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Fix. Default password should be [] not an empty string
author Daniele Nicolodi <nicolodi@science.unitn.it>
date Wed, 07 Dec 2011 17:29:47 +0100
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1
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2 <p>
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3 Poles and zeros can be combined together to create a pole/zero model. In addition to a list of poles
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4 and zeros, a gain factor and a delay can be specified such that the resulting model is of the form:
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5 </p>
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6 <br>
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7 <div align="center">
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8 <img src="images/pzmodel_tf_eqn.png" alt="Pole/zero model TF" border="3">
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9 </div>
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10 <br>
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11 <p>
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12 The following sections introduce how to produce and use pole/zero models in the LTPDA environment.
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13 <ul>
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14 <li><a href="#direct">Direct form</a></li>
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15 <li><a href="#plist">Creating from a <tt>plist</tt></a></li>
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16 <li><a href="#resp">Computing the response of the model</a></li>
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17 </ul>
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18 </p>
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19
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20
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21 <h2><a name="direct">Direct form</a></h2>
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22
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23 The following code fragment creates a pole/zero model consisting of 2 poles and 2 zeros with a gain
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24 factor of 10 and a 10ms delay:
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25 <div class="fragment"><pre>
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26 >> pzm = pzmodel(10, {[1 2], 3}, {5, 10}, 0.01)
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27 ---- pzmodel 1 ----
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28 name: None
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29 gain: 10
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30 delay: 0.01
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31 iunits: []
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32 ounits: []
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33 pole 001: (f=1 Hz,Q=2)
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34 pole 002: (f=3 Hz,Q=NaN)
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35 zero 001: (f=5 Hz,Q=NaN)
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36 zero 002: (f=10 Hz,Q=NaN)
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37 -------------------
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38 </pre></div>
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39 <p>
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40 Notice, you can also pass arrays of <tt>pz</tt> objects to the <tt>pzmodel</tt> constructor, but this
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41 should rarely be necessary.
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42 </p>
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43
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44 <h2><a name="plist">Creating from a <tt>plist</tt></a></h2>
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45
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46 <p>
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47 You can also create a <tt>pzmodel</tt> by passing a parameter list. The following example shows
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48 this
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49 </p>
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50
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51 <div class="fragment"><pre>
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52 >> pl = plist(<span class="string">'name'</span>, <span class="string">'test model'</span>, ...
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53 <span class="string">'gain'</span>, 10, ...
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54 <span class="string">'poles'</span>, {[1 2], 3}, ...
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55 <span class="string">'zeros'</span>, {5, 10}, ...
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56 <span class="string">'delay'</span>, 0.01, ...
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57 <span class="string">'iunits'</span>, 'm', ...
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58 <span class="string">'ounits'</span>, 'V^2');
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59 >> pzm = pzmodel(pl)
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60 ---- pzmodel 1 ----
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61 name: test model
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62 gain: 10
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63 delay: 0.01
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64 iunits: [m]
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65 ounits: [V^2]
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66 pole 001: (f=1 Hz,Q=2)
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67 pole 002: (f=3 Hz,Q=NaN)
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68 zero 001: (f=5 Hz,Q=NaN)
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69 zero 002: (f=10 Hz,Q=NaN)
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70 -------------------
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71 </pre></div>
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72 <p>
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73 Here we also specified the input units of the transfer function ('iunits') and the
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74 output units, ('ounits'). In this case, the model represents a transfer function
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75 from metres to Volts squared.
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76 </p>
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77
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78 <h2><a name="resp">Computing the response of the model</a></h2>
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79
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80 <p>
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81 The frequency response of the model can generated using the <tt>resp</tt> method of the
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82 <tt>pzmodel</tt> class. To compute the response of the model created above:
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83 </p>
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84 <div class="fragment"><pre>
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85 >> resp(pzm)
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86 </pre></div>
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87 <p>
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88 Since no output was specified, this command produces the following plot:
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89 <img src="images/pzmodel_resp.png" alt="Pole/zero model resp" border="3" width="600">
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90 </p>
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91 <p>
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92 You can also specify the frequency band over which to compute the response by passing a <tt>plist</tt>
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93 to the <tt>resp</tt> method, as follows:
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94 </p>
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95 <div class="fragment"><pre>
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96 >> rpl = plist(<span class="string">'f1'</span>, 0.1, ...
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97 <span class="string">'f2'</span>, 1000, ...
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98 <span class="string">'nf'</span>, 10000);
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99 >> a = resp(pzm, rpl)
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100 ----------- ao 01: resp(test model) -----------
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101
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102 name: resp(test model)
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103 description:
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104 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) ...
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105 ----------- fsdata 01 -----------
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106
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107 fs: NaN
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108 x: [1 10000], double
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109 y: [1 10000], double
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110 xunits: [Hz]
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111 yunits: [V^(2)][m^(-1)]
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112 t0: 1970-01-01 00:00:00.000
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113 navs: NaN
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114 ---------------------------------
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115
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116 hist: pzmodel / resp / $Id: pzmodel_model_content.html,v 1.5 2009/02/24 09:44:39 miquel Exp $
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117 mfilename:
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118 mdlfilename:
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119 -----------------------------------------------
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120 </pre></div>
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121 <p>
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122 In this case, the response is returned as an Analysis Object containing <tt>fsdata</tt>. You can now
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123 plot the AO using the <tt>iplot</tt> function.
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124 </p>