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author Daniele Nicolodi <nicolodi@science.unitn.it>
date Wed, 23 Nov 2011 19:22:13 +0100
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1 <!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN"
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2 "http://www.w3.org/TR/1999/REC-html401-19991224/loose.dtd">
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3
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4 <html lang="en">
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5 <head>
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6 <meta name="generator" content=
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7 "HTML Tidy for Mac OS X (vers 1st December 2004), see www.w3.org">
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8 <meta http-equiv="Content-Type" content=
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9 "text/html; charset=us-ascii">
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10
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11 <title>Fitting time series with polynomials (LTPDA Toolbox)</title>
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12 <link rel="stylesheet" href="docstyle.css" type="text/css">
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13 <meta name="generator" content="DocBook XSL Stylesheets V1.52.2">
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14 <meta name="description" content=
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15 "Presents an overview of the features, system requirements, and starting the toolbox.">
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16 </head>
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17
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18 <body>
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19 <a name="top_of_page" id="top_of_page"></a>
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20
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21 <p style="font-size:1px;">&nbsp;</p>
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22
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23 <table class="nav" summary="Navigation aid" border="0" width=
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24 "100%" cellpadding="0" cellspacing="0">
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25 <tr>
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26 <td valign="baseline"><b>LTPDA Toolbox</b></td><td><a href="../helptoc.html">contents</a></td>
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27
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28 <td valign="baseline" align="right"><a href=
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29 "ltpda_training_topic_5_2.html"><img src="b_prev.gif" border="0" align=
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30 "bottom" alt="Generation of noise with given PSD"></a>&nbsp;&nbsp;&nbsp;<a href=
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31 "ltpda_training_topic_5_4.html"><img src="b_next.gif" border="0" align=
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32 "bottom" alt="Non-linear least squares fitting of time series"></a></td>
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33 </tr>
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34 </table>
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35
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36 <h1 class="title"><a name="f3-12899" id="f3-12899"></a>Fitting time series with polynomials</h1>
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37 <hr>
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38
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39 <p>
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40
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41 <p>
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42 Fitting time series with polynomials exploits the function <tt>ao/polyfit</tt>.
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43 Details on the agorithm can be found in the <a href="sigproc_polyfit.html">appropriate help page</a>.
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44 </p>
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45
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46 <h2> Fitting time series with polynomials </h2>
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47
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48 <p>
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49 During this exercise we will:
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50 <ol>
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51 <li> Load time series noise
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52 <li> Fit data with ao/polyfit
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53 <li> Check results
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54 </ol>
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55 </p>
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56
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57 <p>
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58 Let's open a new editor window and load test data.
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59 </p>
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60
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61 <div class="fragment"><pre>
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62 a = ao(plist(<span class="string">'filename'</span>, <span class="string">'topic5/T5_Ex04_TestNoise.xml'</span>));
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63 a.setName;
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64 </pre></div>
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65
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66 <p>
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67 Try to fit data with <tt>ao/polyfit</tt>. We decide to fit with a 6th order polynomial.
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68 </p>
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69
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70 <div class="fragment"><pre>
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71 plfit = plist(<span class="string">'N'</span>, 6);
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72 p = polyfit(a, plfit);
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73 </pre></div>
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74 <p>
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75 The output of the polifit method is a parameter estimation object (pest-object). This object contains the coefficients of the fitted polynomial.
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76 </p>
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77 <div class="fragment"><pre>
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78 ---- pest 1 ----
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79 name: polyfit(a)
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80 param names: {'P1', 'P2', 'P3', 'P4', 'P5', 'P6', 'P7'}
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81 y: [9.17e-15;-1.01e-11;1.15e-08;-2.84e-06;-0.00444;0.138;47.5]
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82 dy: []
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83 yunits: [s^(-6)][s^(-5)][s^(-4)][s^(-3)][s^(-2)][s^(-1)][]
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84 pdf: []
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85 cov: []
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86 corr: []
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87 chain: []
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88 chi2: []
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89 dof: 993
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90 models: smodel(P1*X.^6 + P2*X.^5 + P3*X.^4 + P4*X.^3 + P5*X.^2 + P6*X.^1 + P7*X.^0)
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91 description:
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92 UUID: 58a56ecf-24e8-40ed-a42c-ef6832c747c3
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93 ----------------
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94 </pre></div>
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95
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96 <p>
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97 Once we have the pest object with the coefficients, we can evaluate the pest-object. In order to construct
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98 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
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99 of the output.
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100 </p>
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101
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102 <div class="fragment"><pre>
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103 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>))
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104 b.setName;
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105 </pre></div>
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106
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107 <p>
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108 Now, check fit result with some plotting. Compare data with fitted model
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109 and look at the fit residuals.
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110 </p>
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111
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112 <div class="fragment"><pre>
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113 iplot(a,b)
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114 iplot(a-b)
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115 </pre></div>
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116
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117 <p>
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118 <div align="center">
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119 <IMG src="images/ltpda_training_1/topic5/ltpda_training_5_3_1.png" align="center" border="0">
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120 </div>
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121 <div align="center">
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122 <IMG src="images/ltpda_training_1/topic5/ltpda_training_5_3_2.png" align="center" border="0">
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123 </div>
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124 </p>
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125
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126 <p>
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127 You could also try using <tt>ao/detrend</tt> on the input time-series to yield
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128 a very similar result as that shown in the last plot.
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129 </p>
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130
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131
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133
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134
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135
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136
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137
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138
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139
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140
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141 </p>
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142
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143 <br>
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144 <br>
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145 <table class="nav" summary="Navigation aid" border="0" width=
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146 "100%" cellpadding="0" cellspacing="0">
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147 <tr valign="top">
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148 <td align="left" width="20"><a href="ltpda_training_topic_5_2.html"><img src=
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149 "b_prev.gif" border="0" align="bottom" alt=
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150 "Generation of noise with given PSD"></a>&nbsp;</td>
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151
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152 <td align="left">Generation of noise with given PSD</td>
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153
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154 <td>&nbsp;</td>
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155
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156 <td align="right">Non-linear least squares fitting of time series</td>
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157
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158 <td align="right" width="20"><a href=
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159 "ltpda_training_topic_5_4.html"><img src="b_next.gif" border="0" align=
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160 "bottom" alt="Non-linear least squares fitting of time series"></a></td>
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161 </tr>
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162 </table><br>
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164 <p class="copy">&copy;LTP Team</p>
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165 </body>
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166 </html>