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author Daniele Nicolodi <nicolodi@science.unitn.it>
date Mon, 05 Dec 2011 16:20:06 +0100
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1 <!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN"
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2 "http://www.w3.org/TR/1999/REC-html401-19991224/loose.dtd">
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3
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4 <html lang="en">
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5 <head>
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6 <meta name="generator" content=
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7 "HTML Tidy for Mac OS X (vers 1st December 2004), see www.w3.org">
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8 <meta http-equiv="Content-Type" content=
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9 "text/html; charset=us-ascii">
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10
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11 <title>IIR Filters (LTPDA Toolbox)</title>
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12 <link rel="stylesheet" href="docstyle.css" type="text/css">
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13 <meta name="generator" content="DocBook XSL Stylesheets V1.52.2">
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14 <meta name="description" content=
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15 "Presents an overview of the features, system requirements, and starting the toolbox.">
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16 </head>
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17
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18 <body>
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19 <a name="top_of_page" id="top_of_page"></a>
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20
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21 <p style="font-size:1px;">&nbsp;</p>
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22
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23 <table class="nav" summary="Navigation aid" border="0" width=
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24 "100%" cellpadding="0" cellspacing="0">
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25 <tr>
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26 <td valign="baseline"><b>LTPDA Toolbox</b></td><td><a href="../helptoc.html">contents</a></td>
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27
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28 <td valign="baseline" align="right"><a href=
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29 "sigproc_dfilt.html"><img src="b_prev.gif" border="0" align=
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30 "bottom" alt="Digital Filtering"></a>&nbsp;&nbsp;&nbsp;<a href=
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31 "sigproc_fir.html"><img src="b_next.gif" border="0" align=
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32 "bottom" alt="FIR Filters"></a></td>
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33 </tr>
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34 </table>
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35
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36 <h1 class="title"><a name="f3-12899" id="f3-12899"></a>IIR Filters</h1>
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37 <hr>
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38
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39 <p>
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40 <p>
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41 Infinite Impulse Response filters are those filters present a non-zero infinite length response when excited with a very brief (ideally an infinite peak) input signal. A linear causal IIR filter can be described by the following difference equation
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42 </p>
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43 <div align="center">
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44 <IMG src="images/sigproc_7.png" width="283" height="56" align="middle" border="0">
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45 </div>
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46 <p>
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47 This operation describe a recursive system, i.e. a system that depends on current and past samples of the input x[n], but also on the output data stream y[n].
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48 </p>
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49 <h2><a name="IIRbuild">Creating a IIR filter in the LTPDA</a></h2>
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50
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51 The LTPDA Toolbox allows the implementation of IIR filters by means of the <a href="pzmodel_filter.html"> miir class</a>.
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52
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53 <h2><a name="IIRplist">Creating from a plist</a></h2>
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54 <p>
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55 The following example creates an order 1 highpass filter with high frequency gain 2. Filter is designed for 10 Hz sampled data and has a cut-off frequency of 0.2 Hz.
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56 </p>
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57 <div class="fragment"><pre>
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58
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59 pl = plist(<span class="string">'type'</span>, <span class="string">'highpass'</span>, ...
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60 <span class="string">'order'</span>, 1, ...
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61 <span class="string">'gain'</span>, 2.0, ...
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62 <span class="string">'fs'</span>, 10, ...
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63 <span class="string">'fc'</span>, 0.2);
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64 f = miir(pl)
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65 </pre></div>
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66
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67 <h2><a name="IIRpzmodel">Creating from a pzmodel</a></h2>
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68 <p>
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69 IIR filters can also be <a href="pzmodel_filter.html"> created from a pzmodel </a>.
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70 </p>
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71 <h2><a name="IIRdiff">Creating from a difference equation</a></h2>
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72 <p>
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73 Alternatively, the filter can be defined in terms of two vectors specifying the coefficients of the filter and the sampling frequency. The following example creates a IIR filter with sampling frequency 1 Hz and the following recursive equation:
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74 </p>
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75
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76 <div align="center">
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77 <IMG src="images/sigproc_9.png" width="299" height="28" align="middle" border="0">
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78 </div>
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79
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80 <p><br></p>
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81
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82 <div class="fragment"><pre>
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83
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84 a = [0.5 -0.01];
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85 b = [1 0.1];
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86 fs = 1;
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87 f = miir(a,b,fs)
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88 </pre></div>
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89
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90 <p>
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91 <br>
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92 Notice that the convetion used in this function is the one described in the <a href="sigproc_dfilt.html"> Digital filters classification</a> section
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93 </p>
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94
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95 <h2><a name="IIRimport">Importing an existing model</a></h2>
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96 <p>
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97 The miir constructor also accepts as an input existing models in different formats:
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98 </p>
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99 <li>
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100 <li><p>LISO files:<p>
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101 <div class="fragment"><pre>
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102 f = miir(<span class="string">'foo_iir.fil'</span>)
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103 </pre></div>
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104 </li>
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105 <li><p>XML files:</p>
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106 <div class="fragment"><pre>
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107 f = miir(<span class="string">'foo_iir.xml'</span>)
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108 </pre></div>
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109 <li><p>MAT files:</p>
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110 <div class="fragment"><pre>
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111 f = miir(<span class="string">'foo_iir.mat'</span>)
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112 </pre></div>
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113 </li>
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114 <li><p>From repository:</p>
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115 <div class="fragment"><pre>
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116 f = miir(plist(<span class="string">'hostname'</span>, <span class="string">'localhost'</span>, <span class="string">'database'</span>, <span class="string">'ltpda'</span>, <span class="string">'ID'</span>, []))
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117 </pre></div>
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118 </li>
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119 </ul>
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120
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121
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122 </p>
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123
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124 <br>
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125 <br>
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126 <table class="nav" summary="Navigation aid" border="0" width=
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127 "100%" cellpadding="0" cellspacing="0">
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128 <tr valign="top">
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129 <td align="left" width="20"><a href="sigproc_dfilt.html"><img src=
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130 "b_prev.gif" border="0" align="bottom" alt=
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131 "Digital Filtering"></a>&nbsp;</td>
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132
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133 <td align="left">Digital Filtering</td>
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134
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135 <td>&nbsp;</td>
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136
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137 <td align="right">FIR Filters</td>
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138
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139 <td align="right" width="20"><a href=
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140 "sigproc_fir.html"><img src="b_next.gif" border="0" align=
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141 "bottom" alt="FIR Filters"></a></td>
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142 </tr>
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143 </table><br>
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144
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145 <p class="copy">&copy;LTP Team</p>
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146 </body>
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147 </html>