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Fix. Default password should be [] not an empty string
author Daniele Nicolodi <nicolodi@science.unitn.it>
date Wed, 07 Dec 2011 17:29:47 +0100
parents f0afece42f48
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  <title>Fitting time series with polynomials (LTPDA Toolbox)</title>
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  <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>











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      <td align="left">Generation of noise with given PSD</td>

      <td>&nbsp;</td>

      <td align="right">Non-linear least squares fitting of time series</td>

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