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+ − 3
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+ − 4 <html lang="en">
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+ − 5 <head>
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+ − 10
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+ − 11 <title>Interpolation of 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_3.html"><img src="b_prev.gif" border="0" align=
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+ − 30 "bottom" alt="Resampling a time-series AO"></a> <a href=
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+ − 31 "ltpda_training_topic_2_5.html"><img src="b_next.gif" border="0" align=
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+ − 32 "bottom" alt="Remove trends from a time-series AO"></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>Interpolation of 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</tt> class has a method for interpolating data using different forms of interpolation. This method is
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+ − 42 called <tt>ao/interp</tt>.
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+ − 43 </p>
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+ − 44 <p>
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+ − 45 To configure <tt>ao/interp</tt>, use the following parameters:
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+ − 46 <table cellspacing="0" class="body" cellpadding="2" border="0" width="80%">
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+ − 47 <colgroup>
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+ − 48 <col width="25%"/>
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+ − 49 <col width="75%"/>
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+ − 50 </colgroup>
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+ − 51 <thead>
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+ − 52 <tr valign="top">
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+ − 53 <th class="categorylist">Key</th>
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+ − 54 <th class="categorylist">Description</th>
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+ − 55 </tr>
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+ − 56 </thead>
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+ − 57 <tbody>
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+ − 58 <!-- Key 'Vertices' -->
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+ − 59 <tr valign="top">
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+ − 60 <td bgcolor="#f3f4f5">
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+ − 61 <p><tt>VERTICES</tt></p>
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+ − 62 </td>
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+ − 63 <td bgcolor="#f3f4f5">
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+ − 64 <p>A new set of vertices (relative to the t0) on which to resample.</p>
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+ − 65 </td>
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+ − 66 </tr>
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+ − 67 <!-- Key 'method' -->
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+ − 68 <tr valign="top">
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+ − 69 <td bgcolor="#f3f4f5">
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+ − 70 <p><tt>METHOD</tt></p>
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+ − 71 </td>
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+ − 72 <td bgcolor="#f3f4f5">
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+ − 73 <p>The method by which to interpolate. Choose from
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+ − 74 <ul>
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+ − 75 <li>'nearest' - nearest neighbour</li>
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+ − 76 <li>'linear' - linear interpolation</li>
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+ − 77 <li>'spline' - for spline interpolation</li>
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+ − 78 <li>'cubic' - for cubic interpolation</li>
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+ − 79 </ul></p>
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+ − 80 </td>
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+ − 81 </tr>
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+ − 82 </tbody>
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+ − 83 </table>
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+ − 84 </p>
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+ − 85 <h2>Example</h2>
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+ − 86 <p>
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+ − 87 Here we will interpolate a sinusoid singal on to a new time-grid. The result will be to increase the
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+ − 88 sample rate by a factor 2.
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+ − 89 </p>
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+ − 90 <p>
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+ − 91 First we create a time-series ao:
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+ − 92 </p>
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+ − 93 <div class="fragment"><pre>
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+ − 94 pl = plist(<span class="string">'Name'</span>, <span class="string">'None'</span>, <span class="string">'tsfcn'</span>,<span class="string">'sin(2*pi*1.733*t)'</span>,<span class="string">'fs'</span>,20,<span class="string">'nsecs'</span>,10,<span class="string">'yunits'</span>,<span class="string">'V'</span>);
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+ − 95 x = ao(pl);
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+ − 96 </pre>
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+ − 97 </div>
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+ − 98 <p>
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+ − 99 Then we create the new time-grid we want to resample on to.
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+ − 100 </p>
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+ − 101 <div class="fragment"><pre>
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+ − 102 tt = linspace(0, x.nsecs - 1/x.fs, 2*(x.len));
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+ − 103 </pre>
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+ − 104 </div>
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+ − 105 <p>
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+ − 106 And finally we can apply our new time-grid to the data using <tt>interp</tt>. We test two of the available interpolation methods:
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+ − 107 </p>
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+ − 108 <div class="fragment"><pre>
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+ − 109 pl_spline = plist(<span class="string">'vertices'</span>,tt);
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+ − 110 pl_nearest = plist(<span class="string">'vertices'</span>,tt,<span class="string">'method'</span>,<span class="string">'nearest'</span>);
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+ − 111 x_spline = interp(x,pl_spline);
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+ − 112 x_nearest = interp(x,pl_nearest);
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+ − 113 iplot(x, x_spline, x_nearest, plist(<span class="string">'Markers'</span>, {<span class="string">'o'</span>, <span class="string">'+'</span>, <span class="string">'x'</span>}, ...
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+ − 114 <span class="string">'LineColors'</span>, {<span class="string">'k'</span>, <span class="string">'r'</span>, <span class="string">'g'</span>}, ...
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+ − 115 <span class="string">'XRanges'</span>, [0 1]));
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+ − 116 </pre>
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+ − 117 </div>
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+ − 118 <img src="images/ltpda_training_1/topic2/interp.png" alt="Interpolate" border="3">
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+ − 119 <br>
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+ − 120 <br>
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+ − 121 <p>
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+ − 122 To do the same activity on the workbench, we can use a pipeline like:
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+ − 123 </p>
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+ − 124 <img src="images/ltpda_training_1/topic2/lwb_interp_1.png" alt="Interpolate" border="3">
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+ − 125 <p>
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+ − 126 This teaches some important aspects of the use of the workbench, so it's worth stepping through its construction slowly.
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+ − 127 </p>
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+ − 128 <p>
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+ − 129 To build this pipeline:
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+ − 130 <ol>
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+ − 131 <li>Create a new empty canvas</li>
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+ − 132 <li>Add two MATLAB Expression Blocks:
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+ − 133 <ol>
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+ − 134 <li>Right-click on the canvas and choose "Add Block...->MATBlock". A <tt>MATBlock</tt> is a block which can
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+ − 135 evaluate any valid MATLAB expression and pass that to further blocks via its single output.</li>
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+ − 136 <li>Select the block, then change its name in the block
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+ − 137 property table (located at the top left of the "Properties" tab) to 'fs'. Alternatively, the name of the block can be changed by right-clicking on the block and choosing "Set name"</li>
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+ − 138 <li>Double-click the block to get a pop-up dialog where you can enter the MATLAB expression. In this case
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+ − 139 just enter the value 20.</li>
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+ − 140 <li>Select this 'fs' block and hit <tt>ctrl-d</tt> (<tt>cmd-d</tt> on OS X) to duplicate the block.</li>
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+ − 141 <li>Select the new block and change its name to 'nsecs'</li>
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+ − 142 <li>Double-click the 'nsecs' block to change its expression. Enter the value 10.</li>
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+ − 143 </ol>
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+ − 144 </li>
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+ − 145 <li>Next we need some additional blocks. Add an <tt>ao</tt> block, two <tt>ao/interp</tt> blocks, an
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+ − 146 <tt>ao/x</tt> block, and an <tt>ao/iplot</tt> block.
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+ − 147 </li>
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+ − 148 <li>Connect up the blocks as shown on the pipeline above.
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+ − 149 <table cellspacing="0" class="note" summary="Note" cellpadding="5" border="1">
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+ − 150 <tr width="90%">
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+ − 151 <td>
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+ − 152 To add inputs (or outputs) to a block, right-click on the block and choose "Add input".
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+ − 153 </td>
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+ − 154 </tr>
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+ − 155 </table>
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+ − 156 <table cellspacing="0" class="note" summary="Note" cellpadding="5" border="1">
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+ − 157 <tr width="90%">
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+ − 158 <td>
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+ − 159 Double-click an LTPDA Block to get a dialog box to enter a new name for the block.
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+ − 160 </td>
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+ − 161 </tr>
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+ − 162 </table>
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+ − 163 <table cellspacing="0" class="note" summary="Note" cellpadding="5" border="1">
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+ − 164 <tr width="90%">
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+ − 165 <td>
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+ − 166 To set the color of the pipes eminating from a particular block, right-click on the block
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+ − 167 and choose "Set output pipe color" from the context menu. You can also set the color of
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+ − 168 individual pipes by right-clicking on a pipe and choosing "Set color" from the context menu.
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+ − 169 </td>
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+ − 170 </tr>
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+ − 171 </table>
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+ − 172 </li>
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+ − 173 <li>Next we need to set the various properties of each block. Follow these steps:
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+ − 174 <ol>
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+ − 175 <li>Set the properties of the AO block to look like:<br>
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+ − 176 <img src="images/ltpda_training_1/topic2/lwb_interp_ao_props.png" alt="Interpolate" border="3">
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+ − 177 <table cellspacing="0" class="note" summary="Note" cellpadding="5" border="1">
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+ − 178 <tr width="90%">
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+ − 179 <td>
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+ − 180 The single quotes around the <tt>TSFCN</tt> value are not strictly necessary, but it can
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+ − 181 avoid problems, for example in the case you have a variable <tt>t</tt> already defined in the MATLAB
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+ − 182 workspace.
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+ − 183 </td>
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+ − 184 </tr>
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+ − 185 </table>
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+ − 186 </li>
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+ − 187 <li>
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+ − 188 Set the properties of the first interpolate block (a_spline) to look like:<br>
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+ − 189 <img src="images/ltpda_training_1/topic2/lwb_interp_ao_interp1.png" alt="Interpolate" border="3"> <br>
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+ − 190 Notice that here we have used the keywords <tt>PORT_1</tt> and <tt>PORT_2</tt> to build the expression. These
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+ − 191 refer to the ports of that block, and are connected to the MATLAB Expression Blocks which represent the values
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+ − 192 we are interested in.
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+ − 193 </li>
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+ − 194 <li>
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+ − 195 The block <tt>ao/x</tt> has no properties and simply gets the full x-vector from the output of <tt>a_spline</tt>. This
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+ − 196 is then passed to the next interpolation block where we use the values as the vertices for the next
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+ − 197 interpolation step, thus ensuring that the two interpolations are done on the same grid.
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+ − 198 </li>
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+ − 199 <li>
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+ − 200 Set the properties of the second interpolate block (a_near) to look like:<br>
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+ − 201 <img src="images/ltpda_training_1/topic2/lwb_interp_ao_interp2.png" alt="Interpolate" border="3"> <br>
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+ − 202 </li>
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+ − 203 <li>
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+ − 204 Finally, for the <tt>iplot</tt> block, add three new parameters and give then key names and values
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+ − 205 like:<br>
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+ − 206 <img src="images/ltpda_training_1/topic2/lwb_interp_iplot.png" alt="Interpolate" border="3"> <br>
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+ − 207 </li>
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+ − 208 </ol>
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+ − 209 </li>
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+ − 210 </ol>
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+ − 211 It should now be possible to run this pipeline and see a plot very similar to the one produced above.
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+ − 212 </p>
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+ − 213 </p>
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+ − 214
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+ − 215 <br>
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+ − 216 <br>
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+ − 217 <table class="nav" summary="Navigation aid" border="0" width=
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+ − 218 "100%" cellpadding="0" cellspacing="0">
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+ − 219 <tr valign="top">
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+ − 220 <td align="left" width="20"><a href="ltpda_training_topic_2_3.html"><img src=
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+ − 221 "b_prev.gif" border="0" align="bottom" alt=
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+ − 222 "Resampling a time-series AO"></a> </td>
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+ − 223
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+ − 224 <td align="left">Resampling a time-series AO</td>
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+ − 225
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+ − 226 <td> </td>
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+ − 227
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+ − 228 <td align="right">Remove trends from a time-series AO</td>
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+ − 229
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+ − 230 <td align="right" width="20"><a href=
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+ − 231 "ltpda_training_topic_2_5.html"><img src="b_next.gif" border="0" align=
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+ − 232 "bottom" alt="Remove trends from a time-series AO"></a></td>
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+ − 233 </tr>
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+ − 234 </table><br>
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+ − 235
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+ − 236 <p class="copy">©LTP Team</p>
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+ − 237 </body>
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+ − 238 </html>