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author Daniele Nicolodi <nicolodi@science.unitn.it>
date Wed, 23 Nov 2011 19:22:13 +0100
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11 <title>Remove trends from a time-series AO (LTPDA Toolbox)</title>
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15 "Presents an overview of the features, system requirements, and starting the toolbox.">
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18 <body>
19 <a name="top_of_page" id="top_of_page"></a>
20
21 <p style="font-size:1px;">&nbsp;</p>
22
23 <table class="nav" summary="Navigation aid" border="0" width=
24 "100%" cellpadding="0" cellspacing="0">
25 <tr>
26 <td valign="baseline"><b>LTPDA Toolbox</b></td><td><a href="../helptoc.html">contents</a></td>
27
28 <td valign="baseline" align="right"><a href=
29 "ltpda_training_topic_2_4.html"><img src="b_prev.gif" border="0" align=
30 "bottom" alt="Interpolation of a time-series AO"></a>&nbsp;&nbsp;&nbsp;<a href=
31 "ltpda_training_topic_2_6.html"><img src="b_next.gif" border="0" align=
32 "bottom" alt="Whitening noise"></a></td>
33 </tr>
34 </table>
35
36 <h1 class="title"><a name="f3-12899" id="f3-12899"></a>Remove trends from a time-series AO</h1>
37 <hr>
38
39 <p>
40 <p>
41 The <tt>ao/detrend</tt> method offers the possibility to remove polynomial trends from a data series.
42 </p>
43 <p>
44 The method can be configured with the following parameter:
45 <table cellspacing="0" class="body" cellpadding="2" border="0" width="80%">
46 <colgroup>
47 <col width="25%"/>
48 <col width="75%"/>
49 </colgroup>
50 <thead>
51 <tr valign="top">
52 <th class="categorylist">Key</th>
53 <th class="categorylist">Description</th>
54 </tr>
55 </thead>
56 <tbody>
57 <!-- Key 'N' -->
58 <tr valign="top">
59 <td bgcolor="#f3f4f5">
60 <p><tt>N</tt></p>
61 </td>
62 <td bgcolor="#f3f4f5">
63 <p>The order of the polynomial to fit and remove. For orders below 10, a very fast C-code algorithm
64 is used. For higher orders, the MATLAB functions <tt>polyfit</tt> and <tt>polyval</tt> are used to
65 construct the polynomial which is then subtracted from the data.</p>
66 </td>
67 </tr>
68 </tbody>
69 </table>
70 </p>
71 <br>
72 <h2>Example 1</h2>
73 <p>
74 In this example we will construct a time-series consisting of noise plus a known quadratic trend.
75 We will then remove that trend using <tt>ao/detrend</tt> and compare the detrended time-series with the
76 original noise.
77 </p>
78 <p>
79 First let's create the time-series series consisting of the noise plus trend.
80 </p>
81 <div class="fragment"><pre>
82 <span class="comment">% Construct noise data stream</span>
83 fs = 10;
84 nsecs = 10;
85 pl = plist(<span class="string">'name'</span>, <span class="string">'None'</span>, <span class="string">'tsfcn'</span>, <span class="string">'5+randn(size(t))'</span>, <span class="string">'fs'</span>, fs, <span class="string">'nsecs'</span>, nsecs, <span class="string">'yunits'</span>, <span class="string">'V'</span>);
86 x = ao(pl);
87 <span class="comment">% Construct a quadratic data series</span>
88 pl_trend = plist(<span class="string">'tsfcn'</span>, <span class="string">'t.^2'</span>, <span class="string">'fs'</span>, fs, <span class="string">'nsecs'</span>, nsecs);
89 trend = ao(pl_trend);
90 <span class="comment">% Add them together</span>
91 fcn_trend = x + trend;
92 </pre>
93 </div>
94 <p>
95 <table cellspacing="0" class="note" summary="Note" cellpadding="5" border="1">
96 <tr width="90%">
97 <td>
98 The offset of 5 is added to the noise to ensure the data series
99 doesn't come close to zero; we want to divide by it later in the example.
100 </td>
101 </tr>
102 </table>
103 </p>
104 <p>
105 Next we will detrend the data and compare the result to the noise data <tt>x</tt> we made above.
106 </p>
107 <div class="fragment"><pre>
108 pl_detr = plist(<span class="string">'N'</span>,2);
109 detr = detrend(fcn_trend, pl_detr);
110 iplot(x, fcn_trend, detr, plist(<span class="string">'LineStyles'</span>, {<span class="string">''</span>, <span class="string">''</span>, <span class="string">'--'</span>}));
111 </pre>
112 </div>
113 <p>
114 <table cellspacing="0" class="note" summary="Note" cellpadding="5" border="1">
115 <tr width="90%">
116 <td>
117 In the <tt>plist</tt> we specified 'LineStyles' as empty strings. These just serve as place holders
118 and can be interpreted as "just to the default". If you want a data-series plotted with no line, then
119 specify 'none', for example, <tt>{'none', '-', '--'}</tt>.
120 </td>
121 </tr>
122 </table>
123 </p>
124 <br>
125 <img src="images/ltpda_training_1/topic2/detrend.png" alt="Detrend" border="3">
126 <br>
127 <p>
128 From this plot, it is not very easy to see how well our detrending worked. Let's form
129 the fractional difference of the original <tt>x</tt> data and the detrended data and plot that instead.
130 </p>
131 <div class="fragment"><pre>
132 detr5 = detr + 5;
133 diff = 100.*(x-detr5)./x;
134 iplot(diff);
135 </pre>
136 </div>
137 <p>
138 The result is shown below. We added the value 5 to the detrended time-series
139 just to ensure that we don't divide by any values close to zero.
140 </p>
141 <br>
142 <img src="images/ltpda_training_1/topic2/detrend_diff.png" alt="Detrend" border="3">
143 <br>
144 <p>
145 Try increasing the length of the data series to say, 1000 or 10000 seconds, to see how the
146 detrending improves.
147 </p>
148 <p>
149 <p>The value of the coefficient describing the subracted trend are included in the field <tt>procinfo</tt> of the <tt>ao</tt> objects. The <tt>procinfo</tt> is actually a <tt>plist</tt> object, so we can search for parameters, in this case the key is 'coeffs':
150 <div class="fragment"><pre>
151 c = find(detr.procinfo, 'coeffs');
152
153 <span class="comment">% Remember also, that you will loose the 'coeffs' if you make any operation on "detr"</span>
154 </pre></div>
155 </p>
156 Below is an example pipeline to perform the steps we did above:
157 </p>
158 <br>
159 <img src="images/ltpda_training_1/topic2/detrend_pipeline.png" alt="Detrend" border="3">
160 <br>
161 <p>
162 This introduces a new concept to the pipelines, namely, the use of constant blocks. Constant blocks
163 are executed before the rest of the pipeline and the values are placed in the MATLAB workspace. This means
164 that all parameter lists on the pipeline can refer to these constants. For example, the pipeline above
165 declares two constants: 'fs' and 'nsecs'. The two <tt>ao</tt> blocks refer to these. Below is the parameter
166 list for the first <tt>ao</tt> block, <tt>noise</tt>.
167 </p>
168 <br>
169 <img src="images/ltpda_training_1/topic2/detrend_ao_plist.png" alt="Detrend" border="3">
170 <br>
171 <p>
172 If you want to change the length of this simulation, then you just need to change the value
173 in the constant block, <tt>nsecs</tt>.
174 </p>
175 <p>
176 To add constant blocks to your pipeline, right-click on the canvas and select "Additional Blocks->Constant" from
177 the context menu. You can also add an annotation from the same context menu. The above pipeline shows one
178 annotation. To edit the text on an annotation, double-click it. Right-clicking on an annotation gives a context
179 menu that allows you to configure its appearance.
180 </p>
181 </p>
182
183 <br>
184 <br>
185 <table class="nav" summary="Navigation aid" border="0" width=
186 "100%" cellpadding="0" cellspacing="0">
187 <tr valign="top">
188 <td align="left" width="20"><a href="ltpda_training_topic_2_4.html"><img src=
189 "b_prev.gif" border="0" align="bottom" alt=
190 "Interpolation of a time-series AO"></a>&nbsp;</td>
191
192 <td align="left">Interpolation of a time-series AO</td>
193
194 <td>&nbsp;</td>
195
196 <td align="right">Whitening noise</td>
197
198 <td align="right" width="20"><a href=
199 "ltpda_training_topic_2_6.html"><img src="b_next.gif" border="0" align=
200 "bottom" alt="Whitening noise"></a></td>
201 </tr>
202 </table><br>
203
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