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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>Creating Analysis Objects (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 "ao_intro.html"><img src="b_prev.gif" border="0" align=
30 "bottom" alt="Analysis Objects"></a>&nbsp;&nbsp;&nbsp;<a href=
31 "ao_save.html"><img src="b_next.gif" border="0" align=
32 "bottom" alt="Saving Analysis Objects"></a></td>
33 </tr>
34 </table>
35
36 <h1 class="title"><a name="f3-12899" id="f3-12899"></a>Creating Analysis Objects</h1>
37 <hr>
38
39 <p>
40 <p>Analysis objects can be created in MATLAB in many ways. Apart from being created by the many
41 algorithms in the LTPDA Toolbox, AOs can also be created from initial data or descriptions
42 of data. The various <i>constructors</i>
43 are listed in the function help: <a href="matlab:doc('ao')">ao help</a>.</p>
44
45 <h3>Examples of creating AOs</h3>
46
47 <p>The following examples show some ways to create Analysis Objects.</p>
48
49 <ul>
50 <li><a href="ao_create.html#text">Creating AOs from text files</a></li>
51 <li><a href="ao_create.html#xml">Creating AOs from XML or MAT files</a></li>
52 <li><a href="ao_create.html#fcn">Creating AOs from MATLAB functions</a></li>
53 <li><a href="ao_create.html#tsfcn">Creating AOs from functions of time</a></li>
54 <li><a href="ao_create.html#window">Creating AOs from window functions</a></li>
55 <li><a href="ao_create.html#waveform">Creating AOs from waveform descriptions</a></li>
56 <li><a href="ao_create.html#pzmodel">Creating AOs from pole zero models</a></li>
57 </ul>
58
59 <hr>
60 <h4><a name="text"></a>Creating AOs from text files.</h4>
61
62 <p>Analysis Objects can be created from text files containing two columns of ASCII numbers. Files
63 ending in '.txt' or '.dat' will be handled as ASCII file inputs. The
64 first column is taken to be the time instances; the second column is taken to be the amplitude
65 samples. The created AO is of type <tt>tsdata</tt> with the sample rate set by the difference
66 between the time-stamps of the first two samples in the file. The name of the resulting AO is
67 set to the filename (without the file extension). The filename is also stored as a parameter in
68 the history parameter list. The following code shows this in action:</p>
69
70 <div class="fragment"><pre>
71 >> a = ao(<span class="string">'data.txt'</span>)
72 ----------- ao 01: data.txt_01_02 -----------
73
74 name: data.txt_01_02
75 data: (0,-1.06421341288933) (0.1,1.60345729812004) (0.2,1.23467914689078) ...
76 -------- tsdata 01 ------------
77
78 fs: 10
79 x: [100 1], double
80 y: [100 1], double
81 dx: [0 0], double
82 dy: [0 0], double
83 xunits: [s]
84 yunits: []
85 nsecs: 10
86 t0: 1970-01-01 00:00:00.000
87 -------------------------------
88
89 hist: ao / ao / SId: fromDatafile ... $-->$Id: ao ... S
90 mdlfile: empty
91 description:
92 UUID: e6ccfcb6-da49-4f4c-8c2c-3054fe5d2762
93 ---------------------------------------------
94 </pre></div>
95 <p>As with most constructor calls, an equivalent action can be achieved using an input
96 <a href="plist_intro.html">Parameter List</a>.</p>
97
98 <div class="fragment"><pre>
99 >> a = ao(plist(<span class="string">'filename'</span>, <span class="string">'data.txt'</span>))
100 </pre></div>
101
102 <hr>
103 <h4><a name="xml"></a>Creating AOs from XML or .mat files</h4>
104
105 <p>AOs can be saved as both XML and .MAT files. As such, they can also be created from these
106 files.</p>
107
108 <div class="fragment"><pre>
109 >> a = ao(<span class="string">'a.xml'</span>)
110 ----------- ao 01: a -----------
111
112 name: None
113 data: (0,-0.493009815316451) (0.1,-0.180739356415037) (0.2,0.045841105713705) ...
114 -------- tsdata 01 ------------
115
116 fs: 10
117 x: [100 1], double
118 y: [100 1], double
119 dx: [0 0], double
120 dy: [0 0], double
121 xunits: [s]
122 yunits: []
123 nsecs: 10
124 t0: 1970-01-01 00:00:01.000
125 -------------------------------
126
127 hist: ao / ao / SId: fromVals ... $-->$Id: ao ... S
128 mdlfile: empty
129 description:
130 UUID: 2fed6155-6468-4533-88f6-e4b27bc6e1aa
131 --------------------------------
132 </pre></div>
133
134 <hr>
135 <h4><a name="fcn"></a>Creating AOs from MATLAB functions</h4>
136
137 <p>AOs can be created from any valid MATLAB function which returns a vector or matrix of values.
138 For such calls, a parameter list is used as input. For example, the following code creates
139 an AO containing 1000 random numbers:</p>
140
141 <div class="fragment"><pre>
142 >> a = ao(plist(<span class="string">'fcn'</span>, <span class="string">'randn(1000,1)'</span>))
143 ----------- ao 01: a -----------
144
145 name: None
146 data: -1.28325610460477 -2.32895451628334 0.901931466951714 -1.83563868373519 0.06675 ...
147 -------- cdata 01 ------------
148 y: [1000x1], double
149 dy: [0x0], double
150 yunits: []
151 ------------------------------
152
153 hist: ao / ao / SId: fromFcn ... $-->$Id ... $
154 mdlfile: empty
155 description:
156 UUID: 0072f8d0-f804-472b-a4aa-e9ec6a8de803
157 --------------------------------
158 </pre></div>
159 <p>Here you can see that the AO is a <tt>cdata</tt> type and the name is set to be the function
160 that was input.</p>
161
162 <hr>
163 <h4><a name="tsfcn"></a>Creating AOs from functions of time</h4>
164
165 <p>AOs can be created from any valid MATLAB function which is a function of the variable
166 <tt>t</tt>. For such calls, a parameter list is used as input. For example, the following
167 code creates an AO containing sinusoidal signal at 1Hz with some additional Gaussian noise:</p>
168
169 <div class="fragment"><pre>
170 pl = plist();
171 pl = append(pl, <span class="string">'nsecs'</span>, 100);
172 pl = append(pl, <span class="string">'fs'</span>, 10);
173 pl = append(pl, <span class="string">'tsfcn'</span>, <span class="string">'sin(2*pi*1*t)+randn(size(t))'</span>);
174 a = ao(pl)
175 ----------- ao 01: a -----------
176
177 name: None
178 data: (0,1.37694916561229) (0.1,-0.820427237640771) (0.2,1.09228819960292) ...
179 -------- tsdata 01 ------------
180
181 fs: 10
182 x: [1000 1], double
183 y: [1000 1], double
184 dx: [0 0], double
185 dy: [0 0], double
186 xunits: [s]
187 yunits: []
188 nsecs: 100
189 t0: 1970-01-01 00:00:00.000
190 -------------------------------
191
192 hist: ao / ao / SId: fromTSfcn ... $-->$Id: ao ... S
193 mdlfile: empty
194 description:
195 UUID: c0f481cf-4bdd-4a91-bc78-6d34f8222313
196 --------------------------------
197 </pre></div>
198 <p>Here you can see that the AO is a <tt>tsdata</tt> type, as you would expect. Also note that you
199 need to specify the sample rate (<tt>fs</tt>) and the number of seconds of data you would like
200 to have (<tt>nsecs</tt>).</p>
201
202 <hr>
203 <h4><a name="window"></a>Creating AOs from window functions</h4>
204
205 <p>The LTPDA Toolbox contains a class for designing spectral windows
206 (see <a href="specwin.html">Spectral Windows</a>). A spectral window object can
207 also be used to create an Analysis Object as follows:</p>
208
209 <div class="fragment"><pre>
210 >> w = specwin(<span class="string">'Hanning'</span>, 1000)
211 ------ specwin/1 -------
212 type: Hanning
213 alpha: 0
214 psll: 31.5
215 rov: 50
216 nenbw: 1.5
217 w3db: 1.4382
218 flatness: -1.4236
219 ws: 500
220 ws2: 375.000000000001
221 win: [0 9.86957193144233e-06 3.94778980919441e-05 8.88238095955174e-05 0.0001579 ...
222 version: SId: specwin.m,v 1.67 2009/09/01 09:25:24 ingo Exp S
223 ------------------------
224
225 >> a = ao(w)
226 ----------- ao 01: ao(Hanning) -----------
227
228 name: ao(Hanning)
229 data: 0 9.86957193144233e-06 3.94778980919441e-05 8.88238095955174e-05 0.0001579 ...
230 -------- cdata 01 ------------
231 y: [1x1000], double
232 dy: [0x0], double
233 yunits: []
234 ------------------------------
235
236 hist: ao / ao / SId: fromSpecWin ... $-->$Id: ao ... S
237 mdlfile: empty
238 description:
239 UUID: ea1a9036-b9f5-4bdb-b3a3-211e9d697060
240 ------------------------------------------
241 </pre></div>
242 <p>
243 It is also possible to pass the information about the window as a plist to the ao constructor.
244 </p>
245 <div class="fragment"><pre>
246 >> ao(plist(<span class="string">'win'</span>, <span class="string">'Hanning'</span>, <span class="string">'length'</span>, 1000))
247 ----------- ao 01: ao(Hanning) -----------
248
249 name: ao(Hanning)
250 data: 0 9.86957193144233e-06 3.94778980919441e-05 8.88238095955174e-05 0.0001579 ...
251 -------- cdata 01 ------------
252 y: [1x1000], double
253 dy: [0x0], double
254 yunits: []
255 ------------------------------
256
257 hist: ao / ao / SId: fromSpecWin ... -->$Id: ao ... S
258 mdlfile: empty
259 description:
260 UUID: 5b81f67a-45b9-43f8-a74a-bc5161fd718f
261 ------------------------------------------
262 </pre></div>
263
264 <p>
265 The example code above creates a Hanning window object with 1000 points. The call to the AO
266 constructor then creates a <tt>cdata</tt> type AO with 1000 points. This AO can then be multiplied
267 against other AOs in order to window the data.
268 </p>
269
270 <hr>
271 <h4><a name="waveform"></a>Creating AOs from waveform descriptions</h4>
272
273 <p>
274 MATLAB contains various functions for creating different waveforms, for example,
275 <tt>square</tt>, <tt>sawtooth</tt>. Some of these functions can be called upon to create
276 Analysis Objects. The following code creates an AO with a sawtooth waveform:
277 </p>
278
279 <div class="fragment"><pre>
280 pl = plist();
281 pl = append(pl, <span class="string">'fs'</span>, 100);
282 pl = append(pl, <span class="string">'nsecs'</span>, 5);
283 pl = append(pl, <span class="string">'waveform'</span>, 'Sawtooth');
284 pl = append(pl, <span class="string">'f'</span>, 1);
285 pl = append(pl, <span class="string">'width'</span>, 0.5);
286
287 asaw = ao(pl)
288 ----------- ao 01: Sawtooth -----------
289
290 name: Sawtooth
291 data: (0,-1) (0.01,-0.96) (0.02,-0.92) (0.03,-0.88) (0.04,-0.84) ...
292 -------- tsdata 01 ------------
293
294 fs: 100
295 x: [500 1], double
296 y: [500 1], double
297 dx: [0 0], double
298 dy: [0 0], double
299 xunits: [s]
300 yunits: []
301 nsecs: 5
302 t0: 1970-01-01 00:00:00.000
303 -------------------------------
304
305 hist: ao / ao / SId: fromWaveform ... $-->$Id: ao ... S
306 mdlfile: empty
307 description:
308 UUID: cb76c866-ee3f-47e6-bb29-290074666e43
309 ---------------------------------------
310 </pre></div>
311 <p>
312 You can call the <tt>iplot</tt> function to view the resulting waveform:
313 </p>
314 <div class="fragment"><pre>
315 iplot(asaw);
316 </pre></div>
317 <img src="images/ao_create_sawtooth.png" alt="Sawtooth waveform" border="3" width="600px">
318
319 <hr>
320 <h4><a name="pzmodel"></a>Creating AOs from pole zero models</h4>
321
322 <p>
323 When generating an AO from a pole zero model, the noise generator function is called.
324 This a method to generate arbitrarily long time series with a prescribed spectral density.
325 The algorithm is based on the following paper:
326 </p>
327 <p>Franklin, Joel N.:
328 <i> Numerical simulation of stationary and non-stationary gaussian
329 random processes </i>, SIAM review, Volume {<b> 7</b>}, Issue 1, page 68--80, 1965.
330 </p>
331 <p>
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.
333 The following code creates an AO with a time series having a prescribed spectral density,
334 defined by the input pole zero model:
335 </p>
336
337 <div class="fragment"><pre>
338 f1 = 5;
339 f2 = 10;
340 f3 = 1;
341 gain = 1;
342 fs = 10; <span class="comment">%sampling frequancy</span>
343 nsecs = 100; <span class="comment">%number of seconds to be generated</span>
344
345 p = [pz(f1) pz(f2)];
346 z = [pz(f3)];
347 pzm = pzmodel(gain, p, z);
348 a = ao(pzm, nsecs, fs)
349 ----------- ao 01: noisegen(None) -----------
350
351 name: noisegen(None)
352 data: (0,9.20287001568168) (0.1,-3.88425345108961) (0.2,6.31042718242658) ...
353 -------- tsdata 01 ------------
354
355 fs: 10
356 x: [1000 1], double
357 y: [1000 1], double
358 dx: [0 0], double
359 dy: [0 0], double
360 xunits: [s]
361 yunits: []
362 nsecs: 100
363 t0: 1970-01-01 00:00:00.000
364 -------------------------------
365
366 hist: ao / ao / SId: fromPzmodel ... $-->$Id: ao ... S
367 mdlfile: empty
368 description:
369 UUID: 4a89d910-8672-475f-91cd-4fcc4b52a6b4
370 ---------------------------------------------
371 </pre></div>
372 <p>
373 You can call the <tt>iplot</tt> function to view the resulting noise.
374 </p>
375 <div class="fragment"><pre>
376 iplot(a);
377 </pre></div>
378 <img src="images/ao_create_niose.png" alt="Random time series" border="3" width="600px">
379
380
381 </p>
382
383 <br>
384 <br>
385 <table class="nav" summary="Navigation aid" border="0" width=
386 "100%" cellpadding="0" cellspacing="0">
387 <tr valign="top">
388 <td align="left" width="20"><a href="ao_intro.html"><img src=
389 "b_prev.gif" border="0" align="bottom" alt=
390 "Analysis Objects"></a>&nbsp;</td>
391
392 <td align="left">Analysis Objects</td>
393
394 <td>&nbsp;</td>
395
396 <td align="right">Saving Analysis Objects</td>
397
398 <td align="right" width="20"><a href=
399 "ao_save.html"><img src="b_next.gif" border="0" align=
400 "bottom" alt="Saving Analysis Objects"></a></td>
401 </tr>
402 </table><br>
403
404 <p class="copy">&copy;LTP Team</p>
405 </body>
406 </html>