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author Daniele Nicolodi <nicolodi@science.unitn.it>
date Mon, 05 Dec 2011 16:20:06 +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>Spikes reduction in data (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 "interp.html"><img src="b_prev.gif" border="0" align=
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30 "bottom" alt="Interpolating data"></a>&nbsp;&nbsp;&nbsp;<a href=
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31 "gapfill.html"><img src="b_next.gif" border="0" align=
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32 "bottom" alt="Data gap filling"></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>Spikes reduction in data</h1>
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37 <hr>
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38
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39 <p>
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40 <h2>Description</h2>
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41 <p>
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42 Spikes in data due to different nature can be removed, if desired, from the original data. LTPDA <a href="matlab:doc('ao/spikecleaning')"><tt>spikecleaning</tt></a> detects and replaces
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43 spikes of the input AOs. A spike in data is defined as a single sample exceeding a certain value (usually, the
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44 floor noise of the data) defined by the user:
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45 </p>
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46 <br>
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47 <p>
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48 <div align="center">
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49 <IMG src="images/spike10x.png" width="147" height="15" border="0" />
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50 </div>
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51 </p>
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52 <br>
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53 <p>
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54 where <IMG src="images/spike41x.png" width="50" height="14" border="0" /> is the input data high-pass filtered, <IMG src="images/spike42x.png" width="34" height="13" border="0"/> is a value defined by the user (by default is 3.3) and <IMG src="images/spike43x.png" width="35" height="8" border="0"/> is the standard deviation of <IMG src="images/spike41x.png" width="50" height="14" border="0" /> . In consequence, a spike is defined as the value that exceeds the floor noise of the data by a factor <IMG src="images/spike42x.png" width="34" height="13" border="0"/>, the higher of this parameter the more difficult to "detect" a spike.
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55 <br>
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56 <br>
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57 <h2>Syntax</h2>
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58 </p>
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59 <div class="fragment"><pre>
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60 <br>
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61 b = spikecleaning(a, pl)
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62 </pre>
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63 </div>
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64 <h2>Parameters</h2>
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65 <p>
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66 The following parameters can be set in this method:
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67 <ul>
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68 <li> <tt>'kspike'</tt> - set the <IMG src="images/spike42x.png" width="34" height="13" border="0"/> value (default is 3.3) </li>
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69 <li> <tt>'method'</tt> - method used to replace the "spiky" sample. Three methods are available ---see below for details---:</li>
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70 <ul>
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71 <li> <tt>'random'</tt> </li>
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72 <li> <tt>'mean'</tt> </li>
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73 <li> <tt>'previous'</tt> </li>
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74 </ul>
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75 <li> <tt>'fc'</tt> - frequency cut-off of the high-pass IIR filter (default is 0.025) </li>
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76 <li> <tt>'order'</tt> - specifies the order of the IIR filter (default is 2) </li>
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77 <li> <tt>'ripple'</tt> - specifies pass/stop-band ripple for bandpass and bandreject filters (default is 0.5) </li>
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78 </ul>
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79 </p>
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80 <p>
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81 <h2>Algorithm</h2>
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82 </p>
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83 <p>
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84 <b>Random: </b> this method substitutes the spiky sample by:
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85 </p>
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86 <p>
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87 <br>
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88 <div align="center">
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89 <IMG src="images/spike20x.png" width="197" height="15" align="center" border="0"/>
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90 </div>
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91 <br>
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92 </p>
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93 <p>
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94 where <IMG src="images/spike44x.png" width="42" height="14" border="0"/> is a random number of mean zero and standard deviation 1.
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95 </p>
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96 <p>
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97 <b>Mean: </b>this method uses the following equation to replace the spike detected in data.
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98 </p>
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99 <br>
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100 <p>
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101 <div align="center">
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102 <IMG src="images/spike30x.png" width="158" height="29" align="center" border="0"/>
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103 </div>
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104 </p>
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105 <br>
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106 <p>
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107 <b>Previous: </b>the spike is substitued by the previous sample, i.e.:
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108 </p>
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109 <br>
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110 <p>
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111 <div align="center">
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112 <IMG src="images/spike40x.png" width="90" height="14" align="center" border="0"/>
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113 </div>
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114 </p>
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115 <br>
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116 <p>
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117 <h2>Examples</h2>
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118 </p>
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119 <p>
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120 1. Spike cleaning of a sequence of random data with <tt>kspike = 2</tt>.
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121 </p>
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122 <p>
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123 <div class="fragment"><pre>
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124 <br>
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125 x = ao(plist( <span class="string">'waveform'</span>, <span class="string">'noise'</span>, <span class="string">'nsecs'</span>,1e4, <span class="string">'fs'</span>,10)); <span class="comment">% create an AO of random data sampled at 1 Hz.</span>
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126 pl = plist( <span class="string">'kspike'</span>, 2); <span class="comment">% kspike = 2</span>
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127 y = spikecleaning(x, pl); <span class="comment">% spike cleaning function applied to the input AO, x</span>
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128 iplot(x, y) <span class="comment">% plot original and "cleaned" data</span>
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129 </pre>
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130 </div>
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131 </p>
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132 <p>
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133 <div align="center">
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134 <img src="images/spike1.png" border="1" >
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135 </div>
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136 </p>
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137 <!-- <p>
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138 2. Example of real data: the first image shows data from the real world prior to
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139 the application of the spike cleaning tool. It is clear that some spikes are
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140 present in data and might be convenient to remove them. The second image shows
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141 the same data after the spike samples supression.
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142 </p>
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143 <p>
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144 <img src="images/stat1x.png" border="1" width="400px">
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145 </p>
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146 <p>
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147 <img src="images/stat2x.png" border="1" width="400px">
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148 </p>
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149 -->
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150
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151
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152
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153 </p>
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155 <br>
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156 <br>
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157 <table class="nav" summary="Navigation aid" border="0" width=
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158 "100%" cellpadding="0" cellspacing="0">
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159 <tr valign="top">
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160 <td align="left" width="20"><a href="interp.html"><img src=
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161 "b_prev.gif" border="0" align="bottom" alt=
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162 "Interpolating data"></a>&nbsp;</td>
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163
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164 <td align="left">Interpolating data</td>
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165
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166 <td>&nbsp;</td>
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167
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168 <td align="right">Data gap filling</td>
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169
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170 <td align="right" width="20"><a href=
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171 "gapfill.html"><img src="b_next.gif" border="0" align=
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172 "bottom" alt="Data gap filling"></a></td>
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173 </tr>
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174 </table><br>
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175
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176 <p class="copy">&copy;LTP Team</p>
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177 </body>
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178 </html>