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  <h1 class="title"><a name="f3-12899" id="f3-12899"></a>IFO/Temperature Example -  Spectral Analysis</h1>
  <hr>

  <p>

<h2>Loading the consolidated data sets from topic2</h2>
In the last topic you should have saved your consolidated data files as
<p>
<ul>
		 <li>ifo_temp_example/temp_fixed.xml</li>
		 <li>ifo_temp_example/ifo_fixed.xml</li>
</ul>
</p>

<p>
  In order to proceed with the spectral analysis, we need to use the <tt>ao</tt> constuctor, with the
  set of parameters "From XML File". The key
  parameters are:
  <table cellspacing="0" class="body" cellpadding="2" border="0" width="80%">
    <colgroup>
      <col width="15%"/>
      <col width="35%"/>
      <col width="50%"/>
    </colgroup>
    <thead>
      <tr valign="top">
        <th class="categorylist">Key</th>
        <th class="categorylist">Value</th>
        <th class="categorylist">Description</th>
      </tr>
    </thead>
    <tbody>
      <!-- Key 'filename' for IFO -->
      <tr valign="top">
        <td bgcolor="#f3f4f5">
          <p><tt>FILENAME</tt></p>
        </td>
        <td bgcolor="#f3f4f5">
          <p><span class="string">'ifo_temp_example/ifo_fixed.xml'</span></p>
        </td>
        <td bgcolor="#f3f4f5">
          <p>The name of the file to read the data from.</p>
        </td>
      </tr>
       <!-- Key 'filename' for T -->
      <tr valign="top">
        <td bgcolor="#f3f4f5">
          <p><tt>FILENAME</tt></p>
        </td>
        <td bgcolor="#f3f4f5">
          <p><span class="string">'ifo_temp_example/temp_fixed.xml'</span></p>
        </td>
        <td bgcolor="#f3f4f5">
          <p>The name of the file to read the data from.</p>
        </td>
      </tr>
    </tbody>
  </table>
</p>
<p>Hint: the command-line sequence may be similar to the following:
  <div class="fragment"><pre>
<span class="comment">%% Get the consolidated data</span>
<span class="comment">% Using the xml format</span>

T_filename = <span class="string">'ifo_temp_example/temp_fixed.xml'</span>;
x_filename = <span class="string">'ifo_temp_example/ifo_fixed.xml'</span>;

pl_load_T = plist(<span class="string">'filename'</span>, T_filename);
pl_load_x = plist(<span class="string">'filename'</span>, x_filename);

<span class="comment">% Build the data aos</span>
T = ao(pl_load_T);
x = ao(pl_load_x);
</pre></div>

</p>
  <h2>Estimating the PSD of the signals</h2>

<p>
  To perform the PSD estimation, you can use the method
<p>
  <table cellspacing="0" class="note" summary="Note" cellpadding="5" border="1">
    <tr width="90%">
      <td>
        <tt>ao/lpsd</tt>
      </td>
    </tr>
  </table>
</p>
<p>Hint: the command-line sequence may be similar to the following:
  <div class="fragment"><pre>
<span class="comment">%% plists for spectral estimations</span>

<span class="comment">%% PSD</span>
x_psd = lpsd(x)
x_psd.setName(<span class="string">'Interferometer'</span>);

T_psd = lpsd(T)
T_psd.setName(<span class="string">'Temperature'</span>);

<span class="comment">% Plot estimated PSD</span>
pl_plot = plist(<span class="string">'Arrangement'</span>, <span class="string">'subplots'</span>, <span class="string">'LineStyles'</span>, {<span class="string">'-'</span>,<span class="string">'-'</span>},<span class="string">'Linecolors'</span>, {<span class="string">'b'</span>, <span class="string">'r'</span>});
iplot(sqrt(x_psd), sqrt(T_psd), pl_plot);
</pre></div>
</p>

   <h2>Reducing time interval</h2>

  <p>
    Looking at the output of the analysis it is easy to recognize in the IFO PSD the signature of
    some strong "spike" in the data. Indeed, if we plot the <tt>x</tt> data, we can find it
    around <tt>t = 40800</tt>. There is also a leftover from the filtering process performed during
    consolidation right near to the last data.
  </p>
  <p>
    We can then try to estimate the impact of the "glitch" by comparing the results we obtain by
    passing to <tt>ao/lpsd</tt> a reduced fraction of the data.
  </p>

  <p>
    In order to select a fraction of the data we use the method:

    <table cellspacing="0" class="note" summary="Note" cellpadding="5" border="1">
      <tr width="90%">
        <td>
          <tt>ao/split</tt>
        </td>
      </tr>
    </table>
  </p>
<p>
  The relevant parameters for this method are listed here, together with their recommended values:
</p>
<p>
  <table cellspacing="0" class="body" cellpadding="2" border="0" width="80%">
    <colgroup>
      <col width="15%"/>
      <col width="35%"/>
      <col width="50%"/>
    </colgroup>
    <thead>
      <tr valign="top">
        <th class="categorylist">Key</th>
        <th class="categorylist">Value</th>
        <th class="categorylist">Description</th>
      </tr>
    </thead>
    <tbody>
      <!-- Key 'SPLIT_TYPE' -->
      <tr valign="top">
        <td bgcolor="#f3f4f5">
          <p><tt>SPLIT_TYPE</tt></p>
        </td>
        <td bgcolor="#f3f4f5">
          <p><span class="string">'interval'</span></p>
        </td>
        <td bgcolor="#f3f4f5">
          <p>The method for splitting the <tt>ao</tt></p>
        </td>
      </tr>
      <!-- Key 'START_TIME' -->
      <tr valign="top">
        <td bgcolor="#f3f4f5">
          <p><tt>START_TIME</tt></p>
        </td>
        <td bgcolor="#f3f4f5">
          x.t0 + 40800
        </td>
        <td bgcolor="#f3f4f5">
          <p>A time-object to start at</p>
        </td>
      </tr>
      <!-- Key 'END_TIME' -->
      <tr valign="top">
        <td bgcolor="#f3f4f5">
          <p><tt>END_TIME</tt></p>
        </td>
        <td bgcolor="#f3f4f5">
          x.t0 + 193500
        </td>
        <td bgcolor="#f3f4f5">
          <p>A time-object to end at</p>
        </td>
      </tr>
    </tbody>
  </table>
</p>
<p>
  Notice that in order to perform this action, we access one property of the <tt>ao</tt> object,
  called "t0". The call to the <tt>t0</tt> methods gives as an output an object of the
  <tt>time</tt> class. Additionally, it's possibly to directly add a numer (in seconds) to
  obtain a new time object.
</p>
<p>
  Hint: the command-line sequence may be similar to the following:
</p>
<p>
 <div class="fragment"><pre>
<span class="comment">%% Skip some IFO glitch from the consolidation</span>

pl_split = plist(<span class="string">'start_time'</span>, x.t0 + 40800, ...
  <span class="string">'end_time'</span>, x.t0 + 193500);

x_red = split(x, pl_split);
T_red = split(T, pl_split);
</pre></div>
</p>
<p>
  <table cellspacing="0" class="note" summary="Note" cellpadding="5" border="1">
    <tr width="90%">
      <td>
        Note: you can also use the parameter 'times' for split to specify times relative to the first sample.
        In this case:
        <div class="fragment"><pre>
            plist('times', [40800 193500]).
          </pre>
        </div>
        would work.
      </td>
    </tr>
  </table>
</p>
<p>
  And we can go proceed, evaluating 2 more <tt>ao</tt>s to compare the effect of skipping the
  "glitch". After doing that, we can plot
them in comparison.
</p>
<p>Hint:</p>
<p>
  <div class="fragment"><pre>
      <span class="comment">%% PSD</span>
      x_red_psd = lpsd(x_red);
      x_red_psd.setName(<span class="string">'Interferometer'</span>);

      T_red_psd = lpsd(T_red)
      T_red_psd.setName(<span class="string">'Temperature'</span>);

      <span class="comment">% Plot estimated PSD</span>
      pl_plot = plist(<span class="string">'Arrangement'</span>, <span class="string">'stacked'</span>, <span class="string">'LineStyles'</span>, {<span class="string">'-'</span>,<span class="string">'-'</span>},<span class="string">'Linecolors'</span>, {<span class="string">'b'</span>, <span class="string">'r'</span>});
      iplot(sqrt(x_psd), sqrt(x_red_psd), pl_plot);
      iplot(sqrt(T_psd), sqrt(T_red_psd), pl_plot);
  </pre></div>
</p>
<br>
<br>
<img src="images/ltpda_training_1/topic3/IFO_PSD_1.png" alt="PSD of IFO data" border="1">
<br>
<br>
<img src="images/ltpda_training_1/topic3/T_PSD_1.png" alt="PSD of IFO data" border="1">
<br>
<br>
 <h2>Estimating the cross-spectra</h2>
 <p>
   We can now proceed and use the
   <table cellspacing="0" class="note" summary="Note" cellpadding="5" border="1">
     <tr width="90%">
       <td>
         <tt>ao/lcpsd</tt>
       </td>
     </tr>
   </table>
   method to evaluate the cross-spectra of the signals, employing a shorter window in order to reduce the
   scatter of the estimated values.
 </p>
<p>
  Hint:
</p>
<p>
  <div class="fragment"><pre>
      <span class="comment">%% CPSD estimate</span>
      CTx = lcpsd(T_red, x_red);
      CxT = lcpsd(x_red, T_red);
      <span class="comment">% Plot estimated CPSD</span>
      iplot(CTx);
      iplot(CxT);
  </pre></div>
</p>
<br>
<br>
<img src="images/ltpda_training_1/topic3/IFO_T_CPSD_1.png" alt="CPSD of IFO and T data" border="1">
<br>
<br>
<img src="images/ltpda_training_1/topic3/IFO_T_CPSD_2.png" alt="CPSD of T and IFO data" border="1">
<br>
<br>
<p>
  As expected, there is a strong low-frequency correlation between the IFO data <tt>x</tt> and the
  temperature data <tt>T</tt>.
</p>


 <h2>Estimating the cross-coherence</h2>

<p>
  Similarly, we can now proceed and use the
  <table cellspacing="0" class="note" summary="Note" cellpadding="5" border="1">
    <tr width="90%">
      <td>
        <tt>ao/lcohere</tt>
      </td>
    </tr>
  </table>
  method to evaluate the cross-coherence of the signals. The output will be a [2x2] matrix of <tt>ao</tt>s,
  and we want to look at one of the off-diagonal terms:
</p>
<p>
  <div class="fragment"><pre>
      <span class="comment">%% Coherence estimate</span>
      coh = lcohere(T_red, x_red);
      <span class="comment">% Plot estimated cross-coherence</span>
      iplot(coh, plist(<span class="string">'YScales'</span>, <span class="string">'lin'</span>))
  </pre></div>
</p>
<br>
<br>
<img src="images/ltpda_training_1/topic3/IFO_T_cohere_1.png" alt="Cross-coherence of T and IFO data" border="1">
<br>
<br>
<p>
  The coherence approaches 1 at low frequency.
</p>

 <h2>Estimating the transfer function of temperature</h2>
 <p>
   We want now to perform noise projection, trying to estimate the transfer function of the
   temperature signal into the interferometer output.
   In order to do that, we can use the
   <table cellspacing="0" class="note" summary="Note" cellpadding="5" border="1">
     <tr width="90%">
       <td>
         <tt>ao/ltfe</tt>
       </td>
     </tr>
   </table> method.
 </p>
<p>
 We also want to plot this transfer function to check that the units are correct. <br />
 Hint:

  <div class="fragment"><pre>
      <span class="comment">%% transfer function estimate</span>
      tf = ltfe(T_red, x_red)

      <span class="comment">% Plot estimated TF</span>
      iplot(tf);
  </pre></div>
</p>
<br>
<br>
<img src="images/ltpda_training_1/topic3/IFO_T_TF_1.png" alt="Transfer function T to IFO" border="1">
<br>
<br>
<p>
  As expected, the transfer function T -> IFO is well measured at low frequencies.
</p>

<h2>Noise projection</h2>
<p>
  We can eventually perform the noise projection, estimating the amount of the noise in the IFO
  being actually caused by temperature fluctuations. It's a frequency domain estimate:
</p>
<p>
  <div class="fragment"><pre>
      <span class="comment">%% Noise projection in frequency domain</span>

      proj = T_red_psd.*(abs(tf)).^2;
      proj.simplifyYunits;
      proj.setName(<span class="string">'temp. contrib. projection'</span>)
      <span class="comment">%% Plotting the noise projection in frequency domain</span>
      iplot(x_red_psd, proj);
  </pre></div>
</p>
<p>
  The contribution of the temperature fluctuations is clearly estimated.
</p>
<br>
<br>
<img src="images/ltpda_training_1/topic3/IFO_projection.png" alt="Noise projection of T into IFO" border="1">
<br>
<br>

  <h2>Saving the results</h2>
<p>
  Let's fininsh this section of the exercise by saving the results on disk, in xml format. We want to keep the
  results about the Power Spectral Density and Transfer Function Estimates, at least.
</p>
<p>
  Hint: the command-line sequence may be similar to the following:
  <div class="fragment"><pre>
      <span class="comment">%% Save the PSD data</span>
      <span class="comment">% Plists for the xml format</span>

      pl_save_x_PSD = plist(<span class="string">'filename'</span>, <span class="string">'ifo_temp_example/ifo_psd.xml'</span>);
      pl_save_T_PSD = plist(<span class="string">'filename'</span>, <span class="string">'ifo_temp_example/T_psd.xml'</span>);

      pl_save_xT_CPSD = plist(<span class="string">'filename'</span>, <span class="string">'ifo_temp_example/ifo_T_cpsd.xml'</span>);
      pl_save_xT_cohere = plist(<span class="string">'filename'</span>, <span class="string">'ifo_temp_example/ifo_T_cohere.xml'</span>);

      pl_save_xT_TFE = plist(<span class="string">'filename'</span>, <span class="string">'ifo_temp_example/T_ifo_tf.xml'</span>);
  </pre></div>
</p>
<p>
  or
  <div class="fragment"><pre>
      <span class="comment">% Plists for the mat format</span>

      pl_save_x_PSD = plist(<span class="string">'filename'</span>, <span class="string">'ifo_temp_example/ifo_psd.mat'</span>);
      pl_save_T_PSD = plist(<span class="string">'filename'</span>, <span class="string">'ifo_temp_example/T_psd.mat'</span>);

      pl_save_xT_CPSD = plist(<span class="string">'filename'</span>, <span class="string">'ifo_temp_example/ifo_T_cpsd.mat'</span>);
      pl_save_xT_cohere = plist(<span class="string">'filename'</span>, <span class="string">'ifo_temp_example/ifo_T_cohere.mat'</span>);

      pl_save_xT_TFE = plist(<span class="string">'filename'</span>, <span class="string">'ifo_temp_example/T_ifo_tf.mat'</span>);
  </pre></div>
</p>
<p>and
  <div class="fragment"><pre>
      <span class="comment">% Save</span>
      x_red_psd.save(pl_save_x_PSD);
      T_red_psd.save(pl_save_T_PSD);
      CxT.save(pl_save_xT_CPSD);
      coh.save(pl_save_xT_cohere);
      tf.save(pl_save_xT_TFE);
  </pre></div>
</p>

  </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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