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author Daniele Nicolodi <nicolodi@science.unitn.it>
date Wed, 23 Nov 2011 19:22:13 +0100
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1 <!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN"
2 "http://www.w3.org/TR/1999/REC-html401-19991224/loose.dtd">
3
4 <html lang="en">
5 <head>
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7 "HTML Tidy for Mac OS X (vers 1st December 2004), see www.w3.org">
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10
11 <title>Digital Filtering (LTPDA Toolbox)</title>
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14 <meta name="description" content=
15 "Presents an overview of the features, system requirements, and starting the toolbox.">
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17
18 <body>
19 <a name="top_of_page" id="top_of_page"></a>
20
21 <p style="font-size:1px;">&nbsp;</p>
22
23 <table class="nav" summary="Navigation aid" border="0" width=
24 "100%" cellpadding="0" cellspacing="0">
25 <tr>
26 <td valign="baseline"><b>LTPDA Toolbox</b></td><td><a href="../helptoc.html">contents</a></td>
27
28 <td valign="baseline" align="right"><a href=
29 "sigproc.html"><img src="b_prev.gif" border="0" align=
30 "bottom" alt="Signal Processing in LTPDA"></a>&nbsp;&nbsp;&nbsp;<a href=
31 "sigproc_iir.html"><img src="b_next.gif" border="0" align=
32 "bottom" alt="IIR Filters"></a></td>
33 </tr>
34 </table>
35
36 <h1 class="title"><a name="f3-12899" id="f3-12899"></a>Digital Filtering</h1>
37 <hr>
38
39 <p>
40 <p>
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
42 </p>
43 <div align="center">
44 <IMG src="images/sigproc_1.png" width="173" height="55" align="center" border="0">
45 </div>
46 <p>
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:
48 </p>
49
50 <ul>
51 <li> Causal: if there is no output before input is fed in.
52 <div align="center">
53 <IMG src="images/sigproc_2.png" width="103" height="28" align="center" border="0">
54 </div>
55 </li>
56 <li> Stable: if finite input results in finite output.
57 <div align="center">
58 <IMG src="images/sigproc_3.png" width="105" height="55" align="center" border="0">
59 </div>
60 </li>
61 <li> Shift invariant: if time shift in the input results in a time shift in the output by the same amount.
62 <div align="center">
63 <IMG src="images/sigproc_4.png" width="84" height="28" align="center" border="0">
64 </div>
65 </li>
66 </ul>
67 <br>
68 <h2><a name="ARMA">Digital filters classification</a></h2>
69 <p>
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:
71 </p>
72 <ul>
73 <li> Autoregressive (AR) process: the difference equation in this case is given by:
74 <div align="center">
75 <br>
76 <IMG src="images/sigproc_12.png" width="154" height="56" align="center" border="0">
77 </div>
78 <br>
79 AR processes can be also classified as <a href="sigproc_iir.html"> IIR Filters</a>.
80 <br>
81 <br></li>
82 <li> Moving Averrage (MA) process:the difference equation in this case is given by: <br>
83 <div align="center">
84 <br>
85 <IMG src="images/sigproc_11.png" width="156" height="56" align="center" border="0">
86 </div>
87 <br>
88 MA processes can be also classified as <a href="sigproc_fir.html"> FIR Filters</a>.
89 <br>
90 <br></li>
91 <li>Autoregressive Moving Average (ARMA) process: the difference equation in this case contains both an AR and a MA process:
92 <div align="center">
93 <br>
94 <IMG src="images/sigproc_7.png" width="283" height="56" align="center" border="0">
95 </div>
96 </li>
97
98
99
100 </p>
101
102 <br>
103 <br>
104 <table class="nav" summary="Navigation aid" border="0" width=
105 "100%" cellpadding="0" cellspacing="0">
106 <tr valign="top">
107 <td align="left" width="20"><a href="sigproc.html"><img src=
108 "b_prev.gif" border="0" align="bottom" alt=
109 "Signal Processing in LTPDA"></a>&nbsp;</td>
110
111 <td align="left">Signal Processing in LTPDA</td>
112
113 <td>&nbsp;</td>
114
115 <td align="right">IIR Filters</td>
116
117 <td align="right" width="20"><a href=
118 "sigproc_iir.html"><img src="b_next.gif" border="0" align=
119 "bottom" alt="IIR Filters"></a></td>
120 </tr>
121 </table><br>
122
123 <p class="copy">&copy;LTP Team</p>
124 </body>
125 </html>