<h2>Description</h2><p> 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 by means of a segment of <i>synthetic</i> data. This segment is calculated from the two input AOs. Two different methods are possible to fill the gap in the data: <tt>linear</tt> and <tt>spline</tt>. The former fills the data by means of a linear interpolation whereas the latter uses a smoother curve ---see examples below. <br> <br> <h2>Syntax</h2></p><div class="fragment"><pre> <br> b = gapfilling(a1, a2, pl) </pre></div><p> where <tt>a1</tt> and <tt>a2</tt> are the two segments to join. </p> <h2>Parameters</h2> The following parameters apply for this method: <ul> <li><tt>'method'</tt> - method used to interpolate missing data (see below for details) <ul> <li> <tt>'linear'</tt> (default option) </li> <li> <tt>'spline'</tt> </li> </ul> <li><tt>'addnoise'</tt> - with this option <i>noise</i> can be added to the interpolated data. This noise is defined as a <br> random variable with zero mean and variance equal to the high-frequency noise of the input AO. </li> </ul></p><p> <h2>Algorithm</h2></p><p> <b>Linear :</b> The gap is filled using a linear approximation.</p><p> <div align="center"> <IMG src="images/spike50x.png" width="205" height="27" border="0"> </div></p><br>the notation used in the previous expression is schematically explained in the figure below<br><p> <div align="center"> <img src="images/interplinear1.png" border="1" width="400px"> </div></p><br><br><br><p> <b>Spline :</b> a third order interpolation is used in this case</p><p> <br> <div align="center"> <IMG src="images/spike51x.png" width="237" height="16" border="0"> </div> <br></p><p> The parameters <tt>a</tt>, <tt>b</tt>, <tt>c</tt> and <tt>d</tt> are calculated by solving next system of equations:</p><p> <div align="center"> <IMG src="images/spike52x.png" width="205" height="117" border="0"> </div></p><br>The result is schematically shown in the figure below<br><p> <div align="center"> <img src="images/interpspline.png" border="0" width="400px"> </div></p><br><p> <h2>Examples</h2></p><p> 1. Missing data between two vectors of random data interpolated with the <tt>linear</tt> method.</p><p> <div class="fragment"><pre> <br> 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> xs = split(x1,plist(<span class="string">'chunks'</span>,3)); <span class="comment">% split in three segments</span> 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> y = gapfilling(xs(1),xs(3), pl); <span class="comment">% fill between 2nd and 3rd segment</span> iplot(x1,y) </pre> </div></p><p> <div align="center"> <img src="images/gapexample1.png" border="1" > </div></p><br><br><p> 2. Missing data between two data vectors interpolated with the <tt>spline</tt> method.</p><p> <div class="fragment"><pre> <br> 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> xs = split(x1,plist(<span class="string">'chunks'</span>,3)); <span class="comment">% split in three segments</span> 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> y = gapfilling(xs(1),xs(3), pl); <span class="comment">% fill between 2nd and 3rd segment</span> iplot(x1,y) </pre> </div></p><p> <div align="center"> <img src="images/gapexample2.png" border="1"> </div></p>