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author Daniele Nicolodi <nicolodi@science.unitn.it>
date Wed, 23 Nov 2011 19:22:13 +0100
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1 <!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN"
2 "http://www.w3.org/TR/1999/REC-html401-19991224/loose.dtd">
3
4 <html lang="en">
5 <head>
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7 "HTML Tidy for Mac OS X (vers 1st December 2004), see www.w3.org">
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10
11 <title>Building a model (LTPDA Toolbox)</title>
12 <link rel="stylesheet" href="docstyle.css" type="text/css">
13 <meta name="generator" content="DocBook XSL Stylesheets V1.52.2">
14 <meta name="description" content=
15 "Presents an overview of the features, system requirements, and starting the toolbox.">
16 </head>
17
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 "pzmodel.html"><img src="b_prev.gif" border="0" align=
30 "bottom" alt="Pole/Zero representation"></a>&nbsp;&nbsp;&nbsp;<a href=
31 "pzmodel_gui.html"><img src="b_next.gif" border="0" align=
32 "bottom" alt="Model helper GUI"></a></td>
33 </tr>
34 </table>
35
36 <h1 class="title"><a name="f3-12899" id="f3-12899"></a>Building a model</h1>
37 <hr>
38
39 <p>
40
41 <p>
42 Poles and zeros can be combined together to create a pole/zero model. In addition to a list of poles
43 and zeros, a gain factor and a delay can be specified such that the resulting model is of the form:
44 </p>
45 <br>
46 <div align="center">
47 <img src="images/pzmodel_tf_eqn.png" alt="Pole/zero model TF" border="3">
48 </div>
49 <br>
50 <p>
51 The following sections introduce how to produce and use pole/zero models in the LTPDA environment.
52 <ul>
53 <li><a href="#direct">Direct form</a></li>
54 <li><a href="#plist">Creating from a <tt>plist</tt></a></li>
55 <li><a href="#resp">Computing the response of the model</a></li>
56 </ul>
57 </p>
58
59
60 <h2><a name="direct">Direct form</a></h2>
61
62 The following code fragment creates a pole/zero model consisting of 2 poles and 2 zeros with a gain
63 factor of 10 and a 10ms delay:
64 <div class="fragment"><pre>
65 >> pzm = pzmodel(10, {[1 2], 3}, {5, 10}, 0.01)
66 ---- pzmodel 1 ----
67 name: None
68 gain: 10
69 delay: 0.01
70 iunits: []
71 ounits: []
72 pole 001: (f=1 Hz,Q=2)
73 pole 002: (f=3 Hz,Q=NaN)
74 zero 001: (f=5 Hz,Q=NaN)
75 zero 002: (f=10 Hz,Q=NaN)
76 -------------------
77 </pre></div>
78 <p>
79 Notice, you can also pass arrays of <tt>pz</tt> objects to the <tt>pzmodel</tt> constructor, but this
80 should rarely be necessary.
81 </p>
82
83 <h2><a name="plist">Creating from a <tt>plist</tt></a></h2>
84
85 <p>
86 You can also create a <tt>pzmodel</tt> by passing a parameter list. The following example shows
87 this
88 </p>
89
90 <div class="fragment"><pre>
91 >> pl = plist(<span class="string">'name'</span>, <span class="string">'test model'</span>, ...
92 <span class="string">'gain'</span>, 10, ...
93 <span class="string">'poles'</span>, {[1 2], 3}, ...
94 <span class="string">'zeros'</span>, {5, 10}, ...
95 <span class="string">'delay'</span>, 0.01, ...
96 <span class="string">'iunits'</span>, 'm', ...
97 <span class="string">'ounits'</span>, 'V^2');
98 >> pzm = pzmodel(pl)
99 ---- pzmodel 1 ----
100 name: test model
101 gain: 10
102 delay: 0.01
103 iunits: [m]
104 ounits: [V^2]
105 pole 001: (f=1 Hz,Q=2)
106 pole 002: (f=3 Hz,Q=NaN)
107 zero 001: (f=5 Hz,Q=NaN)
108 zero 002: (f=10 Hz,Q=NaN)
109 -------------------
110 </pre></div>
111 <p>
112 Here we also specified the input units of the transfer function ('iunits') and the
113 output units, ('ounits'). In this case, the model represents a transfer function
114 from metres to Volts squared.
115 </p>
116
117 <h2><a name="resp">Computing the response of the model</a></h2>
118
119 <p>
120 The frequency response of the model can generated using the <tt>resp</tt> method of the
121 <tt>pzmodel</tt> class. To compute the response of the model created above:
122 </p>
123 <div class="fragment"><pre>
124 >> resp(pzm)
125 </pre></div>
126 <p>
127 Since no output was specified, this command produces the following plot:
128 <img src="images/pzmodel_resp.png" alt="Pole/zero model resp" border="3" width="600">
129 </p>
130 <p>
131 You can also specify the frequency band over which to compute the response by passing a <tt>plist</tt>
132 to the <tt>resp</tt> method, as follows:
133 </p>
134 <div class="fragment"><pre>
135 >> rpl = plist(<span class="string">'f1'</span>, 0.1, ...
136 <span class="string">'f2'</span>, 1000, ...
137 <span class="string">'nf'</span>, 10000);
138 >> a = resp(pzm, rpl)
139 ----------- ao 01: resp(test model) -----------
140
141 name: resp(test model)
142 description:
143 data: (0.1,10.0668830776529-i*0.605439551995965) (0.100092155051679,10.067006787497-i*0.606014805088671) (0.100184395028894,10.0671307268392-i*0.606590636924472) (0.100276720009908,10.0672548961078-i*0.607167048174596) (0.100369130073055,10.0673792957318-i*0.607744039511284) ...
144 ----------- fsdata 01 -----------
145
146 fs: NaN
147 x: [1 10000], double
148 y: [1 10000], double
149 xunits: [Hz]
150 yunits: [V^(2)][m^(-1)]
151 t0: 1970-01-01 00:00:00.000
152 navs: NaN
153 ---------------------------------
154
155 hist: pzmodel / resp / $Id: pzmodel_model_content.html,v 1.5 2009/02/24 09:44:39 miquel Exp $
156 mfilename:
157 mdlfilename:
158 -----------------------------------------------
159 </pre></div>
160 <p>
161 In this case, the response is returned as an Analysis Object containing <tt>fsdata</tt>. You can now
162 plot the AO using the <tt>iplot</tt> function.
163 </p>
164
165 </p>
166
167 <br>
168 <br>
169 <table class="nav" summary="Navigation aid" border="0" width=
170 "100%" cellpadding="0" cellspacing="0">
171 <tr valign="top">
172 <td align="left" width="20"><a href="pzmodel.html"><img src=
173 "b_prev.gif" border="0" align="bottom" alt=
174 "Pole/Zero representation"></a>&nbsp;</td>
175
176 <td align="left">Pole/Zero representation</td>
177
178 <td>&nbsp;</td>
179
180 <td align="right">Model helper GUI</td>
181
182 <td align="right" width="20"><a href=
183 "pzmodel_gui.html"><img src="b_next.gif" border="0" align=
184 "bottom" alt="Model helper GUI"></a></td>
185 </tr>
186 </table><br>
187
188 <p class="copy">&copy;LTP Team</p>
189 </body>
190 </html>