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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_3_6.html Wed Nov 23 19:22:13 2011 +0100 @@ -0,0 +1,487 @@ +<!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>IFO/Temperature Example - Spectral Analysis (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_3_5.html"><img src="b_prev.gif" border="0" align= + "bottom" alt="Empirical Transfer Function estimation"></a> <a href= + "ltpda_training_topic_4.html"><img src="b_next.gif" border="0" align= + "bottom" alt="Topic 4 - Transfer function models and digital filtering"></a></td> + </tr> + </table> + + <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> + + <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_3_5.html"><img src= + "b_prev.gif" border="0" align="bottom" alt= + "Empirical Transfer Function estimation"></a> </td> + + <td align="left">Empirical Transfer Function estimation</td> + + <td> </td> + + <td align="right">Topic 4 - Transfer function models and digital filtering</td> + + <td align="right" width="20"><a href= + "ltpda_training_topic_4.html"><img src="b_next.gif" border="0" align= + "bottom" alt="Topic 4 - Transfer function models and digital filtering"></a></td> + </tr> + </table><br> + + <p class="copy">©LTP Team</p> +</body> +</html>