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| author | Daniele Nicolodi <nicolodi@science.unitn.it> |
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| date | Wed, 23 Nov 2011 19:22:13 +0100 |
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--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/m-toolbox/html_help/help/ug/ltpda_training_topic_2_4.html Wed Nov 23 19:22:13 2011 +0100 @@ -0,0 +1,238 @@ +<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN" + "http://www.w3.org/TR/1999/REC-html401-19991224/loose.dtd"> + +<html lang="en"> +<head> + <meta name="generator" content= + "HTML Tidy for Mac OS X (vers 1st December 2004), see www.w3.org"> + <meta http-equiv="Content-Type" content= + "text/html; charset=us-ascii"> + + <title>Interpolation of a time-series AO (LTPDA Toolbox)</title> + <link rel="stylesheet" href="docstyle.css" type="text/css"> + <meta name="generator" content="DocBook XSL Stylesheets V1.52.2"> + <meta name="description" content= + "Presents an overview of the features, system requirements, and starting the toolbox."> + </head> + +<body> + <a name="top_of_page" id="top_of_page"></a> + + <p style="font-size:1px;"> </p> + + <table class="nav" summary="Navigation aid" border="0" width= + "100%" cellpadding="0" cellspacing="0"> + <tr> + <td valign="baseline"><b>LTPDA Toolbox</b></td><td><a href="../helptoc.html">contents</a></td> + + <td valign="baseline" align="right"><a href= + "ltpda_training_topic_2_3.html"><img src="b_prev.gif" border="0" align= + "bottom" alt="Resampling a time-series AO"></a> <a href= + "ltpda_training_topic_2_5.html"><img src="b_next.gif" border="0" align= + "bottom" alt="Remove trends from a time-series AO"></a></td> + </tr> + </table> + + <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> + + <br> + <br> + <table class="nav" summary="Navigation aid" border="0" width= + "100%" cellpadding="0" cellspacing="0"> + <tr valign="top"> + <td align="left" width="20"><a href="ltpda_training_topic_2_3.html"><img src= + "b_prev.gif" border="0" align="bottom" alt= + "Resampling a time-series AO"></a> </td> + + <td align="left">Resampling a time-series AO</td> + + <td> </td> + + <td align="right">Remove trends from a time-series AO</td> + + <td align="right" width="20"><a href= + "ltpda_training_topic_2_5.html"><img src="b_next.gif" border="0" align= + "bottom" alt="Remove trends from a time-series AO"></a></td> + </tr> + </table><br> + + <p class="copy">©LTP Team</p> +</body> +</html>