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Update ao_model_retrieve_in_timespan
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>Digital Filtering (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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18 <body>
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19 <a name="top_of_page" id="top_of_page"></a>
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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.html"><img src="b_prev.gif" border="0" align=
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30 "bottom" alt="Signal Processing in LTPDA"></a>&nbsp;&nbsp;&nbsp;<a href=
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31 "sigproc_iir.html"><img src="b_next.gif" border="0" align=
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32 "bottom" alt="IIR 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>Digital Filtering</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 A digital filter is an operation that associates an input time series x[n] into an output one, y[n]. Methods developed in the LTPDA Toolbox deal with linear digital filters, i.e. those which fulfill that a linear combination of inputs results in a linear combination of outputs with the same coefficients (provided that these are not time dependent). In these conditions, the filter can be expressed as
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42 </p>
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43 <div align="center">
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44 <IMG src="images/sigproc_1.png" width="173" height="55" align="center" border="0">
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45 </div>
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46 <p>
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47 described in these terms, the filter is completely described by the impulse response h[k], and can then be subdivided into the following classes:
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48 </p>
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49
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50 <ul>
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51 <li> Causal: if there is no output before input is fed in.
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52 <div align="center">
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53 <IMG src="images/sigproc_2.png" width="103" height="28" align="center" border="0">
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54 </div>
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55 </li>
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56 <li> Stable: if finite input results in finite output.
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57 <div align="center">
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58 <IMG src="images/sigproc_3.png" width="105" height="55" align="center" border="0">
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59 </div>
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60 </li>
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61 <li> Shift invariant: if time shift in the input results in a time shift in the output by the same amount.
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62 <div align="center">
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63 <IMG src="images/sigproc_4.png" width="84" height="28" align="center" border="0">
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64 </div>
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65 </li>
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66 </ul>
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67 <br>
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68 <h2><a name="ARMA">Digital filters classification</a></h2>
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69 <p>
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70 Digital filters can be described as difference equations. If we consider an input time series x and an output y, three specific cases can then be distinguished:
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71 </p>
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72 <ul>
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73 <li> Autoregressive (AR) process: the difference equation in this case is given by:
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74 <div align="center">
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75 <br>
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76 <IMG src="images/sigproc_12.png" width="154" height="56" align="center" border="0">
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77 </div>
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78 <br>
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79 AR processes can be also classified as <a href="sigproc_iir.html"> IIR Filters</a>.
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80 <br>
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81 <br></li>
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82 <li> Moving Averrage (MA) process:the difference equation in this case is given by: <br>
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83 <div align="center">
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84 <br>
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85 <IMG src="images/sigproc_11.png" width="156" height="56" align="center" border="0">
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86 </div>
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87 <br>
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88 MA processes can be also classified as <a href="sigproc_fir.html"> FIR Filters</a>.
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89 <br>
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90 <br></li>
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91 <li>Autoregressive Moving Average (ARMA) process: the difference equation in this case contains both an AR and a MA process:
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92 <div align="center">
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93 <br>
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94 <IMG src="images/sigproc_7.png" width="283" height="56" align="center" border="0">
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95 </div>
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96 </li>
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97
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99
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100 </p>
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101
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102 <br>
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103 <br>
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104 <table class="nav" summary="Navigation aid" border="0" width=
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105 "100%" cellpadding="0" cellspacing="0">
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106 <tr valign="top">
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107 <td align="left" width="20"><a href="sigproc.html"><img src=
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108 "b_prev.gif" border="0" align="bottom" alt=
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109 "Signal Processing in LTPDA"></a>&nbsp;</td>
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110
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111 <td align="left">Signal Processing in LTPDA</td>
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112
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113 <td>&nbsp;</td>
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114
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115 <td align="right">IIR Filters</td>
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116
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117 <td align="right" width="20"><a href=
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118 "sigproc_iir.html"><img src="b_next.gif" border="0" align=
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119 "bottom" alt="IIR Filters"></a></td>
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120 </tr>
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121 </table><br>
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122
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123 <p class="copy">&copy;LTP Team</p>
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124 </body>
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125 </html>