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author Daniele Nicolodi <nicolodi@science.unitn.it>
date Mon, 05 Dec 2011 16:20:06 +0100
parents f0afece42f48
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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>Remove trends from a time-series AO (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_4.html"><img src="b_prev.gif" border="0" align=
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30 "bottom" alt="Interpolation of a time-series AO"></a>&nbsp;&nbsp;&nbsp;<a href=
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31 "ltpda_training_topic_2_6.html"><img src="b_next.gif" border="0" align=
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32 "bottom" alt="Whitening noise"></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>Remove trends from a time-series AO</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 <tt>ao/detrend</tt> method offers the possibility to remove polynomial trends from a data series.
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42 </p>
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43 <p>
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44 The method can be configured with the following parameter:
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45 <table cellspacing="0" class="body" cellpadding="2" border="0" width="80%">
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46 <colgroup>
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47 <col width="25%"/>
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48 <col width="75%"/>
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49 </colgroup>
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50 <thead>
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51 <tr valign="top">
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52 <th class="categorylist">Key</th>
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53 <th class="categorylist">Description</th>
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54 </tr>
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55 </thead>
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56 <tbody>
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57 <!-- Key 'N' -->
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58 <tr valign="top">
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59 <td bgcolor="#f3f4f5">
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60 <p><tt>N</tt></p>
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61 </td>
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62 <td bgcolor="#f3f4f5">
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63 <p>The order of the polynomial to fit and remove. For orders below 10, a very fast C-code algorithm
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64 is used. For higher orders, the MATLAB functions <tt>polyfit</tt> and <tt>polyval</tt> are used to
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65 construct the polynomial which is then subtracted from the data.</p>
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66 </td>
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67 </tr>
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68 </tbody>
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69 </table>
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70 </p>
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71 <br>
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72 <h2>Example 1</h2>
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73 <p>
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74 In this example we will construct a time-series consisting of noise plus a known quadratic trend.
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75 We will then remove that trend using <tt>ao/detrend</tt> and compare the detrended time-series with the
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76 original noise.
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77 </p>
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78 <p>
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79 First let's create the time-series series consisting of the noise plus trend.
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80 </p>
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81 <div class="fragment"><pre>
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82 <span class="comment">% Construct noise data stream</span>
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83 fs = 10;
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84 nsecs = 10;
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85 pl = plist(<span class="string">'name'</span>, <span class="string">'None'</span>, <span class="string">'tsfcn'</span>, <span class="string">'5+randn(size(t))'</span>, <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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86 x = ao(pl);
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87 <span class="comment">% Construct a quadratic data series</span>
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88 pl_trend = plist(<span class="string">'tsfcn'</span>, <span class="string">'t.^2'</span>, <span class="string">'fs'</span>, fs, <span class="string">'nsecs'</span>, nsecs);
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89 trend = ao(pl_trend);
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90 <span class="comment">% Add them together</span>
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91 fcn_trend = x + trend;
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92 </pre>
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93 </div>
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94 <p>
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95 <table cellspacing="0" class="note" summary="Note" cellpadding="5" border="1">
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96 <tr width="90%">
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97 <td>
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98 The offset of 5 is added to the noise to ensure the data series
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99 doesn't come close to zero; we want to divide by it later in the example.
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100 </td>
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101 </tr>
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102 </table>
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103 </p>
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104 <p>
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105 Next we will detrend the data and compare the result to the noise data <tt>x</tt> we made above.
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106 </p>
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107 <div class="fragment"><pre>
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108 pl_detr = plist(<span class="string">'N'</span>,2);
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109 detr = detrend(fcn_trend, pl_detr);
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110 iplot(x, fcn_trend, detr, plist(<span class="string">'LineStyles'</span>, {<span class="string">''</span>, <span class="string">''</span>, <span class="string">'--'</span>}));
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111 </pre>
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112 </div>
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113 <p>
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114 <table cellspacing="0" class="note" summary="Note" cellpadding="5" border="1">
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115 <tr width="90%">
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116 <td>
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117 In the <tt>plist</tt> we specified 'LineStyles' as empty strings. These just serve as place holders
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118 and can be interpreted as "just to the default". If you want a data-series plotted with no line, then
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119 specify 'none', for example, <tt>{'none', '-', '--'}</tt>.
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120 </td>
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121 </tr>
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122 </table>
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123 </p>
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124 <br>
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125 <img src="images/ltpda_training_1/topic2/detrend.png" alt="Detrend" border="3">
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126 <br>
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127 <p>
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128 From this plot, it is not very easy to see how well our detrending worked. Let's form
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129 the fractional difference of the original <tt>x</tt> data and the detrended data and plot that instead.
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130 </p>
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131 <div class="fragment"><pre>
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132 detr5 = detr + 5;
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133 diff = 100.*(x-detr5)./x;
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134 iplot(diff);
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135 </pre>
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136 </div>
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137 <p>
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138 The result is shown below. We added the value 5 to the detrended time-series
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139 just to ensure that we don't divide by any values close to zero.
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140 </p>
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141 <br>
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142 <img src="images/ltpda_training_1/topic2/detrend_diff.png" alt="Detrend" border="3">
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143 <br>
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144 <p>
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145 Try increasing the length of the data series to say, 1000 or 10000 seconds, to see how the
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146 detrending improves.
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147 </p>
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148 <p>
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149 <p>The value of the coefficient describing the subracted trend are included in the field <tt>procinfo</tt> of the <tt>ao</tt> objects. The <tt>procinfo</tt> is actually a <tt>plist</tt> object, so we can search for parameters, in this case the key is 'coeffs':
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150 <div class="fragment"><pre>
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151 c = find(detr.procinfo, 'coeffs');
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152
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153 <span class="comment">% Remember also, that you will loose the 'coeffs' if you make any operation on "detr"</span>
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154 </pre></div>
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155 </p>
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156 Below is an example pipeline to perform the steps we did above:
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157 </p>
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158 <br>
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159 <img src="images/ltpda_training_1/topic2/detrend_pipeline.png" alt="Detrend" border="3">
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160 <br>
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161 <p>
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162 This introduces a new concept to the pipelines, namely, the use of constant blocks. Constant blocks
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163 are executed before the rest of the pipeline and the values are placed in the MATLAB workspace. This means
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164 that all parameter lists on the pipeline can refer to these constants. For example, the pipeline above
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165 declares two constants: 'fs' and 'nsecs'. The two <tt>ao</tt> blocks refer to these. Below is the parameter
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166 list for the first <tt>ao</tt> block, <tt>noise</tt>.
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167 </p>
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168 <br>
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169 <img src="images/ltpda_training_1/topic2/detrend_ao_plist.png" alt="Detrend" border="3">
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170 <br>
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171 <p>
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172 If you want to change the length of this simulation, then you just need to change the value
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173 in the constant block, <tt>nsecs</tt>.
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174 </p>
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175 <p>
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176 To add constant blocks to your pipeline, right-click on the canvas and select "Additional Blocks->Constant" from
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177 the context menu. You can also add an annotation from the same context menu. The above pipeline shows one
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178 annotation. To edit the text on an annotation, double-click it. Right-clicking on an annotation gives a context
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179 menu that allows you to configure its appearance.
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180 </p>
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181 </p>
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182
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183 <br>
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184 <br>
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185 <table class="nav" summary="Navigation aid" border="0" width=
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186 "100%" cellpadding="0" cellspacing="0">
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187 <tr valign="top">
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188 <td align="left" width="20"><a href="ltpda_training_topic_2_4.html"><img src=
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189 "b_prev.gif" border="0" align="bottom" alt=
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190 "Interpolation of a time-series AO"></a>&nbsp;</td>
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191
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192 <td align="left">Interpolation of a time-series AO</td>
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193
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194 <td>&nbsp;</td>
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195
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196 <td align="right">Whitening noise</td>
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197
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198 <td align="right" width="20"><a href=
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199 "ltpda_training_topic_2_6.html"><img src="b_next.gif" border="0" align=
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200 "bottom" alt="Whitening noise"></a></td>
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201 </tr>
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202 </table><br>
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203
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204 <p class="copy">&copy;LTP Team</p>
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205 </body>
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206 </html>