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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>FIR 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_iir.html"><img src="b_prev.gif" border="0" align=
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30 "bottom" alt="IIR Filters"></a>&nbsp;&nbsp;&nbsp;<a href=
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31 "sigproc_filterbanks.html"><img src="b_next.gif" border="0" align=
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32 "bottom" alt="Filter banks"></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>FIR 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 Finite Impulse Response filters are those filters present a non-zero finite length response
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42 when excited with a very brief (ideally an infinite peak) input signal. A linear causal
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43 FIR filter can be described by the following difference equation
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44 </p>
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45 <div align="center">
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46 <IMG src="images/sigproc_8.png" width="157" height="56" align="middle" border="0">
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47 </div>
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48 <p>
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49 This operation describe a nonrecursive system, i.e. a system that only depends on current
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50 and past samples of the input data stream <tt>x[n]</tt>
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51 </p>
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52 <h2><a name="FIRbuild">Creating a FIR filter in the LTPDA</a></h2>
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53 <p>
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54 The LTPDA Toolbox allows the implementation of FIR filters by means of the
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55 <a href="class_desc_mfir.html"> mfir class</a>.
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56 </p>
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57 <h2><a name="FIRplist">Creating from a plist</a></h2>
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58 <p>
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59 The following example creates an order 64 highpass filter with high frequency gain 2.
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60 The filter is designed for 1 Hz sampled data and has a cut-off frequency of 0.2 Hz.
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61 </p>
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62 <div class="fragment"><pre>
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63
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64 pl = plist(<span class="string">'type'</span>, <span class="string">'highpass'</span>, ...
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65 <span class="string">'order'</span>, 64, ...
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66 <span class="string">'gain'</span>, 2.0, ...
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67 <span class="string">'fs'</span>, 1, ...
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68 <span class="string">'fc'</span>, 0.2);
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69 f = mfir(pl)
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70 </pre></div>
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71
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72 <h2><a name="FIRdiff">Creating from a difference equation</a></h2>
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73 <p>
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74 The filter can be defined in terms of two vectors specifying the coefficients of the filter
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75 and the sampling frequency. The following example creates a FIR filter with sampling frequency
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76 1 Hz and the following recursive equation:
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77 </p>
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78
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79 <div align="center">
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80 <IMG src="images/sigproc_10.png" width="202" height="28" align="middle" border="0"></div>
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81 </div>
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82
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83 <p><br></p>
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84
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85 <div class="fragment"><pre>
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86
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87 b = [-0.8 10];
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88 fs = 1;
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89 f = mfir(b,fs)
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90 </pre></div>
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91
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92 <h2><a name="FIRfromAO">Creating from an Analysis Object</a></h2>
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93 <p>
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94 A FIR filter can be generated based on the magnitude of the input Analysis Object or fsdata object.
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95 In the following example a fsdata object is first generated and then passed to the mfir constructor
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96 to obtain the equivalent FIR filter.
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97 </p>
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98
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99 <div class="fragment"><pre>
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100
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101 fs = 10; <span class="comment">% sampling frequency</span>
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102 f = linspace(0, fs/2, 1000);
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103 y = 1./(1+(0.1*2*pi*f).^2); <span class="comment">% an arbitrary function</span>
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104 fsd = fsdata(f,y,fs); <span class="comment">% build the fsdata object</span>
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105 f = mfir(ao(fsd));
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106
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107 </pre></div>
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108 <br>
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109 <p>
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110 Available methods for this option are: 'frequency-sampling' (uses fir2), 'least-squares' (uses firls)
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111 and 'Parks-McClellan' (uses firpm)
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112 </p>
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113 <h2><a name="IIRimport">Importing an existing model</a></h2>
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114 <p>
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115 The mfir constructor also accepts as an input existing models in different formats:
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116 </p>
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117 <li>
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118 <li><p>LISO files:<p>
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119 <div class="fragment"><pre>
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120 f = mfir(<span class="string">'foo_fir.fil'</span>)
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121 </pre></div>
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122 </li>
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123 <li><p>XML files:</p>
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124 <div class="fragment"><pre>
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125 f = mfir(<span class="string">'foo_fir.xml'</span>)
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126 </pre></div>
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127 <li><p>MAT files:</p>
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128 <div class="fragment"><pre>
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129 f = mfir(<span class="string">'foo_fir.mat'</span>)
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130 </pre></div>
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131 </li>
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132 <li><p>From repository:</p>
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133 <div class="fragment"><pre>
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134 f = mfir(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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135 </pre></div>
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136 </li>
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137 </ul>
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138
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139 </p>
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140
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141 <br>
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142 <br>
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143 <table class="nav" summary="Navigation aid" border="0" width=
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144 "100%" cellpadding="0" cellspacing="0">
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145 <tr valign="top">
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146 <td align="left" width="20"><a href="sigproc_iir.html"><img src=
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147 "b_prev.gif" border="0" align="bottom" alt=
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148 "IIR Filters"></a>&nbsp;</td>
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149
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150 <td align="left">IIR Filters</td>
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151
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152 <td>&nbsp;</td>
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153
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154 <td align="right">Filter banks</td>
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155
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156 <td align="right" width="20"><a href=
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Daniele Nicolodi <nicolodi@science.unitn.it>
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157 "sigproc_filterbanks.html"><img src="b_next.gif" border="0" align=
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Daniele Nicolodi <nicolodi@science.unitn.it>
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158 "bottom" alt="Filter banks"></a></td>
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159 </tr>
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Daniele Nicolodi <nicolodi@science.unitn.it>
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160 </table><br>
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161
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Daniele Nicolodi <nicolodi@science.unitn.it>
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162 <p class="copy">&copy;LTP Team</p>
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163 </body>
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164 </html>