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  <title>Interpolation of a time-series AO (LTPDA Toolbox)</title>
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  <h1 class="title"><a name="f3-12899" id="f3-12899"></a>Interpolation of a time-series AO</h1>
  <hr>

  <p>
	<p>
  The <tt>ao</tt> class has a method for interpolating data using different forms of interpolation. This method is
  called <tt>ao/interp</tt>.
</p>
<p>
  To configure <tt>ao/interp</tt>, use the following parameters:
  <table cellspacing="0" class="body" cellpadding="2" border="0" width="80%">
    <colgroup>
      <col width="25%"/>
      <col width="75%"/>
    </colgroup>
    <thead>
      <tr valign="top">
        <th class="categorylist">Key</th>
        <th class="categorylist">Description</th>
      </tr>
    </thead>
    <tbody>
      <!-- Key 'Vertices' -->
      <tr valign="top">
        <td bgcolor="#f3f4f5">
          <p><tt>VERTICES</tt></p>
        </td>
        <td bgcolor="#f3f4f5">
          <p>A new set of vertices (relative to the t0) on which to resample.</p>
        </td>
      </tr>
      <!-- Key 'method' -->
      <tr valign="top">
        <td bgcolor="#f3f4f5">
          <p><tt>METHOD</tt></p>
        </td>
        <td bgcolor="#f3f4f5">
          <p>The method by which to interpolate. Choose from
            <ul>
              <li>'nearest' - nearest neighbour</li>
              <li>'linear'  - linear interpolation</li>
              <li>'spline'  - for spline interpolation</li>
              <li>'cubic'   - for cubic interpolation</li>
          </ul></p>
        </td>
      </tr>
    </tbody>
  </table>
</p>
<h2>Example</h2>
<p>
  Here we will interpolate a sinusoid singal on to a new time-grid. The result will be to increase the
  sample rate by a factor 2.
</p>
<p>
  First we create a time-series ao:
</p>
<div class="fragment"><pre>
    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>);
    x  = ao(pl);
  </pre>
</div>
<p>
  Then we create the new time-grid we want to resample on to.
</p>
<div class="fragment"><pre>
   tt   = linspace(0, x.nsecs - 1/x.fs, 2*(x.len));
  </pre>
</div>
<p>
  And finally we can apply our new time-grid to the data using <tt>interp</tt>. We test two of the available interpolation methods:
</p>
<div class="fragment"><pre>
    pl_spline  = plist(<span class="string">'vertices'</span>,tt);
    pl_nearest = plist(<span class="string">'vertices'</span>,tt,<span class="string">'method'</span>,<span class="string">'nearest'</span>);
    x_spline   = interp(x,pl_spline);
    x_nearest  = interp(x,pl_nearest);
    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>}, ...
    <span class="string">'LineColors'</span>, {<span class="string">'k'</span>, <span class="string">'r'</span>, <span class="string">'g'</span>}, ...
    <span class="string">'XRanges'</span>, [0 1]));
  </pre>
</div>
<img src="images/ltpda_training_1/topic2/interp.png" alt="Interpolate" border="3">
<br>
<br>
<p>
  To do the same activity on the workbench, we can use a pipeline like:
</p>
<img src="images/ltpda_training_1/topic2/lwb_interp_1.png" alt="Interpolate" border="3">
<p>
  This teaches some important aspects of the use of the workbench, so it's worth stepping through its construction slowly.
</p>
<p>
  To build this pipeline:
  <ol>
    <li>Create a new empty canvas</li>
    <li>Add two MATLAB Expression Blocks:
      <ol>
        <li>Right-click on the canvas and choose "Add Block...->MATBlock". A <tt>MATBlock</tt> is a block which can
        evaluate any valid MATLAB expression and pass that to further blocks via its single output.</li>
        <li>Select the block, then change its name in the block
  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>
        <li>Double-click the block to get a pop-up dialog where you can enter the MATLAB expression. In this case
        just enter the value 20.</li>
        <li>Select this 'fs' block and hit <tt>ctrl-d</tt> (<tt>cmd-d</tt> on OS X) to duplicate the block.</li>
        <li>Select the new block and change its name to 'nsecs'</li>
        <li>Double-click the 'nsecs' block to change its expression. Enter the value 10.</li>
      </ol>
    </li>
    <li>Next we need some additional blocks. Add an <tt>ao</tt> block, two <tt>ao/interp</tt> blocks, an
      <tt>ao/x</tt> block, and an <tt>ao/iplot</tt> block.
    </li>
    <li>Connect up the blocks as shown on the pipeline above.
      <table cellspacing="0" class="note" summary="Note" cellpadding="5" border="1">
        <tr width="90%">
          <td>
            To add inputs (or outputs) to a block, right-click on the block and choose "Add input".
          </td>
        </tr>
      </table>
      <table cellspacing="0" class="note" summary="Note" cellpadding="5" border="1">
        <tr width="90%">
          <td>
            Double-click an LTPDA Block to get a dialog box to enter a new name for the block.
          </td>
        </tr>
      </table>
      <table cellspacing="0" class="note" summary="Note" cellpadding="5" border="1">
        <tr width="90%">
          <td>
            To set the color of the pipes eminating from a particular block, right-click on the block
            and choose "Set output pipe color" from the context menu. You can also set the color of
            individual pipes by right-clicking on a pipe and choosing "Set color" from the context menu.
          </td>
        </tr>
      </table>
    </li>
    <li>Next we need to set the various properties of each block. Follow these steps:
      <ol>
        <li>Set the properties of the AO block to look like:<br>
          <img src="images/ltpda_training_1/topic2/lwb_interp_ao_props.png" alt="Interpolate" border="3">
          <table cellspacing="0" class="note" summary="Note" cellpadding="5" border="1">
            <tr width="90%">
              <td>
                The single quotes around the <tt>TSFCN</tt> value are not strictly necessary, but it can
                avoid problems, for example in the case you have a variable <tt>t</tt> already defined in the MATLAB
                workspace.
              </td>
            </tr>
          </table>
        </li>
        <li>
          Set the properties of the first interpolate block (a_spline) to look like:<br>
          <img src="images/ltpda_training_1/topic2/lwb_interp_ao_interp1.png" alt="Interpolate" border="3"> <br>
          Notice that here we have used the keywords <tt>PORT_1</tt> and <tt>PORT_2</tt> to build the expression. These
          refer to the ports of that block, and are connected to the MATLAB Expression Blocks which represent the values
          we are interested in.
        </li>
        <li>
          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
          is then passed to the next interpolation block where we use the values as the vertices for the next
          interpolation step, thus ensuring that the two interpolations are done on the same grid.
        </li>
        <li>
          Set the properties of the second interpolate block (a_near) to look like:<br>
          <img src="images/ltpda_training_1/topic2/lwb_interp_ao_interp2.png" alt="Interpolate" border="3"> <br>
        </li>
        <li>
          Finally, for the <tt>iplot</tt> block, add three new parameters and give then key names and values
          like:<br>
          <img src="images/ltpda_training_1/topic2/lwb_interp_iplot.png" alt="Interpolate" border="3"> <br>
        </li>
      </ol>
    </li>
  </ol>
  It should now be possible to run this pipeline and see a plot very similar to the one produced above.
</p>
  </p>

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      <td align="left">Resampling a time-series AO</td>

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      <td align="right">Remove trends from a time-series AO</td>

      <td align="right" width="20"><a href=
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  <p class="copy">&copy;LTP Team</p>
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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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