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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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+ − 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;"> </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> <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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+ − 180 </p>
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+ − 181 </p>
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+ − 183 <br>
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+ − 188 <td align="left" width="20"><a href="ltpda_training_topic_2_4.html"><img src=
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+ − 190 "Interpolation of a time-series AO"></a> </td>
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+ − 200 "bottom" alt="Whitening noise"></a></td>
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+ − 205 </body>
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