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author Daniele Nicolodi <nicolodi@science.unitn.it>
date Wed, 23 Nov 2011 19:22:13 +0100
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1 <h2>Description</h2>
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2 <p>
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3 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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4 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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5 floor noise of the data) defined by the user:
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6 </p>
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7 <br>
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8 <p>
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9 <div align="center">
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10 <IMG src="images/spike10x.png" width="147" height="15" border="0" />
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11 </div>
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12 </p>
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13 <br>
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14 <p>
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15 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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16 <br>
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17 <br>
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18 <h2>Syntax</h2>
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19 </p>
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20 <div class="fragment"><pre>
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21 <br>
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22 b = spikecleaning(a, pl)
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23 </pre>
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24 </div>
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25 <h2>Parameters</h2>
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26 <p>
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27 The following parameters can be set in this method:
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28 <ul>
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29 <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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30 <li> <tt>'method'</tt> - method used to replace the "spiky" sample. Three methods are available ---see below for details---:</li>
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31 <ul>
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32 <li> <tt>'random'</tt> </li>
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33 <li> <tt>'mean'</tt> </li>
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34 <li> <tt>'previous'</tt> </li>
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35 </ul>
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36 <li> <tt>'fc'</tt> - frequency cut-off of the high-pass IIR filter (default is 0.025) </li>
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37 <li> <tt>'order'</tt> - specifies the order of the IIR filter (default is 2) </li>
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38 <li> <tt>'ripple'</tt> - specifies pass/stop-band ripple for bandpass and bandreject filters (default is 0.5) </li>
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39 </ul>
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40 </p>
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41 <p>
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42 <h2>Algorithm</h2>
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43 </p>
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44 <p>
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45 <b>Random: </b> this method substitutes the spiky sample by:
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46 </p>
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47 <p>
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48 <br>
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49 <div align="center">
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50 <IMG src="images/spike20x.png" width="197" height="15" align="center" border="0"/>
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51 </div>
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52 <br>
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53 </p>
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54 <p>
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55 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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56 </p>
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57 <p>
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58 <b>Mean: </b>this method uses the following equation to replace the spike detected in data.
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59 </p>
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60 <br>
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61 <p>
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62 <div align="center">
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63 <IMG src="images/spike30x.png" width="158" height="29" align="center" border="0"/>
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64 </div>
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65 </p>
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66 <br>
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67 <p>
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68 <b>Previous: </b>the spike is substitued by the previous sample, i.e.:
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69 </p>
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70 <br>
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71 <p>
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72 <div align="center">
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73 <IMG src="images/spike40x.png" width="90" height="14" align="center" border="0"/>
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74 </div>
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75 </p>
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76 <br>
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77 <p>
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78 <h2>Examples</h2>
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79 </p>
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80 <p>
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81 1. Spike cleaning of a sequence of random data with <tt>kspike = 2</tt>.
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82 </p>
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83 <p>
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84 <div class="fragment"><pre>
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85 <br>
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86 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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87 pl = plist( <span class="string">'kspike'</span>, 2); <span class="comment">% kspike = 2</span>
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88 y = spikecleaning(x, pl); <span class="comment">% spike cleaning function applied to the input AO, x</span>
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89 iplot(x, y) <span class="comment">% plot original and "cleaned" data</span>
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90 </pre>
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91 </div>
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92 </p>
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93 <p>
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94 <div align="center">
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95 <img src="images/spike1.png" border="1" >
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96 </div>
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97 </p>
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98 <!-- <p>
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99 2. Example of real data: the first image shows data from the real world prior to
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100 the application of the spike cleaning tool. It is clear that some spikes are
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101 present in data and might be convenient to remove them. The second image shows
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102 the same data after the spike samples supression.
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103 </p>
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104 <p>
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105 <img src="images/stat1x.png" border="1" width="400px">
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106 </p>
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107 <p>
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108 <img src="images/stat2x.png" border="1" width="400px">
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109 </p>
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110 -->
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111
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