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comparison m-toolbox/html_help/help/ug/gapfill_content.html @ 0:f0afece42f48
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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| 1 <h2>Description</h2> | |
| 2 <p> | |
| 3 Gaps in data can be filled with <i>interpolated</i> data if desired. LTPDA <a href="matlab:doc('ao/gapfilling')"><tt>gapfilling</tt></a> joins two AOs | |
| 4 by means of a segment of <i>synthetic</i> data. This segment is calculated from the two input AOs. Two different | |
| 5 methods are possible to fill the gap in the data: <tt>linear</tt> and <tt>spline</tt>. The former fills the data | |
| 6 by means of a linear interpolation whereas the latter uses a smoother curve ---see examples below. | |
| 7 <br> | |
| 8 <br> | |
| 9 <h2>Syntax</h2> | |
| 10 </p> | |
| 11 <div class="fragment"><pre> | |
| 12 <br> | |
| 13 b = gapfilling(a1, a2, pl) | |
| 14 </pre> | |
| 15 </div> | |
| 16 <p> | |
| 17 where <tt>a1</tt> and <tt>a2</tt> are the two segments to join. | |
| 18 </p> | |
| 19 <h2>Parameters</h2> | |
| 20 The following parameters apply for this method: | |
| 21 <ul> | |
| 22 <li><tt>'method'</tt> - method used to interpolate missing data (see below for details) | |
| 23 <ul> | |
| 24 <li> <tt>'linear'</tt> (default option) </li> | |
| 25 <li> <tt>'spline'</tt> </li> | |
| 26 </ul> | |
| 27 <li><tt>'addnoise'</tt> - with this option <i>noise</i> can be | |
| 28 added to the interpolated data. | |
| 29 This noise is defined as a <br> | |
| 30 random variable with | |
| 31 zero mean and variance equal to the high-frequency | |
| 32 noise of the input AO. </li> | |
| 33 | |
| 34 </ul> | |
| 35 </p> | |
| 36 <p> | |
| 37 <h2>Algorithm</h2> | |
| 38 </p> | |
| 39 <p> | |
| 40 <b>Linear :</b> The gap is filled using a linear approximation. | |
| 41 </p> | |
| 42 <p> | |
| 43 <div align="center"> | |
| 44 <IMG src="images/spike50x.png" width="205" height="27" border="0"> | |
| 45 </div> | |
| 46 </p> | |
| 47 <br> | |
| 48 the notation used in the previous expression is schematically explained in the figure below | |
| 49 <br> | |
| 50 <p> | |
| 51 <div align="center"> | |
| 52 <img src="images/interplinear1.png" border="1" width="400px"> | |
| 53 </div> | |
| 54 </p> | |
| 55 <br> | |
| 56 <br> | |
| 57 <br> | |
| 58 <p> | |
| 59 <b>Spline :</b> a third order interpolation is used in this case | |
| 60 </p> | |
| 61 <p> | |
| 62 <br> | |
| 63 <div align="center"> | |
| 64 <IMG src="images/spike51x.png" width="237" height="16" border="0"> | |
| 65 </div> | |
| 66 <br> | |
| 67 </p> | |
| 68 <p> | |
| 69 The parameters <tt>a</tt>, <tt>b</tt>, <tt>c</tt> and <tt>d</tt> are calculated | |
| 70 by solving next system of equations: | |
| 71 </p> | |
| 72 <p> | |
| 73 <div align="center"> | |
| 74 <IMG src="images/spike52x.png" width="205" height="117" border="0"> | |
| 75 </div> | |
| 76 </p> | |
| 77 <br> | |
| 78 The result is schematically shown in the figure below | |
| 79 <br> | |
| 80 <p> | |
| 81 <div align="center"> | |
| 82 <img src="images/interpspline.png" border="0" width="400px"> | |
| 83 </div> | |
| 84 </p> | |
| 85 <br> | |
| 86 <p> | |
| 87 <h2>Examples</h2> | |
| 88 </p> | |
| 89 <p> | |
| 90 1. Missing data between two vectors of random data interpolated with the <tt>linear</tt> method. | |
| 91 </p> | |
| 92 <p> | |
| 93 <div class="fragment"><pre> | |
| 94 <br> | |
| 95 x1 = ao(plist(<span class="string">'waveform'</span>,<span class="string">'noise'</span>,<span class="string">'nsecs'</span>,1e3,<span class="string">'fs'</span>,10,<span class="string">'name'</span>,<span class="string">'noise'</span>)); <span class="comment">% create an AO of random data</span> | |
| 96 xs = split(x1,plist(<span class="string">'chunks'</span>,3)); <span class="comment">% split in three segments</span> | |
| 97 pl = plist( <span class="string">'method'</span>, <span class="string"> 'linear'</span>, <span class="string">'addnoise'</span>, <span class="string">'no'</span>); <span class="comment">% linear gapfilling</span> | |
| 98 y = gapfilling(xs(1),xs(3), pl); <span class="comment">% fill between 2nd and 3rd segment</span> | |
| 99 iplot(x1,y) | |
| 100 </pre> | |
| 101 </div> | |
| 102 </p> | |
| 103 <p> | |
| 104 <div align="center"> | |
| 105 <img src="images/gapexample1.png" border="1" > | |
| 106 </div> | |
| 107 </p> | |
| 108 <br> | |
| 109 <br> | |
| 110 <p> | |
| 111 2. Missing data between two data vectors interpolated with the <tt>spline</tt> method. | |
| 112 </p> | |
| 113 <p> | |
| 114 <div class="fragment"><pre> | |
| 115 <br> | |
| 116 x1 = ao(plist(<span class="string">'tsfcn'</span>,<span class="string">'t.^1.8 + 1e6*rand(size(t))'</span>,<span class="string">'nsecs'</span>,5e3,<span class="string">'fs'</span>,10,<span class="string">'name'</span>,<span class="string">'noise'</span>)); <span class="comment">% create an AO</span> | |
| 117 xs = split(x1,plist(<span class="string">'chunks'</span>,3)); <span class="comment">% split in three segments</span> | |
| 118 pl = plist( <span class="string">'method'</span>, <span class="string"> 'spline'</span>, <span class="string">'addnoise'</span>, <span class="string">'no'</span>); <span class="comment">% cubic gapfilling</span> | |
| 119 y = gapfilling(xs(1),xs(3), pl); <span class="comment">% fill between 2nd and 3rd segment</span> | |
| 120 iplot(x1,y) | |
| 121 </pre> | |
| 122 </div> | |
| 123 </p> | |
| 124 <p> | |
| 125 <div align="center"> | |
| 126 <img src="images/gapexample2.png" border="1"> | |
| 127 </div> | |
| 128 </p> | |
| 129 | |
| 130 | |
| 131 |