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2 "http://www.w3.org/TR/1999/REC-html401-19991224/loose.dtd">
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7 "HTML Tidy for Mac OS X (vers 1st December 2004), see www.w3.org">
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11 <title>Empirical Transfer Function estimation (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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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 "ltpda_training_topic_3_2_3.html"><img src="b_prev.gif" border="0" align=
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30 "bottom" alt="Example 3: Log-scale PSD on MDC1 data"></a> <a href=
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31 "ltpda_training_topic_3_6.html"><img src="b_next.gif" border="0" align=
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32 "bottom" alt="IFO/Temperature Example - Spectral Analysis"></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>Empirical Transfer Function estimation</h1>
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37 <hr>
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38
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Daniele Nicolodi <nicolodi@science.unitn.it>
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39 <p>
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40 <p>
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41 Let's run this exercise on empirical estimation of Transfer
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42 Functions on the Matlab terminal.</p>
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43
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44 <p>The idea of the exercise is the following:
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45 <ol>
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46 <li>simulate some white noise <em>x(t)</em></li>
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47 <li>build a band-pass filter <em>F</em></li>
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48 <li>pass the input noise <em>x(t)</em> through the filter and add some more noise
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49 <em>yn(t)</em> at the output so to have <em>y = F*x(t) + yn(t)</em></li>
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50 <li>evaluate and plot the transfer function <em>x -> y</em> </li>
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51 </ol>
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52 In a flow diagram, the representation is as follows:
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53 </p>
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54 <img src="images/ltpda_training_1/topic3/TFE_1_flowchart.png"
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55 alt="Dataflow for the 1St example of ao/tfe" width="600px" border="1">
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56
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57 <p>The command-line sequence is the following:
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58 <div class="fragment"><pre>
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59 <span class="comment">%% General definitions</span>
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60 nsecs = 10000;
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61 fs = 1;
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62 <span class="comment">%% Input noise</span>
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63 x = ao(plist(<span class="string">'waveform'</span>, <span class="string">'noise'</span>, <span class="string">'sigma'</span>, 3, <span class="string">'fs'</span>, fs, <span class="string"> 'nsecs'</span>, nsecs, <span class="string">'yunits'</span>, <span class="string">'V'</span>))
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64
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65 <span class="comment">%% Filter</span>
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66 bp_filter = miir(plist(<span class="string">'type'</span>, <span class="string">'bandpass'</span>, <span class="string">'fc'</span>, [0.01 0.1], <span class="string">'fs'</span>, 1, <span class="string">'order'</span>, 3,<span class="string">'iunits'</span>, <span class="string">'V'</span>, <span class="string">'ounits'</span>, <span class="string">'A'</span>))
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67 xf = simplifyYunits(filter(x, bp_filter))
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68
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69 <span class="comment">%% Output noise</span>
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70 yn = ao(plist(<span class="string">'waveform'</span>,<span class="string">'noise'</span>, <span class="string">'sigma'</span>, 1, <span class="string">'fs'</span>, fs, <span class="string">'nsecs'</span>, xf.nsecs, <span class="string">'yunits'</span>, <span class="string">'A'</span>))
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71 y = xf + yn
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72
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73 <span class="comment">%% Plotting input and output noise</span>
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74 xx = psd(x, plist(<span class="string">'scale'</span>,...
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75 <span class="string">'ASD'</span>,...
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76 <span class="string">'nfft'</span>, 1000))
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77 yy = psd(y, plist(<span class="string">'scale'</span>,<span class="string">'ASD'</span>, ...
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78 <span class="string">'nfft'</span>, 1000))
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79 iplot(xx, yy, plist(<span class="string">'Arrangement'</span>, <span class="string">'subplots'</span>, <span class="string">'YRanges'</span>, {[1e-1 1e1], [1e-2 1e2]}));
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80
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81 </pre></div>
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82 <img src="images/ltpda_training_1/topic3/TFE_in_out.png" alt="Ohmic admittance between y and x" border="1">
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83 <br>
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84 <p>Now we can proceed with the call to the <tt>ao/tfe</tt> method. The
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85 parameter list is very similar to the one employed for the other spectral
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86 estimators:</p>
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87
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88 <table cellspacing="0" class="body" cellpadding="2" border="0" width="80%">
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89 <colgroup>
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90 <col width="15%"/>
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91 <col width="20%"/>
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92 <col width="65%"/>
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93 </colgroup>
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94 <thead>
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95 <tr valign="top">
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96 <th class="categorylist">Key</th>
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97 <th class="categorylist">Value</th>
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98 <th class="categorylist">Description</th>
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99 </tr>
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100 </thead>
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101 <tbody>
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102 <!-- Key 'NFFT' -->
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103 <tr valign="top">
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104 <td bgcolor="#f3f4f5">
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105 <p><tt>NFFT</tt></p>
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106 </td>
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107 <td bgcolor="#f3f4f5">
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108 <p><span class="string">1000</span></p>
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109 </td>
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110 <td bgcolor="#f3f4f5">
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111 <p>The number of samples defining the length of the window to apply</p>
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112 </td>
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113 </tr>
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114 <!-- Key 'WIN' -->
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115 <tr valign="top">
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116 <td bgcolor="#f3f4f5">
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117 <p><tt>WIN</tt></p>
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118 </td>
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119 <td bgcolor="#f3f4f5">
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120 <p><span class="string">'BH92'</span></p>
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121 </td>
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122 <td bgcolor="#f3f4f5">
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123 <p>Or a different one, if you want.</p>
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124 </td>
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125 </tr>
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126 <!-- Key 'OLAP' -->
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127 <tr valign="top">
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128 <td bgcolor="#f3f4f5">
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129 <p><tt>OLAP</tt></p>
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130 </td>
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131 <td bgcolor="#f3f4f5">
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132 <p><span class="string">-1</span></p>
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133 </td>
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134 <td bgcolor="#f3f4f5">
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135 <p>Overlap will be chosen based on the window properties</p>
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136 </td>
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137 </tr>
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138 <!-- Key 'ORDER' -->
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139 <tr valign="top">
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140 <td bgcolor="#f3f4f5">
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141 <p><tt>ORDER</tt></p>
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142 </td>
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143 <td bgcolor="#f3f4f5">
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144 <p><span class="string">0</span></p>
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145 </td>
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146 <td bgcolor="#f3f4f5">
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147 <p>Segment-wise detrending up to order 0</p>
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148 </td>
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149 </tr>
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150 </tbody>
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151 </table>
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152 </p>
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153 <p>The command line is the following:</p>
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154 <div class="fragment"><pre>
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155 <span class="comment">%% Estimate the x->y transfer function</span>
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156 tfxy = tfe(x, y, plist(<span class="string">'nfft'</span>, 1000, <span class="string">'win'</span>, <span class="string">'BH92'</span>, <span class="string">'olap'</span>, -1, <span class="string">'order'</span>, 0));
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157 </pre></div>
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158 <p>We also would like to evaluate the expected transfer function x->y, which is obviously the filter transfer function, or response. This can be calculated by means of the
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159 <table cellspacing="0" class="note" summary="Note" cellpadding="5" border="1">
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160 <tr width="90%">
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161 <td>
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162 <tt>miir/resp</tt>
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163 </td>
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164 </tr>
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165 </table> method. A detailed description of digital filtering is available in the User Manual dedicated <a href="sigproc_dfilt.html" >section</a> and will be touched upon in <a href="ltpda_training_topic_4_4_2.html" >this</a> topic; here let's just use the simplest form, where the needed parameter is a list of the frequency to evaluate the response at:</p>
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166 <table cellspacing="0" class="body" cellpadding="2" border="0" width="80%">
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167 <colgroup>
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168 <col width="15%"/>
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169 <col width="35%"/>
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170 <col width="50%"/>
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171 </colgroup>
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172 <thead>
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173 <tr valign="top">
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174 <th class="categorylist">Key</th>
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175 <th class="categorylist">Value</th>
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176 <th class="categorylist">Description</th>
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177 </tr>
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178 </thead>
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179 <tbody>
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180 <!-- Key 'f' -->
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181 <tr valign="top">
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182 <td bgcolor="#f3f4f5">
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183 <p><tt>F</tt></p>
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184 </td>
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185 <td bgcolor="#f3f4f5">
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186 <p><span class="string">tfxy.x</span></p>
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187 </td>
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188 <td bgcolor="#f3f4f5">
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189 <p>a vector of frequency values or an <tt>ao</tt> whereby the x-axis is taken for the frequency values</p>
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190 </td>
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191 </tr>
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192 </tbody>
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193 </table>
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194 <p>
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195 So we can just pass the x field of the fsdata <tt>ao</tt> containing the transfer function estimate. However,
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196 we can also just pass the AO itself. In which case, the <tt>resp</tt> function will take the X values from
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197 the AO.
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198 </p>
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199 <p>
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200 The command line is the following:</p>
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201 <div class="fragment"><pre>
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202 <span class="comment">%% Evaluate the expected x->y transfer function</span>
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203 rf = resp(bp_filter, plist(<span class="string">'f'</span>, tfxy))
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204 </pre></div>
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205
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206 <p>Eventually let's look at the results:
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207 <div class="fragment"><pre>
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208 <span class="comment">%% Plotting estimated and expected transfer functions</span>
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209 iplot(tfxy, rf, plist(<span class="string">'colors'</span>,{[1 0 0],[0 0 0]},<span class="string">'YRanges'</span>, {[1e-2 1e2], [-200 200]}))
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210 </pre></div>
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211 </p>
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212 <img src="images/ltpda_training_1/topic3/TFE_result_1.png" alt="TFE of x into y" border="1">
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213 <br>
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214
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215
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216 </p>
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217
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218 <br>
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219 <br>
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220 <table class="nav" summary="Navigation aid" border="0" width=
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221 "100%" cellpadding="0" cellspacing="0">
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222 <tr valign="top">
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223 <td align="left" width="20"><a href="ltpda_training_topic_3_2_3.html"><img src=
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224 "b_prev.gif" border="0" align="bottom" alt=
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225 "Example 3: Log-scale PSD on MDC1 data"></a> </td>
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226
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227 <td align="left">Example 3: Log-scale PSD on MDC1 data</td>
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228
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229 <td> </td>
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230
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231 <td align="right">IFO/Temperature Example - Spectral Analysis</td>
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232
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233 <td align="right" width="20"><a href=
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234 "ltpda_training_topic_3_6.html"><img src="b_next.gif" border="0" align=
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235 "bottom" alt="IFO/Temperature Example - Spectral Analysis"></a></td>
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236 </tr>
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237 </table><br>
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238
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239 <p class="copy">©LTP Team</p>
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240 </body>
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241 </html>
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