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author Daniele Nicolodi <nicolodi@science.unitn.it>
date Mon, 05 Dec 2011 16:20:06 +0100
parents f0afece42f48
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1 <!-- $Id: zdomainfit_content.html,v 1.6 2009/08/27 11:38:58 luigi Exp $ -->
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2
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3 <!-- ================================================== -->
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4 <!-- BEGIN CONTENT FILE -->
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5 <!-- ================================================== -->
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6 <!-- ===== link box: Begin ===== -->
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7 <p>
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8 <table border="1" width="80%">
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9 <tr>
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10 <td>
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11 <table border="0" cellpadding="5" class="categorylist" width="100%">
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12 <colgroup>
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13 <col width="37%"/>
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14 <col width="63%"/>
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15 </colgroup>
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16 <tbody>
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17 <tr valign="top">
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18 <td>
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19 <a href="#description">Description</a>
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20 </td>
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21 <td>Z-domain system identification in LTPDA.</td>
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22 </tr>
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23 <tr valign="top">
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24 <td>
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25 <a href="#algorithm">Algorithm</a>
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26 </td>
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27 <td>Fit Algorithm.</td>
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28 </tr>
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29 <tr valign="top">
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30 <td>
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31 <a href="#examples">Examples</a>
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32 </td>
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33 <td>Usage example of z-domain system identification tool.</td>
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34 </tr>
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35 <tr valign="top">
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36 <td>
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37 <a href="#references">References</a>
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38 </td>
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39 <td>Bibliographic references.</td>
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40 </tr>
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41 </tbody>
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42 </table>
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43 </td>
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44 </tr>
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45 </table>
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46 </p>
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47 <!-- ===== link box: End ====== -->
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48
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49
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50
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51 <h2><a name="description">Z-domain system identification in LTPDA</a></h2>
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52 <p>
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53 System identification in z-domain is performed with the function
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Daniele Nicolodi <nicolodi@science.unitn.it>
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54 <a href="matlab:doc('ao/zDomainFit')">zDomainFit</a>.
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55 It is based on a modeified version of the vector fitting algorithm that was
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56 adapted to fit in z-domain. Details on the core agorithm can be found in [1 - 3].
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57 </p>
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58 <p>
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59 If you provide more than one AO as input, they will be fitted
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60 together with a common set of poles.
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61 Only frequency domain (<a href="matlab:doc('fsdata')">fsdata</a>) data can be
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62 fitted. Each non fsdata object is ignored. Input
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63 objects must have the same number of elements.
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64 </p>
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65
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66
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67 <h2><a name="algorithm">Fit algorithm</a></h2>
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68
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69 <p>
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70 The function performs a fitting loop to automatically identify model
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Daniele Nicolodi <nicolodi@science.unitn.it>
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71 order and parameters in z-domain. Output is a z-domain model expanded
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Daniele Nicolodi <nicolodi@science.unitn.it>
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72 in partial fractions:
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73 </p>
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74 <p>
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75 <div>
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Daniele Nicolodi <nicolodi@science.unitn.it>
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76 <IMG src="images/zdomainfit_1.gif" border="0">
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77 </div>
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78 </p>
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79 <p>
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80 Each element of the partial fraction expansion can be seen as a
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81 <a href="sigproc_iir.html">miir</a> filter. Therefore the complete expansion
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82 is simply a parallel <a href="sigproc_filterbanks.html">filterbank</a> of
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83 <a href="sigproc_iir.html">miir</a> filters.
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84 Since the function can fit more than one input analysis object at a time
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85 with a common set of poles, output filterbank are embedded in a
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86 <a href="class_desc_matrix.html">matrix</a> (note that this characteristic
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87 will be probably changed becausse of the introduction of the
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88 <a href="class_desc_collection.html">collection</a> class).
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89 </p>
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90 <p>
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91 Identification loop stops when the stop condition is reached.
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92 Stop criterion is based on three different approaches:
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93 <ol>
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94 <li> Mean Squared Error and variation <br>
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95 Check if the normalized mean squared error is lower than the value specified in
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96 <tt>FITTOL</tt> and if the relative variation of the mean squared error is lower
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97 than the value specified in <tt>MSEVARTOL</tt>.
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98 E.g. <tt>FITTOL = 1e-3</tt>, <tt>MSEVARTOL = 1e-2</tt> search for a fit with
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99 normalized meam square error lower than <tt>1e-3</tt> and <tt>MSE</tt> relative
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100 variation lower than <tt>1e-2</tt>.
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101 </li>
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102 <li> Log residuals difference and root mean squared error
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103 <ul>
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104 <li> Log Residuals difference <br>
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105 Check if the minimum of the logarithmic difference between data and
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106 residuals is larger than a specified value. ie. if the conditioning
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107 value is <tt>2</tt>, the function ensures that the difference between data and
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108 residuals is at lest two order of magnitude lower than data itsleves.
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109 <li> Root Mean Squared Error <br>
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110 Check that the variation of the root mean squared error is lower than
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111 <tt>10^(-1*value)</tt>.
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112 </ul>
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113 </li>
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114 <li> Residuals spectral flatness and root mean squared error
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115 <ul>
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116 <li> Residuals Spectral Flatness <br>
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117 In case of a fit on noisy data, the residuals from a good fit are
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118 expected to be as much as possible similar to a white noise. This
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119 property can be used to test the accuracy of a fit procedure. In
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120 particular it can be tested that the spectral flatness coefficient of
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121 the residuals is larger than a certain qiantity sf such that <tt>0 < sf < 1</tt>.
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122 <li> Root Mean Squared Error <br>
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123 Check that the variation of the root mean squared error is lower than
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124 <tt>10^(-1*value)</tt>.
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125 </ul>
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126 </li>
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127 </ol>
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128 Fitting loop stops when the two stopping conditions are satisfied, in both cases.
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129 </p>
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130 <p>
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131 The function can also perform a single loop without taking care of
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132 the stop conditions. This happens when <span class="string">'AUTOSEARCH'</span> parameter is
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133 set to <span class="string">'OFF'</span>.
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134 </p>
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135
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136
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137
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138 <h2><a name="examples">Usage example of z-domain system identification tool</a></h2>
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139 <p>
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140 In this example we fit a given frequency response to get a stable <tt>miir</tt> filter.
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141 For the meaning of any parameter please refer to
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142 <a href="matlab:doc('ao')">ao</a> and
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143 <a href="matlab:doc('ao/zDomainFit')">zDomainFit</a>
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144 documentation pages.
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145 </p>
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146
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147 <div class="fragment"><pre>
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148 pl = plist(...
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149 <span class="string">'fsfcn'</span>, <span class="string">'(1e-3./(2.*pi.*1i.*f).^2 + 1e3./(0.001+2.*pi.*1i.*f) + 1e5.*(2.*pi.*1i.*f).^2).*1e-10'</span>,...
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150 <span class="string">'f1'</span>, 1e-6,...
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151 <span class="string">'f2'</span>, 5,...
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152 <span class="string">'nf'</span>, 100);
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153
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154 a = ao(pl);
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155 a.setName;
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156
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157 <span class="comment">% Fit parameter list</span>
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158 pl_fit = plist(<span class="string">'FS'</span>,10,...
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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159 <span class="string">'AutoSearch'</span>,<span class="string">'on'</span>,...
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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160 <span class="string">'StartPolesOpt'</span>,<span class="string">'clog'</span>,...
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
161 <span class="string">'maxiter'</span>,50,...
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
162 <span class="string">'minorder'</span>,15,...
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
163 <span class="string">'maxorder'</span>,30,...
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
164 <span class="string">'weightparam'</span>,<span class="string">'abs'</span>,...
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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165 <span class="string">'CONDTYPE'</span>,<span class="string">'MSE'</span>,...
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
166 <span class="string">'FITTOL'</span>,1e-2,...
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
167 <span class="string">'MSEVARTOL'</span>,1e-1,...
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
168 <span class="string">'Plot'</span>,<span class="string">'on'</span>,...
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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169 <span class="string">'ForceStability'</span>,<span class="string">'on'</span>);
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
170
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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171 <span class="comment">% Do fit</span>
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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172 mod = zDomainFit(a, pl_fit);
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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173 </pre></div>
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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174
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
175 <p>
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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176 <tt>mod</tt> is a <tt>matrix</tt> object containing a <tt>filterbank</tt> object.
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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177 </p>
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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178
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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179 <div class="fragment"><pre>
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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180 >> mod
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
181 ---- matrix 1 ----
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
182 name: fit(a)
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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183 size: 1x1
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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184 01: filterbank | filterbank(fit(a)(fs=10.00, ntaps=2.00, a=[-1.19e+005 0], b=[1 0.0223]), fit(a)(fs=10.00, ntaps=2.00, a=[1.67e+005 0], b=[1 0.137]), fit(a)(fs=10.00, ntaps=2.00, a=[-5.41e+004 0], b=[1 0.348]), fit(a)(fs=10.00, ntaps=2.00, a=[1.15e+004 0], b=[1 0.603]), fit(a)(fs=10.00, ntaps=2.00, a=[-1.69e+005 0], b=[1 0.639]), fit(a)(fs=10.00, ntaps=2.00, a=[1.6e+005 0], b=[1 0.64]), fit(a)(fs=10.00, ntaps=2.00, a=[9.99e-009 0], b=[1 -1]), fit(a)(fs=10.00, ntaps=2.00, a=[-4.95e-010 0], b=[1 1]), fit(a)(fs=10.00, ntaps=2.00, a=[9.4e+003-i*3.7e+003 0], b=[1 -0.0528-i*0.0424]), fit(a)(fs=10.00, ntaps=2.00, a=[9.4e+003+i*3.7e+003 0], b=[1 -0.0528+i*0.0424]), fit(a)(fs=10.00, ntaps=2.00, a=[1.66e+003-i*1.45e+004 0], b=[1 0.0233-i*0.112]), fit(a)(fs=10.00, ntaps=2.00, a=[1.66e+003+i*1.45e+004 0], b=[1 0.0233+i*0.112]), fit(a)(fs=10.00, ntaps=2.00, a=[-1.67e+004+i*432 0], b=[1 0.171-i*0.14]), fit(a)(fs=10.00, ntaps=2.00, a=[-1.67e+004-i*432 0], b=[1 0.171+i*0.14]), fit(a)(fs=10.00, ntaps=2.00, a=[7.61e+003+i*7.36e+003 0], b=[1 0.378-i*0.112]), fit(a)(fs=10.00, ntaps=2.00, a=[7.61e+003-i*7.36e+003 0], b=[1 0.378+i*0.112]), fit(a)(fs=10.00, ntaps=2.00, a=[3.67e-015-i*4.61e-006 0], b=[1 -1-i*1.08e-010]), fit(a)(fs=10.00, ntaps=2.00, a=[3.67e-015+i*4.61e-006 0], b=[1 -1+i*1.08e-010]))
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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185 description:
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
186 UUID: 9274455a-68e8-4bf1-b1ad-db81551f3cd6
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
187 ------------------
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
188 </pre></div>
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
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189
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
190 <p>
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
191 The <tt>filterbank</tt> object contains a parallel bank of 18 filters.
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
192 </p>
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
193
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
194 <div class="fragment"><pre>
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
195 >> mod.objs
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
196 ---- filterbank 1 ----
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
197 name: fit(a)
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
198 type: parallel
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
199 01: fit(a)(fs=10.00, ntaps=2.00, a=[-1.19e+005 0], b=[1 0.0223])
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
200 02: fit(a)(fs=10.00, ntaps=2.00, a=[1.67e+005 0], b=[1 0.137])
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
201 03: fit(a)(fs=10.00, ntaps=2.00, a=[-5.41e+004 0], b=[1 0.348])
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
202 04: fit(a)(fs=10.00, ntaps=2.00, a=[1.15e+004 0], b=[1 0.603])
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
203 05: fit(a)(fs=10.00, ntaps=2.00, a=[-1.69e+005 0], b=[1 0.639])
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
204 06: fit(a)(fs=10.00, ntaps=2.00, a=[1.6e+005 0], b=[1 0.64])
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
205 07: fit(a)(fs=10.00, ntaps=2.00, a=[9.99e-009 0], b=[1 -1])
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
206 08: fit(a)(fs=10.00, ntaps=2.00, a=[-4.95e-010 0], b=[1 1])
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
207 09: fit(a)(fs=10.00, ntaps=2.00, a=[9.4e+003-i*3.7e+003 0], b=[1 -0.0528-i*0.0424])
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
208 10: fit(a)(fs=10.00, ntaps=2.00, a=[9.4e+003+i*3.7e+003 0], b=[1 -0.0528+i*0.0424])
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
209 11: fit(a)(fs=10.00, ntaps=2.00, a=[1.66e+003-i*1.45e+004 0], b=[1 0.0233-i*0.112])
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
210 12: fit(a)(fs=10.00, ntaps=2.00, a=[1.66e+003+i*1.45e+004 0], b=[1 0.0233+i*0.112])
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
211 13: fit(a)(fs=10.00, ntaps=2.00, a=[-1.67e+004+i*432 0], b=[1 0.171-i*0.14])
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
212 14: fit(a)(fs=10.00, ntaps=2.00, a=[-1.67e+004-i*432 0], b=[1 0.171+i*0.14])
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
213 15: fit(a)(fs=10.00, ntaps=2.00, a=[7.61e+003+i*7.36e+003 0], b=[1 0.378-i*0.112])
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
214 16: fit(a)(fs=10.00, ntaps=2.00, a=[7.61e+003-i*7.36e+003 0], b=[1 0.378+i*0.112])
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
215 17: fit(a)(fs=10.00, ntaps=2.00, a=[3.67e-015-i*4.61e-006 0], b=[1 -1-i*1.08e-010])
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
216 18: fit(a)(fs=10.00, ntaps=2.00, a=[3.67e-015+i*4.61e-006 0], b=[1 -1+i*1.08e-010])
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
217 description:
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
218 UUID: 21af6960-61a8-4351-b504-e6f2b5e55b06
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
219 ----------------------
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
220 </pre></div>
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
221
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
222 <p>
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
223 Each object of the <tt>filterbank</tt> is a <tt>miir</tt> filter.
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
224 </p>
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
225
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
226 <div class="fragment"><pre>
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
227 filt = mod.objs.filters.index(3)
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
228 ------ miir/1 -------
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
229 b: [1 0.348484501572296]
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
230 histin: 0
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
231 version: $Id: zdomainfit_content.html,v 1.6 2009/08/27 11:38:58 luigi Exp $
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
232 ntaps: 2
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
233 fs: 10
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
234 infile:
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
235 a: [-54055.7700068032 0]
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
236 histout: 0
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
237 iunits: [] [1x1 unit]
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
238 ounits: [] [1x1 unit]
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
239 hist: miir.hist [1x1 history]
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
240 procinfo: (empty-plist) [1x1 plist]
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
241 plotinfo: (empty-plist) [1x1 plist]
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
242 name: (fit(a)(3,1))(3)
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
243 description:
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
244 mdlfile:
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
245 UUID: 6e2a1cd8-f17d-4c9d-aea9-4d9a96e41e68
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
246 ---------------------
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
247 </pre></div>
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
248
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
249
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
250 <h2><a name="references">References</a></h2>
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
251 <p>
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
252 <ol>
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
253 <li> B. Gustavsen and A. Semlyen, "Rational approximation of frequency
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
254 domain responses by Vector Fitting", IEEE Trans. Power Delivery
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
255 vol. 14, no. 3, pp. 1052-1061, July 1999.
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
256 <li> B. Gustavsen, "Improving the Pole Relocating Properties of Vector
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
257 Fitting", IEEE Trans. Power Delivery vol. 21, no. 3, pp.
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
258 1587-1592, July 2006.
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
259 <li> Y. S. Mekonnen and J. E. Schutt-Aine, "Fast broadband
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
260 macromodeling technique of sampled time/frequency data using
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
261 z-domain vector-fitting method", Electronic Components and
f0afece42f48 Import.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
262 Technology Conference, 2008. ECTC 2008. 58th 27-30 May 2008 pp.
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
263 1231 - 1235.
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
264 </ol>
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Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff changeset
265 </p>