 ----
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67 name: None
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68 gain: 10
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69 delay: 0.01
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70 iunits: []
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71 ounits: []
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72 pole 001: (f=1 Hz,Q=2)
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73 pole 002: (f=3 Hz,Q=NaN)
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74 zero 001: (f=5 Hz,Q=NaN)
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75 zero 002: (f=10 Hz,Q=NaN)
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76 -------------------
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77 </pre></div>
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78 <p>
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79 Notice, you can also pass arrays of <tt>pz</tt> objects to the <tt>pzmodel</tt> constructor, but this
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80 should rarely be necessary.
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81 </p>
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82
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83 <h2><a name="plist">Creating from a <tt>plist</tt></a></h2>
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84
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85 <p>
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86 You can also create a <tt>pzmodel</tt> by passing a parameter list. The following example shows
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87 this
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88 </p>
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89
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90 <div class="fragment"><pre>
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91 >> pl = plist(<span class="string">'name'</span>, <span class="string">'test model'</span>, ...
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92 <span class="string">'gain'</span>, 10, ...
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93 <span class="string">'poles'</span>, {[1 2], 3}, ...
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94 <span class="string">'zeros'</span>, {5, 10}, ...
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95 <span class="string">'delay'</span>, 0.01, ...
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96 <span class="string">'iunits'</span>, 'm', ...
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97 <span class="string">'ounits'</span>, 'V^2');
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98 >> pzm = pzmodel(pl)
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99 ---- pzmodel 1 ----
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100 name: test model
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101 gain: 10
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102 delay: 0.01
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103 iunits: [m]
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104 ounits: [V^2]
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105 pole 001: (f=1 Hz,Q=2)
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106 pole 002: (f=3 Hz,Q=NaN)
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107 zero 001: (f=5 Hz,Q=NaN)
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108 zero 002: (f=10 Hz,Q=NaN)
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109 -------------------
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110 </pre></div>
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111 <p>
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112 Here we also specified the input units of the transfer function ('iunits') and the
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113 output units, ('ounits'). In this case, the model represents a transfer function
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114 from metres to Volts squared.
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115 </p>
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116
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117 <h2><a name="resp">Computing the response of the model</a></h2>
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118
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119 <p>
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120 The frequency response of the model can generated using the <tt>resp</tt> method of the
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121 <tt>pzmodel</tt> class. To compute the response of the model created above:
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122 </p>
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123 <div class="fragment"><pre>
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124 >> resp(pzm)
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125 </pre></div>
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126 <p>
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127 Since no output was specified, this command produces the following plot:
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128 <img src="images/pzmodel_resp.png" alt="Pole/zero model resp" border="3" width="600">
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129 </p>
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130 <p>
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131 You can also specify the frequency band over which to compute the response by passing a <tt>plist</tt>
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132 to the <tt>resp</tt> method, as follows:
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133 </p>
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134 <div class="fragment"><pre>
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135 >> rpl = plist(<span class="string">'f1'</span>, 0.1, ...
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136 <span class="string">'f2'</span>, 1000, ...
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137 <span class="string">'nf'</span>, 10000);
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138 >> a = resp(pzm, rpl)
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139 ----------- ao 01: resp(test model) -----------
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140
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141 name: resp(test model)
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142 description:
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143 data: (0.1,10.0668830776529-i*0.605439551995965) (0.100092155051679,10.067006787497-i*0.606014805088671) (0.100184395028894,10.0671307268392-i*0.606590636924472) (0.100276720009908,10.0672548961078-i*0.607167048174596) (0.100369130073055,10.0673792957318-i*0.607744039511284) ...
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144 ----------- fsdata 01 -----------
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145
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146 fs: NaN
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147 x: [1 10000], double
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148 y: [1 10000], double
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149 xunits: [Hz]
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150 yunits: [V^(2)][m^(-1)]
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151 t0: 1970-01-01 00:00:00.000
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152 navs: NaN
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153 ---------------------------------
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154
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155 hist: pzmodel / resp / $Id: pzmodel_model_content.html,v 1.5 2009/02/24 09:44:39 miquel Exp $
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156 mfilename:
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157 mdlfilename:
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158 -----------------------------------------------
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159 </pre></div>
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160 <p>
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161 In this case, the response is returned as an Analysis Object containing <tt>fsdata</tt>. You can now
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162 plot the AO using the <tt>iplot</tt> function.
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163 </p>
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164
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165 </p>
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166
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167 <br>
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168 <br>
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169 <table class="nav" summary="Navigation aid" border="0" width=
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170 "100%" cellpadding="0" cellspacing="0">
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171 <tr valign="top">
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172 <td align="left" width="20"><a href="pzmodel.html"><img src=
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173 "b_prev.gif" border="0" align="bottom" alt=
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174 "Pole/Zero representation"></a> </td>
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175
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176 <td align="left">Pole/Zero representation</td>
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177
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178 <td> </td>
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179
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180 <td align="right">Model helper GUI</td>
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181
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182 <td align="right" width="20"><a href=
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183 "pzmodel_gui.html"><img src="b_next.gif" border="0" align=
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184 "bottom" alt="Model helper GUI"></a></td>
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185 </tr>
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186 </table><br>
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187
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188 <p class="copy">©LTP Team</p>
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189 </body>
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190 </html>
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