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  <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>
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</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">


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author	Daniele Nicolodi <nicolodi@science.unitn.it>
date	Mon, 05 Dec 2011 18:04:34 +0100
parents	f0afece42f48
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