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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_4_5.html Wed Nov 23 19:22:13 2011 +0100 @@ -0,0 +1,581 @@ +<!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 - Simulation (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_4_4_2.html"><img src="b_prev.gif" border="0" align= + "bottom" alt="By defining filter properties"></a> <a href= + "ltpda_training_topic_5.html"><img src="b_next.gif" border="0" align= + "bottom" alt="Topic 5 - Model fitting"></a></td> + </tr> + </table> + + <h1 class="title"><a name="f3-12899" id="f3-12899"></a>IFO/Temperature Example - Simulation</h1> + <hr> + + <p> + <p> + We now come back to the IFO/Temperature working example. Our interest here is not + to add more tools to the data analysis chain that you've been developing but + to create a simple toy model that allows you to reproduce the steps done up + to now but with synthetic data. +</p> +<p> + The problem is shown schematically in the figure below. We will generate temperature and interferometer + noisy data by applying a filter (<b>TMP</b> and <b>IFO</b>) to white noise data + (<b>WN1</b> and <b>WN2</b>). We will then add a temperature coupling (<b>K2RAD</b>) to the + interferometer and from the measured interferometer and temperature data we will then estimate + the temperature to interferometer coupling. +</p> + +<p align="center"> + <img src="images/ltpda_training_1/topic4/IFO2TSimulation.png" alt="temperature substraction scheme" border="1" > +</p> +<p> + Since we've been through the same steps that you need to apply here in the previous + section we will give here the step by step description of the task and let you + play with the models. +</p> + +<h2> Build the models<h2> +<p> + We need three models: one to generate temperature-like data, another modelling the + interferometer and a third one acting as the K-to-rad transfer function. +</p> + +<h3> STEP 1: Build a temperature noise PZMODEL with the following properties<h4> + +<table cellspacing="0" class="body" cellpadding="2" border="0" width="50%"> + <colgroup> + <col width="15%"/> + <col width="35%"/> + </colgroup> + <thead> + <tr valign="top"> + <th class="categorylist">Key</th> + <th class="categorylist">Value</th> + </tr> + </thead> + <tbody> + <!-- Key 'filename' --> + <tr valign="top"> + <td bgcolor="#f3f4f5"> + <p><tt><span class="string">'name'</span></tt></p> + </td> + <td bgcolor="#f3f4f5"> + <span class="string">'TMP'</span> + </td> + </tr> + <!-- Key 'filename' --> + <tr valign="top"> + <td bgcolor="#f3f4f5"> + <p><tt><span class="string">'ounits'</span></tt></p> + </td> + <td bgcolor="#f3f4f5"> + <span class="string">'K'</span> + </td> + </tr> + <!-- Key 'filename' --> + <tr valign="top"> + <td bgcolor="#f3f4f5"> + <p><tt>GAIN</tt></p> + </td> + <td bgcolor="#f3f4f5"> + 10 + </td> + </tr> + <!-- Key 'filename' --> + <tr valign="top"> + <td bgcolor="#f3f4f5"> + <p><tt>POLE 1</tt></p> + </td> + <td bgcolor="#f3f4f5"> + 1e-5 + </td> + </tbody> +</table> +<p> + For example, this few lines would do the job +</p> +<div class="fragment"><pre> + TMP = pzmodel(10,1e-5,[]); + TMP.setOunits(<span class="string">'K'</span>) + TMP.setName(<span class="string">'TMP'</span>) +</pre></div> + +<h3> STEP 2: Build a interferometer noise PZMODEL with the following properties<h4> + +<table cellspacing="0" class="body" cellpadding="2" border="0" width="50%"> + <colgroup> + <col width="15%"/> + <col width="35%"/> + </colgroup> + <thead> + <tr valign="top"> + <th class="categorylist">Key</th> + <th class="categorylist">Value</th> + </tr> + </thead> + <tbody> + <!-- Key 'filename' --> + <tr valign="top"> + <td bgcolor="#f3f4f5"> + <p><tt><span class="string">'name'</span></tt></p> + </td> + <td bgcolor="#f3f4f5"> + <span class="string">'IFO'</span> + </td> + </tr> + <!-- Key 'filename' --> + <tr valign="top"> + <td bgcolor="#f3f4f5"> + <p><tt><span class="string">'ounits'</span></tt></p> + </td> + <td bgcolor="#f3f4f5"> + <span class="string">'rad'</span> + </td> + </tr> + <!-- Key 'filename' --> + <tr valign="top"> + <td bgcolor="#f3f4f5"> + <p><tt>GAIN</tt></p> + </td> + <td bgcolor="#f3f4f5"> + 1e-3 + </td> + </tr> + <!-- Key 'filename' --> + <tr valign="top"> + <td bgcolor="#f3f4f5"> + <p><tt>POLE 1</tt></p> + </td> + <td bgcolor="#f3f4f5"> + 0.4 + </td> + </tr> + </tbody> +</table> + + +<h3> STEP 3: Build temperature to interferometer coupling PZMODEL with the following properties<h4> + +<table cellspacing="0" class="body" cellpadding="2" border="0" width="50%"> + <colgroup> + <col width="15%"/> + <col width="35%"/> + </colgroup> + <thead> + <tr valign="top"> + <th class="categorylist">Key</th> + <th class="categorylist">Value</th> + </tr> + </thead> + <tbody> + <!-- Key 'filename' --> + <tr valign="top"> + <td bgcolor="#f3f4f5"> + <p><tt><span class="string">'name'</span></tt></p> + </td> + <td bgcolor="#f3f4f5"> + <span class="string">'K2RAD'</span> + </td> + </tr> + <!-- Key 'filename' --> + <tr valign="top"> + <td bgcolor="#f3f4f5"> + <p><tt><span class="string">'iunits'</span></tt></p> + </td> + <td bgcolor="#f3f4f5"> + <span class="string">'K'</span> + </td> + </tr> + <!-- Key 'filename' --> + <tr valign="top"> + <td bgcolor="#f3f4f5"> + <p><tt><span class="string">'ounits'</span></tt></p> + </td> + <td bgcolor="#f3f4f5"> + <span class="string">'rad'</span> + </td> + </tr> + <!-- Key 'filename' --> + <tr valign="top"> + <td bgcolor="#f3f4f5"> + <p><tt>GAIN</tt></p> + </td> + <td bgcolor="#f3f4f5"> + 1e-1 + </td> + </tr> + <!-- Key 'filename' --> + <tr valign="top"> + <td bgcolor="#f3f4f5"> + <p><tt>POLE 1</tt></p> + </td> + <td bgcolor="#f3f4f5"> + 5e-4 + </td> + </tr> + </tbody> +</table> + +<p> + You can take a look at your models. Since we are interested in the projection of temperature + into interferometric data, we can plot the response of TMP*K2RAD against the IFO +</p> +<div class="fragment"><pre> + pl = plist(<span class="string">'f1'</span>,1e-5,<span class="string">'f2'</span>,0.01) + resp(K2RAD*TMP,IFO,pl) +</pre></div> +<p> + <img src="images/ltpda_training_1/topic4/Ifo2TempEx_T4_1.png" alt="inteferometer data" border="1" > +</p> + +<h2>Discretize the models<h2> +<p> + Now discretize the models at fs = 1Hz using the <tt>miir</tt> constructor. + After that you will obtain three digital filters +</p> +<h3> STEP 4: Discretize the three transfer (<b>TMP</b>,<b>IFO</b>,<b>K2RAD</b>) with the +MIIR constructor<h3> +<p> + For example, the model related to temperature noise would be discretized like this: +</p> +<div class="fragment"><pre> + TMPd = miir(TMP,plist(<span class="string">'fs'</span>,1)); +</pre></div> +<h2> Generate white noise data<h2> +<p> + We will need two initial white noise time series, <b>WN1</b> and <b>WN2</b>, that we will use as a seed + to apply our filters and get noise shaped time series. +</p> +<h3> STEP 5: Generate white noise with the AO constructor<h3> +<p> + You will need the ao constructor for that. You could use the following settings +</p> +<table cellspacing="0" class="body" cellpadding="2" border="0" width="50%"> + <colgroup> + <col width="15%"/> + <col width="35%"/> + </colgroup> + <thead> + <tr valign="top"> + <th class="categorylist">Key</th> + <th class="categorylist">Value</th> + </tr> + </thead> + <tbody> + <!-- Key 'filename' --> + <tr valign="top"> + <td bgcolor="#f3f4f5"> + <p><tt><span class="string">'name'</span></tt></p> + </td> + <td bgcolor="#f3f4f5"> + <span class="string">'WN1'</span> + </td> + </tr> + <!-- Key 'filename' --> + <tr valign="top"> + <td bgcolor="#f3f4f5"> + <p><tt><span class="string">'tsfcn'</span></tt></p> + </td> + <td bgcolor="#f3f4f5"> + <span class="string">'randn(size(t))'</span> + </td> + </tr> + <!-- Key 'filename' --> + <tr valign="top"> + <td bgcolor="#f3f4f5"> + <p><tt><span class="string">'fs'</span></tt></p> + </td> + <td bgcolor="#f3f4f5"> + 1 + </td> + </tr> + <!-- Key 'filename' --> + <tr valign="top"> + <td bgcolor="#f3f4f5"> + <p><tt><span class="string">'nsecs'</span></tt></p> + </td> + <td bgcolor="#f3f4f5"> + 250000 + </td> + </tr> + </tbody> +</table> + +<table cellspacing="0" class="body" cellpadding="2" border="0" width="50%"> + <colgroup> + <col width="15%"/> + <col width="35%"/> + </colgroup> + <thead> + <tr valign="top"> + <th class="categorylist">Key</th> + <th class="categorylist">Value</th> + </tr> + </thead> + <tbody> + <!-- Key 'filename' --> + <tr valign="top"> + <td bgcolor="#f3f4f5"> + <p><tt><span class="string">'name'</span></tt></p> + </td> + <td bgcolor="#f3f4f5"> + <span class="string">'WN2'</span> + </td> + </tr> + <!-- Key 'filename' --> + <tr valign="top"> + <td bgcolor="#f3f4f5"> + <p><tt><span class="string">'tsfcn'</span></tt></p> + </td> + <td bgcolor="#f3f4f5"> + <span class="string">'randn(size(t))'</span> + </td> + </tr> + <!-- Key 'filename' --> + <tr valign="top"> + <td bgcolor="#f3f4f5"> + <p><tt><span class="string">'fs'</span></tt></p> + </td> + <td bgcolor="#f3f4f5"> + 1 + </td> + </tr> + <!-- Key 'filename' --> + <tr valign="top"> + <td bgcolor="#f3f4f5"> + <p><tt><span class="string">'nsecs'</span></tt></p> + </td> + <td bgcolor="#f3f4f5"> + 250000 + </td> + </tr> + </tbody> +</table> + + +<h2>Generate the noise data streams<h2> +<p> + For each noise source you will need to apply the filter that you have designed to + the white noise data: +</p> + +<h3> STEP 6: Filter white noise WN1 with the TMPd filter </h3> +<p> + For example, following our notation: +</p> +<div class="fragment"><pre> + T = filter(WN1,TMPd); +</pre></div> +<h3> STEP 7: Filter white noise WN2 with the IFOd filter</h3> +<p> + Temperature and interferometric noise are uncorrelated, so we need to use here the + second noise time series <b>WN2</b> +</p> +<p> + For example, following our notation: +</p> +<div class="fragment"><pre> + IFO = filter(WN2,IFOd); +</pre></div> +<h3> STEP 8: Filter white noise WN1 with the TMPd and the K2RADd filter</h3> +<p> + In this case you need to apply both filters in serial, you can do this in one command + by using the 'bank' property of the <tt>filter</tt> method. +</p> +<p> + <table cellspacing="0" class="note" summary="Note" cellpadding="5" border="1"> + <tr width="90%"> + <td> + Hint: you can input a vector of filters into the <tt>filter</tt> method and + ask it to filter the data in 'parallel' or in 'serial' (the one we are interested + here) by doing the following + <div class="fragment"><pre> + b = filter(<b>WN1</b>,[<b>TMPd</b> <b>K2RADd</b>],plist(<span class="string">'bank'</span>,<span class="string">'serial'</span>)); + </pre></div> + + </td> + </tr> + </table> +</p> +<h3> STEP 9: Add the IFO noise to the K2RAD noise</h3> +<p> + At this point the IFO represents the purely interferometric noise and the K2RAD the + contribution to interferometric noise coming from temperature. You need to add both to + get the final interferometric data. This only requires to add both AOs. +</p> + +<h2>Perform the noise projection<h3> +<p> + Here we will reproduce the main steps performed in topic 3 analysis: power spectral and + transfer function estimation. +</p> + +<h3> STEP 10: Split the data streams </h3> +<p> + We will do the analysis with data in the region going from 1e5 to 2e5 seconds to avoid + initial transients. You must then split your two data streams introducing the following + parameters in the <tt>split</tt> method. +</p> + +<table cellspacing="0" class="body" cellpadding="2" border="0" width="50%"> + <colgroup> + <col width="15%"/> + <col width="35%"/> + </colgroup> + <thead> + <tr valign="top"> + <th class="categorylist">Key</th> + <th class="categorylist">Value</th> + </tr> + </thead> + <tbody> + <!-- Key 'filename' --> + <tr valign="top"> + <td bgcolor="#f3f4f5"> + <p><tt><span class="string">'times'</span></tt></p> + </td> + <td bgcolor="#f3f4f5"> + [1e5 2e5] + </td> + </tr> + </tbody> +</table> +<p> +After the splitting you must have two data streams that plot together should look like the +ones below. The code should be similar to one in the following lines + +<div class="fragment"><pre> + Ts = split(T,plist(<span class="string">'times'</span>,[1e5 2e5])) + Ts.setName(<span class="string">'Temperature'</span>) + IFOs = split(IFO_all,plist(<span class="string">'times'</span>,[1e5 2e5])) + IFOs.setName(<span class="string">'Interferometer'</span>) + <span class="comment">% Plot in different panels with 'subplots' options</span> + iplot(Ts,IFOs,plist(<span class="string">'arrangement'</span>,<span class="string">'subplots'</span>)) +</pre></div> + +<p> + <img src="images/ltpda_training_1/topic4/Ifo2TempEx_T4_3.png" alt="inteferometer data" border="1" > +</p> + +<h3> STEP 11: Compute power spectral estimates for the temperature and interferometric data </h3> +<p> + Here you need to apply <tt>lpsd</tt> or <tt>psd</tt> methods. For example: +</p> +<div class="fragment"><pre> + pl = plist(<span class="string">'order'</span>,1,<span class="string">'scale'</span>,<span class="string">'ASD'</span>) + psd_T = lpsd(Ts,pl) + psd_IFO = lpsd(IFOs,pl) +</pre></div> +<p> + The resulting spectrum should look like this +</p> +<p> + <img src="images/ltpda_training_1/topic4/Ifo2TempEx_T4_4.png" alt="inteferometer data" width="800px" border="1" > +</p> + +<h3> STEP 12: Compute transfer function estimate for the temperature and interferometric data </h3> +<p> + Here you need to apply <tt>ltfe</tt> or <tt>tfe</tt> methods. For example: +</p> +<div class="fragment"><pre> + T2IFO = ltfe(Ts,IFOs) + T2IFO.setName(<span class="string">'Transfer function'</span>) +</pre></div> +<p> + You can now compare the transfer function model with the estimation obtained from the data: +</p> +<div class="fragment"><pre> + pl = plist(<span class="string">'f1'</span>,1e-5,<span class="string">'f2'</span>,1) + iplot(T2IFO,resp(K2RAD,pl)) +</pre></div> +<p> + <img src="images/ltpda_training_1/topic4/Ifo2TempEx_T4_5.png" alt="inteferometer data" width="800px" border="1" > +</p> +<h3> STEP 13: Project the temperature noise </h3> +<p> + Reproducing the analysis performed in topic 3 you will be able to project the temperature noise contribution + into interferometric noise. The result obtained should be the one in the figure below and the code you will need + for that should be similar to this: +</p> + +<div class="fragment"><pre> + <span class="comment">% Compute projection</span> + Projection = abs(T2IFO).*psd_T; + Projection.simplifyYunits + Projection.setName; + <span class="comment">% Plot against interferometer noise</span> + iplot(psd_IFO,Projection) +</pre></div> + +<p> + <img src="images/ltpda_training_1/topic4/Ifo2TempEx_T4_6.png" alt="inteferometer data" width="800px" border="1" > +</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_4_4_2.html"><img src= + "b_prev.gif" border="0" align="bottom" alt= + "By defining filter properties"></a> </td> + + <td align="left">By defining filter properties</td> + + <td> </td> + + <td align="right">Topic 5 - Model fitting</td> + + <td align="right" width="20"><a href= + "ltpda_training_topic_5.html"><img src="b_next.gif" border="0" align= + "bottom" alt="Topic 5 - Model fitting"></a></td> + </tr> + </table><br> + + <p class="copy">©LTP Team</p> +</body> +</html>