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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_5.html Wed Nov 23 19:22:13 2011 +0100 @@ -0,0 +1,241 @@ +<!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>Empirical Transfer Function estimation (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_2_3.html"><img src="b_prev.gif" border="0" align= + "bottom" alt="Example 3: Log-scale PSD on MDC1 data"></a> <a href= + "ltpda_training_topic_3_6.html"><img src="b_next.gif" border="0" align= + "bottom" alt="IFO/Temperature Example - Spectral Analysis"></a></td> + </tr> + </table> + + <h1 class="title"><a name="f3-12899" id="f3-12899"></a>Empirical Transfer Function estimation</h1> + <hr> + + <p> + <p> +Let's run this exercise on empirical estimation of Transfer +Functions on the Matlab terminal.</p> + +<p>The idea of the exercise is the following: +<ol> +<li>simulate some white noise <em>x(t)</em></li> +<li>build a band-pass filter <em>F</em></li> +<li>pass the input noise <em>x(t)</em> through the filter and add some more noise + <em>yn(t)</em> at the output so to have <em>y = F*x(t) + yn(t)</em></li> +<li>evaluate and plot the transfer function <em>x -> y</em> </li> +</ol> +In a flow diagram, the representation is as follows: +</p> +<img src="images/ltpda_training_1/topic3/TFE_1_flowchart.png" +alt="Dataflow for the 1St example of ao/tfe" width="600px" border="1"> + +<p>The command-line sequence is the following: +<div class="fragment"><pre> +<span class="comment">%% General definitions</span> +nsecs = 10000; +fs = 1; +<span class="comment">%% Input noise</span> +x = ao(plist(<span class="string">'waveform'</span>, <span class="string">'noise'</span>, <span class="string">'sigma'</span>, 3, <span class="string">'fs'</span>, fs, <span class="string"> 'nsecs'</span>, nsecs, <span class="string">'yunits'</span>, <span class="string">'V'</span>)) + +<span class="comment">%% Filter</span> +bp_filter = miir(plist(<span class="string">'type'</span>, <span class="string">'bandpass'</span>, <span class="string">'fc'</span>, [0.01 0.1], <span class="string">'fs'</span>, 1, <span class="string">'order'</span>, 3,<span class="string">'iunits'</span>, <span class="string">'V'</span>, <span class="string">'ounits'</span>, <span class="string">'A'</span>)) +xf = simplifyYunits(filter(x, bp_filter)) + +<span class="comment">%% Output noise</span> +yn = ao(plist(<span class="string">'waveform'</span>,<span class="string">'noise'</span>, <span class="string">'sigma'</span>, 1, <span class="string">'fs'</span>, fs, <span class="string">'nsecs'</span>, xf.nsecs, <span class="string">'yunits'</span>, <span class="string">'A'</span>)) +y = xf + yn + +<span class="comment">%% Plotting input and output noise</span> +xx = psd(x, plist(<span class="string">'scale'</span>,... + <span class="string">'ASD'</span>,... + <span class="string">'nfft'</span>, 1000)) +yy = psd(y, plist(<span class="string">'scale'</span>,<span class="string">'ASD'</span>, ... + <span class="string">'nfft'</span>, 1000)) +iplot(xx, yy, plist(<span class="string">'Arrangement'</span>, <span class="string">'subplots'</span>, <span class="string">'YRanges'</span>, {[1e-1 1e1], [1e-2 1e2]})); + +</pre></div> +<img src="images/ltpda_training_1/topic3/TFE_in_out.png" alt="Ohmic admittance between y and x" border="1"> +<br> +<p>Now we can proceed with the call to the <tt>ao/tfe</tt> method. The +parameter list is very similar to the one employed for the other spectral +estimators:</p> + +<table cellspacing="0" class="body" cellpadding="2" border="0" width="80%"> + <colgroup> + <col width="15%"/> + <col width="20%"/> + <col width="65%"/> + </colgroup> + <thead> + <tr valign="top"> + <th class="categorylist">Key</th> + <th class="categorylist">Value</th> + <th class="categorylist">Description</th> + </tr> + </thead> + <tbody> + <!-- Key 'NFFT' --> + <tr valign="top"> + <td bgcolor="#f3f4f5"> + <p><tt>NFFT</tt></p> + </td> + <td bgcolor="#f3f4f5"> + <p><span class="string">1000</span></p> + </td> + <td bgcolor="#f3f4f5"> + <p>The number of samples defining the length of the window to apply</p> + </td> + </tr> + <!-- Key 'WIN' --> + <tr valign="top"> + <td bgcolor="#f3f4f5"> + <p><tt>WIN</tt></p> + </td> + <td bgcolor="#f3f4f5"> + <p><span class="string">'BH92'</span></p> + </td> + <td bgcolor="#f3f4f5"> + <p>Or a different one, if you want.</p> + </td> + </tr> + <!-- Key 'OLAP' --> + <tr valign="top"> + <td bgcolor="#f3f4f5"> + <p><tt>OLAP</tt></p> + </td> + <td bgcolor="#f3f4f5"> + <p><span class="string">-1</span></p> + </td> + <td bgcolor="#f3f4f5"> + <p>Overlap will be chosen based on the window properties</p> + </td> + </tr> + <!-- Key 'ORDER' --> + <tr valign="top"> + <td bgcolor="#f3f4f5"> + <p><tt>ORDER</tt></p> + </td> + <td bgcolor="#f3f4f5"> + <p><span class="string">0</span></p> + </td> + <td bgcolor="#f3f4f5"> + <p>Segment-wise detrending up to order 0</p> + </td> + </tr> + </tbody> + </table> +</p> + <p>The command line is the following:</p> + <div class="fragment"><pre> +<span class="comment">%% Estimate the x->y transfer function</span> +tfxy = tfe(x, y, plist(<span class="string">'nfft'</span>, 1000, <span class="string">'win'</span>, <span class="string">'BH92'</span>, <span class="string">'olap'</span>, -1, <span class="string">'order'</span>, 0)); +</pre></div> +<p>We also would like to evaluate the expected transfer function x->y, which is obviously the filter transfer function, or response. This can be calculated by means of the + <table cellspacing="0" class="note" summary="Note" cellpadding="5" border="1"> + <tr width="90%"> + <td> + <tt>miir/resp</tt> + </td> + </tr> + </table> method. A detailed description of digital filtering is available in the User Manual dedicated <a href="sigproc_dfilt.html" >section</a> and will be touched upon in <a href="ltpda_training_topic_4_4_2.html" >this</a> topic; here let's just use the simplest form, where the needed parameter is a list of the frequency to evaluate the response at:</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 'f' --> + <tr valign="top"> + <td bgcolor="#f3f4f5"> + <p><tt>F</tt></p> + </td> + <td bgcolor="#f3f4f5"> + <p><span class="string">tfxy.x</span></p> + </td> + <td bgcolor="#f3f4f5"> + <p>a vector of frequency values or an <tt>ao</tt> whereby the x-axis is taken for the frequency values</p> + </td> + </tr> + </tbody> + </table> + <p> + So we can just pass the x field of the fsdata <tt>ao</tt> containing the transfer function estimate. However, + we can also just pass the AO itself. In which case, the <tt>resp</tt> function will take the X values from + the AO. + </p> + <p> + The command line is the following:</p> + <div class="fragment"><pre> +<span class="comment">%% Evaluate the expected x->y transfer function</span> +rf = resp(bp_filter, plist(<span class="string">'f'</span>, tfxy)) + </pre></div> + + <p>Eventually let's look at the results: + <div class="fragment"><pre> +<span class="comment">%% Plotting estimated and expected transfer functions</span> +iplot(tfxy, rf, plist(<span class="string">'colors'</span>,{[1 0 0],[0 0 0]},<span class="string">'YRanges'</span>, {[1e-2 1e2], [-200 200]})) +</pre></div> + </p> +<img src="images/ltpda_training_1/topic3/TFE_result_1.png" alt="TFE of x into y" border="1"> +<br> + + + </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_2_3.html"><img src= + "b_prev.gif" border="0" align="bottom" alt= + "Example 3: Log-scale PSD on MDC1 data"></a> </td> + + <td align="left">Example 3: Log-scale PSD on MDC1 data</td> + + <td> </td> + + <td align="right">IFO/Temperature Example - Spectral Analysis</td> + + <td align="right" width="20"><a href= + "ltpda_training_topic_3_6.html"><img src="b_next.gif" border="0" align= + "bottom" alt="IFO/Temperature Example - Spectral Analysis"></a></td> + </tr> + </table><br> + + <p class="copy">©LTP Team</p> +</body> +</html>