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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>Creating Analysis Objects (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;"> </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 "ao_intro.html"><img src="b_prev.gif" border="0" align=
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+ − 30 "bottom" alt="Analysis Objects"></a> <a href=
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+ − 31 "ao_save.html"><img src="b_next.gif" border="0" align=
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+ − 32 "bottom" alt="Saving Analysis Objects"></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>Creating Analysis Objects</h1>
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+ − 37 <hr>
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+ − 38
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+ − 39 <p>
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+ − 40 <p>Analysis objects can be created in MATLAB in many ways. Apart from being created by the many
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+ − 41 algorithms in the LTPDA Toolbox, AOs can also be created from initial data or descriptions
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+ − 42 of data. The various <i>constructors</i>
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+ − 43 are listed in the function help: <a href="matlab:doc('ao')">ao help</a>.</p>
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+ − 44
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+ − 45 <h3>Examples of creating AOs</h3>
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+ − 46
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+ − 47 <p>The following examples show some ways to create Analysis Objects.</p>
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+ − 48
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+ − 49 <ul>
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+ − 50 <li><a href="ao_create.html#text">Creating AOs from text files</a></li>
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+ − 51 <li><a href="ao_create.html#xml">Creating AOs from XML or MAT files</a></li>
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+ − 52 <li><a href="ao_create.html#fcn">Creating AOs from MATLAB functions</a></li>
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+ − 53 <li><a href="ao_create.html#tsfcn">Creating AOs from functions of time</a></li>
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+ − 54 <li><a href="ao_create.html#window">Creating AOs from window functions</a></li>
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+ − 55 <li><a href="ao_create.html#waveform">Creating AOs from waveform descriptions</a></li>
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+ − 56 <li><a href="ao_create.html#pzmodel">Creating AOs from pole zero models</a></li>
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+ − 57 </ul>
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+ − 58
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+ − 59 <hr>
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+ − 60 <h4><a name="text"></a>Creating AOs from text files.</h4>
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+ − 61
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+ − 62 <p>Analysis Objects can be created from text files containing two columns of ASCII numbers. Files
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+ − 63 ending in '.txt' or '.dat' will be handled as ASCII file inputs. The
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+ − 64 first column is taken to be the time instances; the second column is taken to be the amplitude
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+ − 65 samples. The created AO is of type <tt>tsdata</tt> with the sample rate set by the difference
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+ − 66 between the time-stamps of the first two samples in the file. The name of the resulting AO is
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+ − 67 set to the filename (without the file extension). The filename is also stored as a parameter in
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+ − 68 the history parameter list. The following code shows this in action:</p>
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+ − 69
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+ − 70 <div class="fragment"><pre>
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+ − 71 >> a = ao(<span class="string">'data.txt'</span>)
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+ − 72 ----------- ao 01: data.txt_01_02 -----------
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+ − 73
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+ − 74 name: data.txt_01_02
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+ − 75 data: (0,-1.06421341288933) (0.1,1.60345729812004) (0.2,1.23467914689078) ...
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+ − 76 -------- tsdata 01 ------------
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+ − 77
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+ − 78 fs: 10
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+ − 79 x: [100 1], double
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+ − 80 y: [100 1], double
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+ − 81 dx: [0 0], double
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+ − 82 dy: [0 0], double
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+ − 83 xunits: [s]
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+ − 84 yunits: []
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+ − 85 nsecs: 10
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+ − 86 t0: 1970-01-01 00:00:00.000
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+ − 87 -------------------------------
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+ − 88
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+ − 89 hist: ao / ao / SId: fromDatafile ... $-->$Id: ao ... S
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+ − 90 mdlfile: empty
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+ − 91 description:
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+ − 92 UUID: e6ccfcb6-da49-4f4c-8c2c-3054fe5d2762
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+ − 93 ---------------------------------------------
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+ − 94 </pre></div>
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+ − 95 <p>As with most constructor calls, an equivalent action can be achieved using an input
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+ − 96 <a href="plist_intro.html">Parameter List</a>.</p>
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+ − 97
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+ − 98 <div class="fragment"><pre>
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+ − 99 >> a = ao(plist(<span class="string">'filename'</span>, <span class="string">'data.txt'</span>))
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+ − 100 </pre></div>
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+ − 101
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+ − 102 <hr>
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+ − 103 <h4><a name="xml"></a>Creating AOs from XML or .mat files</h4>
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+ − 104
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+ − 105 <p>AOs can be saved as both XML and .MAT files. As such, they can also be created from these
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+ − 106 files.</p>
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+ − 107
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+ − 108 <div class="fragment"><pre>
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+ − 109 >> a = ao(<span class="string">'a.xml'</span>)
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+ − 110 ----------- ao 01: a -----------
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+ − 111
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+ − 112 name: None
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+ − 113 data: (0,-0.493009815316451) (0.1,-0.180739356415037) (0.2,0.045841105713705) ...
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+ − 114 -------- tsdata 01 ------------
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+ − 115
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+ − 116 fs: 10
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+ − 117 x: [100 1], double
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+ − 118 y: [100 1], double
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+ − 119 dx: [0 0], double
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+ − 120 dy: [0 0], double
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+ − 121 xunits: [s]
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+ − 122 yunits: []
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+ − 123 nsecs: 10
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+ − 124 t0: 1970-01-01 00:00:01.000
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+ − 125 -------------------------------
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+ − 126
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+ − 127 hist: ao / ao / SId: fromVals ... $-->$Id: ao ... S
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+ − 128 mdlfile: empty
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+ − 129 description:
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+ − 130 UUID: 2fed6155-6468-4533-88f6-e4b27bc6e1aa
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+ − 131 --------------------------------
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+ − 132 </pre></div>
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+ − 133
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+ − 134 <hr>
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+ − 135 <h4><a name="fcn"></a>Creating AOs from MATLAB functions</h4>
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+ − 136
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+ − 137 <p>AOs can be created from any valid MATLAB function which returns a vector or matrix of values.
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+ − 138 For such calls, a parameter list is used as input. For example, the following code creates
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+ − 139 an AO containing 1000 random numbers:</p>
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+ − 140
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+ − 141 <div class="fragment"><pre>
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+ − 142 >> a = ao(plist(<span class="string">'fcn'</span>, <span class="string">'randn(1000,1)'</span>))
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+ − 143 ----------- ao 01: a -----------
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+ − 144
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+ − 145 name: None
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+ − 146 data: -1.28325610460477 -2.32895451628334 0.901931466951714 -1.83563868373519 0.06675 ...
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+ − 147 -------- cdata 01 ------------
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+ − 148 y: [1000x1], double
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+ − 149 dy: [0x0], double
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+ − 150 yunits: []
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+ − 151 ------------------------------
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+ − 152
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+ − 153 hist: ao / ao / SId: fromFcn ... $-->$Id ... $
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+ − 154 mdlfile: empty
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+ − 155 description:
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+ − 156 UUID: 0072f8d0-f804-472b-a4aa-e9ec6a8de803
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+ − 157 --------------------------------
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+ − 158 </pre></div>
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+ − 159 <p>Here you can see that the AO is a <tt>cdata</tt> type and the name is set to be the function
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+ − 160 that was input.</p>
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+ − 161
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+ − 162 <hr>
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+ − 163 <h4><a name="tsfcn"></a>Creating AOs from functions of time</h4>
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+ − 164
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+ − 165 <p>AOs can be created from any valid MATLAB function which is a function of the variable
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+ − 166 <tt>t</tt>. For such calls, a parameter list is used as input. For example, the following
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+ − 167 code creates an AO containing sinusoidal signal at 1Hz with some additional Gaussian noise:</p>
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+ − 168
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+ − 169 <div class="fragment"><pre>
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+ − 170 pl = plist();
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+ − 171 pl = append(pl, <span class="string">'nsecs'</span>, 100);
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+ − 172 pl = append(pl, <span class="string">'fs'</span>, 10);
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+ − 173 pl = append(pl, <span class="string">'tsfcn'</span>, <span class="string">'sin(2*pi*1*t)+randn(size(t))'</span>);
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+ − 174 a = ao(pl)
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+ − 175 ----------- ao 01: a -----------
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+ − 176
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+ − 177 name: None
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+ − 178 data: (0,1.37694916561229) (0.1,-0.820427237640771) (0.2,1.09228819960292) ...
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+ − 179 -------- tsdata 01 ------------
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+ − 180
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+ − 181 fs: 10
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff
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+ − 182 x: [1000 1], double
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff
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+ − 183 y: [1000 1], double
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff
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+ − 184 dx: [0 0], double
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff
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+ − 185 dy: [0 0], double
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff
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+ − 186 xunits: [s]
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff
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+ − 187 yunits: []
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff
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+ − 188 nsecs: 100
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff
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+ − 189 t0: 1970-01-01 00:00:00.000
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff
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+ − 190 -------------------------------
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff
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+ − 191
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff
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+ − 192 hist: ao / ao / SId: fromTSfcn ... $-->$Id: ao ... S
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff
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+ − 193 mdlfile: empty
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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+ − 194 description:
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff
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+ − 195 UUID: c0f481cf-4bdd-4a91-bc78-6d34f8222313
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff
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+ − 196 --------------------------------
Daniele Nicolodi <nicolodi@science.unitn.it>
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+ − 197 </pre></div>
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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+ − 198 <p>Here you can see that the AO is a <tt>tsdata</tt> type, as you would expect. Also note that you
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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+ − 199 need to specify the sample rate (<tt>fs</tt>) and the number of seconds of data you would like
Daniele Nicolodi <nicolodi@science.unitn.it>
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+ − 200 to have (<tt>nsecs</tt>).</p>
Daniele Nicolodi <nicolodi@science.unitn.it>
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+ − 201
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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+ − 202 <hr>
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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+ − 203 <h4><a name="window"></a>Creating AOs from window functions</h4>
Daniele Nicolodi <nicolodi@science.unitn.it>
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+ − 204
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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+ − 205 <p>The LTPDA Toolbox contains a class for designing spectral windows
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff
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+ − 206 (see <a href="specwin.html">Spectral Windows</a>). A spectral window object can
Daniele Nicolodi <nicolodi@science.unitn.it>
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diff
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+ − 207 also be used to create an Analysis Object as follows:</p>
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff
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+ − 208
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff
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+ − 209 <div class="fragment"><pre>
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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+ − 210 >> w = specwin(<span class="string">'Hanning'</span>, 1000)
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff
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+ − 211 ------ specwin/1 -------
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff
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+ − 212 type: Hanning
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff
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+ − 213 alpha: 0
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff
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+ − 214 psll: 31.5
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff
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+ − 215 rov: 50
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff
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+ − 216 nenbw: 1.5
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff
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+ − 217 w3db: 1.4382
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff
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+ − 218 flatness: -1.4236
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff
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+ − 219 ws: 500
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff
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+ − 220 ws2: 375.000000000001
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff
changeset
+ − 221 win: [0 9.86957193144233e-06 3.94778980919441e-05 8.88238095955174e-05 0.0001579 ...
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff
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+ − 222 version: SId: specwin.m,v 1.67 2009/09/01 09:25:24 ingo Exp S
Daniele Nicolodi <nicolodi@science.unitn.it>
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+ − 223 ------------------------
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff
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+ − 224
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff
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+ − 225 >> a = ao(w)
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff
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+ − 226 ----------- ao 01: ao(Hanning) -----------
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff
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+ − 227
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff
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+ − 228 name: ao(Hanning)
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff
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+ − 229 data: 0 9.86957193144233e-06 3.94778980919441e-05 8.88238095955174e-05 0.0001579 ...
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff
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+ − 230 -------- cdata 01 ------------
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff
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+ − 231 y: [1x1000], double
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff
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+ − 232 dy: [0x0], double
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff
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+ − 233 yunits: []
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff
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+ − 234 ------------------------------
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff
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+ − 235
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff
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+ − 236 hist: ao / ao / SId: fromSpecWin ... $-->$Id: ao ... S
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff
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+ − 237 mdlfile: empty
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff
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+ − 238 description:
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff
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+ − 239 UUID: ea1a9036-b9f5-4bdb-b3a3-211e9d697060
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff
changeset
+ − 240 ------------------------------------------
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff
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+ − 241 </pre></div>
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff
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+ − 242 <p>
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff
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+ − 243 It is also possible to pass the information about the window as a plist to the ao constructor.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff
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+ − 244 </p>
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff
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+ − 245 <div class="fragment"><pre>
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff
changeset
+ − 246 >> ao(plist(<span class="string">'win'</span>, <span class="string">'Hanning'</span>, <span class="string">'length'</span>, 1000))
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff
changeset
+ − 247 ----------- ao 01: ao(Hanning) -----------
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff
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+ − 248
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff
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+ − 249 name: ao(Hanning)
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff
changeset
+ − 250 data: 0 9.86957193144233e-06 3.94778980919441e-05 8.88238095955174e-05 0.0001579 ...
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff
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+ − 251 -------- cdata 01 ------------
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff
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+ − 252 y: [1x1000], double
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff
changeset
+ − 253 dy: [0x0], double
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff
changeset
+ − 254 yunits: []
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff
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+ − 255 ------------------------------
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff
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+ − 256
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff
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+ − 257 hist: ao / ao / SId: fromSpecWin ... -->$Id: ao ... S
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff
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+ − 258 mdlfile: empty
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff
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+ − 259 description:
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff
changeset
+ − 260 UUID: 5b81f67a-45b9-43f8-a74a-bc5161fd718f
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff
changeset
+ − 261 ------------------------------------------
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff
changeset
+ − 262 </pre></div>
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff
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+ − 263
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff
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+ − 264 <p>
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff
changeset
+ − 265 The example code above creates a Hanning window object with 1000 points. The call to the AO
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff
changeset
+ − 266 constructor then creates a <tt>cdata</tt> type AO with 1000 points. This AO can then be multiplied
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff
changeset
+ − 267 against other AOs in order to window the data.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff
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+ − 268 </p>
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff
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+ − 269
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff
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+ − 270 <hr>
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff
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+ − 271 <h4><a name="waveform"></a>Creating AOs from waveform descriptions</h4>
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff
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+ − 272
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff
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+ − 273 <p>
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff
changeset
+ − 274 MATLAB contains various functions for creating different waveforms, for example,
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff
changeset
+ − 275 <tt>square</tt>, <tt>sawtooth</tt>. Some of these functions can be called upon to create
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff
changeset
+ − 276 Analysis Objects. The following code creates an AO with a sawtooth waveform:
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff
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+ − 277 </p>
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff
changeset
+ − 278
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff
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+ − 279 <div class="fragment"><pre>
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff
changeset
+ − 280 pl = plist();
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff
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+ − 281 pl = append(pl, <span class="string">'fs'</span>, 100);
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff
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+ − 282 pl = append(pl, <span class="string">'nsecs'</span>, 5);
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff
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+ − 283 pl = append(pl, <span class="string">'waveform'</span>, 'Sawtooth');
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff
changeset
+ − 284 pl = append(pl, <span class="string">'f'</span>, 1);
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff
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+ − 285 pl = append(pl, <span class="string">'width'</span>, 0.5);
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff
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+ − 286
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff
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+ − 287 asaw = ao(pl)
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff
changeset
+ − 288 ----------- ao 01: Sawtooth -----------
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff
changeset
+ − 289
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff
changeset
+ − 290 name: Sawtooth
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff
changeset
+ − 291 data: (0,-1) (0.01,-0.96) (0.02,-0.92) (0.03,-0.88) (0.04,-0.84) ...
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff
changeset
+ − 292 -------- tsdata 01 ------------
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff
changeset
+ − 293
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff
changeset
+ − 294 fs: 100
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff
changeset
+ − 295 x: [500 1], double
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff
changeset
+ − 296 y: [500 1], double
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff
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+ − 297 dx: [0 0], double
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff
changeset
+ − 298 dy: [0 0], double
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff
changeset
+ − 299 xunits: [s]
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff
changeset
+ − 300 yunits: []
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff
changeset
+ − 301 nsecs: 5
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff
changeset
+ − 302 t0: 1970-01-01 00:00:00.000
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff
changeset
+ − 303 -------------------------------
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff
changeset
+ − 304
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff
changeset
+ − 305 hist: ao / ao / SId: fromWaveform ... $-->$Id: ao ... S
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff
changeset
+ − 306 mdlfile: empty
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff
changeset
+ − 307 description:
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff
changeset
+ − 308 UUID: cb76c866-ee3f-47e6-bb29-290074666e43
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff
changeset
+ − 309 ---------------------------------------
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff
changeset
+ − 310 </pre></div>
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff
changeset
+ − 311 <p>
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff
changeset
+ − 312 You can call the <tt>iplot</tt> function to view the resulting waveform:
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff
changeset
+ − 313 </p>
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff
changeset
+ − 314 <div class="fragment"><pre>
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff
changeset
+ − 315 iplot(asaw);
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff
changeset
+ − 316 </pre></div>
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff
changeset
+ − 317 <img src="images/ao_create_sawtooth.png" alt="Sawtooth waveform" border="3" width="600px">
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff
changeset
+ − 318
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff
changeset
+ − 319 <hr>
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff
changeset
+ − 320 <h4><a name="pzmodel"></a>Creating AOs from pole zero models</h4>
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff
changeset
+ − 321
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff
changeset
+ − 322 <p>
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff
changeset
+ − 323 When generating an AO from a pole zero model, the noise generator function is called.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff
changeset
+ − 324 This a method to generate arbitrarily long time series with a prescribed spectral density.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff
changeset
+ − 325 The algorithm is based on the following paper:
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff
changeset
+ − 326 </p>
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff
changeset
+ − 327 <p>Franklin, Joel N.:
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff
changeset
+ − 328 <i> Numerical simulation of stationary and non-stationary gaussian
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff
changeset
+ − 329 random processes </i>, SIAM review, Volume {<b> 7</b>}, Issue 1, page 68--80, 1965.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff
changeset
+ − 330 </p>
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff
changeset
+ − 331 <p>
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff
changeset
+ − 332 The Document <i> Generation of Random time series with prescribed spectra </i> by Gerhard Heinzel (S2-AEI-TN-3034) <br> corrects a mistake in the aforesaid paper and describes the practical implementation.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff
changeset
+ − 333 The following code creates an AO with a time series having a prescribed spectral density,
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff
changeset
+ − 334 defined by the input pole zero model:
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff
changeset
+ − 335 </p>
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff
changeset
+ − 336
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff
changeset
+ − 337 <div class="fragment"><pre>
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff
changeset
+ − 338 f1 = 5;
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff
changeset
+ − 339 f2 = 10;
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff
changeset
+ − 340 f3 = 1;
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff
changeset
+ − 341 gain = 1;
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff
changeset
+ − 342 fs = 10; <span class="comment">%sampling frequancy</span>
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff
changeset
+ − 343 nsecs = 100; <span class="comment">%number of seconds to be generated</span>
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff
changeset
+ − 344
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff
changeset
+ − 345 p = [pz(f1) pz(f2)];
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff
changeset
+ − 346 z = [pz(f3)];
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff
changeset
+ − 347 pzm = pzmodel(gain, p, z);
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff
changeset
+ − 348 a = ao(pzm, nsecs, fs)
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff
changeset
+ − 349 ----------- ao 01: noisegen(None) -----------
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff
changeset
+ − 350
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff
changeset
+ − 351 name: noisegen(None)
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff
changeset
+ − 352 data: (0,9.20287001568168) (0.1,-3.88425345108961) (0.2,6.31042718242658) ...
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff
changeset
+ − 353 -------- tsdata 01 ------------
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff
changeset
+ − 354
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff
changeset
+ − 355 fs: 10
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff
changeset
+ − 356 x: [1000 1], double
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff
changeset
+ − 357 y: [1000 1], double
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff
changeset
+ − 358 dx: [0 0], double
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff
changeset
+ − 359 dy: [0 0], double
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff
changeset
+ − 360 xunits: [s]
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff
changeset
+ − 361 yunits: []
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff
changeset
+ − 362 nsecs: 100
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff
changeset
+ − 363 t0: 1970-01-01 00:00:00.000
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff
changeset
+ − 364 -------------------------------
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff
changeset
+ − 365
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff
changeset
+ − 366 hist: ao / ao / SId: fromPzmodel ... $-->$Id: ao ... S
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff
changeset
+ − 367 mdlfile: empty
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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+ − 368 description:
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+ − 369 UUID: 4a89d910-8672-475f-91cd-4fcc4b52a6b4
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+ − 370 ---------------------------------------------
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+ − 371 </pre></div>
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+ − 372 <p>
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+ − 373 You can call the <tt>iplot</tt> function to view the resulting noise.
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+ − 374 </p>
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+ − 375 <div class="fragment"><pre>
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+ − 376 iplot(a);
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+ − 377 </pre></div>
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+ − 378 <img src="images/ao_create_niose.png" alt="Random time series" border="3" width="600px">
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+ − 379
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+ − 380
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+ − 381 </p>
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+ − 382
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+ − 383 <br>
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+ − 384 <br>
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+ − 385 <table class="nav" summary="Navigation aid" border="0" width=
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+ − 386 "100%" cellpadding="0" cellspacing="0">
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+ − 387 <tr valign="top">
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+ − 388 <td align="left" width="20"><a href="ao_intro.html"><img src=
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+ − 389 "b_prev.gif" border="0" align="bottom" alt=
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+ − 390 "Analysis Objects"></a> </td>
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+ − 391
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+ − 392 <td align="left">Analysis Objects</td>
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+ − 393
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+ − 394 <td> </td>
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+ − 395
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+ − 396 <td align="right">Saving Analysis Objects</td>
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+ − 397
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+ − 398 <td align="right" width="20"><a href=
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+ − 399 "ao_save.html"><img src="b_next.gif" border="0" align=
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+ − 400 "bottom" alt="Saving Analysis Objects"></a></td>
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+ − 401 </tr>
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+ − 402 </table><br>
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+ − 403
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+ − 404 <p class="copy">©LTP Team</p>
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+ − 405 </body>
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+ − 406 </html>