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Import.
| 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_5_3.html Wed Nov 23 19:22:13 2011 +0100 @@ -0,0 +1,166 @@ +<!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>Fitting time series with polynomials (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_5_2.html"><img src="b_prev.gif" border="0" align= + "bottom" alt="Generation of noise with given PSD"></a> <a href= + "ltpda_training_topic_5_4.html"><img src="b_next.gif" border="0" align= + "bottom" alt="Non-linear least squares fitting of time series"></a></td> + </tr> + </table> + + <h1 class="title"><a name="f3-12899" id="f3-12899"></a>Fitting time series with polynomials</h1> + <hr> + + <p> + +<p> + Fitting time series with polynomials exploits the function <tt>ao/polyfit</tt>. + Details on the agorithm can be found in the <a href="sigproc_polyfit.html">appropriate help page</a>. +</p> + +<h2> Fitting time series with polynomials </h2> + +<p> + During this exercise we will: + <ol> + <li> Load time series noise + <li> Fit data with ao/polyfit + <li> Check results + </ol> +</p> + +<p> + Let's open a new editor window and load test data. +</p> + +<div class="fragment"><pre> + a = ao(plist(<span class="string">'filename'</span>, <span class="string">'topic5/T5_Ex04_TestNoise.xml'</span>)); + a.setName; +</pre></div> + +<p> + Try to fit data with <tt>ao/polyfit</tt>. We decide to fit with a 6th order polynomial. +</p> + +<div class="fragment"><pre> + plfit = plist(<span class="string">'N'</span>, 6); + p = polyfit(a, plfit); +</pre></div> +<p> + The output of the polifit method is a parameter estimation object (pest-object). This object contains the coefficients of the fitted polynomial. +</p> +<div class="fragment"><pre> +---- pest 1 ---- + name: polyfit(a) +param names: {'P1', 'P2', 'P3', 'P4', 'P5', 'P6', 'P7'} + y: [9.17e-15;-1.01e-11;1.15e-08;-2.84e-06;-0.00444;0.138;47.5] + dy: [] + yunits: [s^(-6)][s^(-5)][s^(-4)][s^(-3)][s^(-2)][s^(-1)][] + pdf: [] + cov: [] + corr: [] + chain: [] + chi2: [] + dof: 993 + models: smodel(P1*X.^6 + P2*X.^5 + P3*X.^4 + P4*X.^3 + P5*X.^2 + P6*X.^1 + P7*X.^0) +description: + UUID: 58a56ecf-24e8-40ed-a42c-ef6832c747c3 +---------------- +</pre></div> + +<p> + Once we have the pest object with the coefficients, we can evaluate the pest-object. In order to construct + an object with the same time base we can pass the input AO, and specify to use its 'x' field to build the 'x' field + of the output. +</p> + +<div class="fragment"><pre> + b = p.eval(a, plist(<span class="string">'type'</span>, <span class="string">'tsdata'</span>, <span class="string">'xfield'</span>, <span class="string">'x'</span>)) + b.setName; +</pre></div> + +<p> + Now, check fit result with some plotting. Compare data with fitted model + and look at the fit residuals. +</p> + +<div class="fragment"><pre> + iplot(a,b) + iplot(a-b) +</pre></div> + +<p> + <div align="center"> + <IMG src="images/ltpda_training_1/topic5/ltpda_training_5_3_1.png" align="center" border="0"> + </div> + <div align="center"> + <IMG src="images/ltpda_training_1/topic5/ltpda_training_5_3_2.png" align="center" border="0"> + </div> +</p> + +<p> + You could also try using <tt>ao/detrend</tt> on the input time-series to yield + a very similar result as that shown in the last plot. +</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_5_2.html"><img src= + "b_prev.gif" border="0" align="bottom" alt= + "Generation of noise with given PSD"></a> </td> + + <td align="left">Generation of noise with given PSD</td> + + <td> </td> + + <td align="right">Non-linear least squares fitting of time series</td> + + <td align="right" width="20"><a href= + "ltpda_training_topic_5_4.html"><img src="b_next.gif" border="0" align= + "bottom" alt="Non-linear least squares fitting of time series"></a></td> + </tr> + </table><br> + + <p class="copy">©LTP Team</p> +</body> +</html>