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author Daniele Nicolodi <nicolodi@science.unitn.it>
date Wed, 23 Nov 2011 19:22:13 +0100
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+<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN"
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+
+<html lang="en">
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+  "HTML Tidy for Mac OS X (vers 1st December 2004), see www.w3.org">
+  <meta http-equiv="Content-Type" content=
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+
+  <title>Upsampling 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;">&nbsp;</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_1.html"><img src="b_prev.gif" border="0" align=
+      "bottom" alt="Downsampling a time-series AO"></a>&nbsp;&nbsp;&nbsp;<a href=
+      "ltpda_training_topic_2_3.html"><img src="b_next.gif" border="0" align=
+      "bottom" alt="Resampling a time-series AO"></a></td>
+    </tr>
+  </table>
+
+  <h1 class="title"><a name="f3-12899" id="f3-12899"></a>Upsampling a time-series AO</h1>
+  <hr>
+  
+  <p>
+	<p>
+  Upsampling increases the sampling rate of the input AOs by an integer factor
+</p>
+
+<p>The <tt>ao/upsample</tt> method can take 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 'N' -->
+      <tr valign="top">
+        <td bgcolor="#f3f4f5">
+          <p><tt>N</tt></p>
+        </td>
+        <td bgcolor="#f3f4f5">
+          <p>The upsample factor. The algorithm places 'N-1' zeros between each of the original samples.</p>
+        </td>
+      </tr>
+      <!-- Key 'offset' -->
+      <tr valign="top">
+        <td bgcolor="#f3f4f5">
+          <p><tt>PHASE</tt></p>
+        </td>
+        <td bgcolor="#f3f4f5">
+          <p>This parameter specifies an additional sample offet. The value must be between 0 and N-1.</p>
+        </td>
+      </tr>
+    </tbody>
+  </table>
+</p>
+<h2>Example 1</h2>
+<p>        
+  We will upsample a sine-wave by a factor of 3 with no initial phase offset.
+</p>
+<p>
+  Start by creating a sine-wave at 1Hz with a 30Hz sample rate and 10 seconds long. We can use 
+  the <tt>ao</tt> "From Waveform" parameter set to do this. (Equally, we can do this with the "From Time-series Function" 
+  parameter set.)
+</p>
+<div class="fragment"><pre>
+    pl = plist(<span class="string">'Waveform'</span>, <span class="string">'sine wave'</span>, <span class="string">'f'</span>, 1, <span class="string">'fs'</span>, 30, <span class="string">'nsecs'</span>, 10);
+    x  = ao(pl);</pre></div>
+<p>
+  Now we can proceed to upsample this data by a factor 3. This will place 2 zero samples between each of the 
+  original samples.
+</p>
+<div class="fragment"><pre>
+    pl_up = plist(<span class="string">'N'</span>, 3); <span class="comment">% increase the sampling frequency by a factor of 10</span>
+    x_up  = upsample(x, pl_up); <span class="comment">% resample the input AO (x) to obtain the upsampled AO (y) </span>
+    iplot(x, x_up, plist(<span class="string">'XRanges'</span>, [0 1], <span class="string">'Markers'</span>, {<span class="string">'o'</span>, <span class="string">'s'</span>})) <span class="comment">% plot original and upsampled data</span>
+  </pre>
+</div>
+<img src="images/ltpda_training_1/topic2/up1.png" alt="Upsample" border="3">
+<br>
+<br>
+<h2>Example 2</h2>
+
+<p>
+  In this second example, we will upsample some random noise by a factor 4 with a phase offset of 2 samples.
+</p>
+<p>
+  Again, start by constructing some test data, in this case a white-noise data stream. We can do this 
+  again using the "From Waveform" parameter set with an <tt>ao</tt> constructor.
+</p>
+<div class="fragment"><pre>
+pl         = plist(<span class="string">'Waveform'</span>, <span class="string">'noise'</span>, <span class="string">'fs'</span>, 10, <span class="string">'nsecs'</span>, 10, <span class="string">'yunits'</span>, <span class="string">'m'</span>);
+x          = ao(pl);
+pl_upphase = plist(<span class="string">'N'</span>, 4,<span class="string">'phase'</span>, 2); <span class="comment">% increase the sampling frequency and add phase of 2 samples to the upsampled data</span>
+x_upphase  = upsample(x, pl_upphase); <span class="comment">% resample the input AO (x) to obtain the upsampled and delayed AO</span>
+iplot(x, x_upphase, plist(<span class="string">'XRanges'</span>, [0 1], <span class="string">'Markers'</span>, {<span class="string">'o'</span>, <span class="string">'s'</span>})) <span class="comment">% plot original and upsampled data</span>
+  </pre>
+</div>
+<img src="images/ltpda_training_1/topic2/up2.png" alt="Upsample" border="3">
+
+
+  </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_1.html"><img src=
+      "b_prev.gif" border="0" align="bottom" alt=
+      "Downsampling a time-series AO"></a>&nbsp;</td>
+
+      <td align="left">Downsampling a time-series AO</td>
+
+      <td>&nbsp;</td>
+
+      <td align="right">Resampling a time-series AO</td>
+
+      <td align="right" width="20"><a href=
+      "ltpda_training_topic_2_3.html"><img src="b_next.gif" border="0" align=
+      "bottom" alt="Resampling a time-series AO"></a></td>
+    </tr>
+  </table><br>
+
+  <p class="copy">&copy;LTP Team</p>
+</body>
+</html>