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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"
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10
11 <title>FIR Filters (LTPDA Toolbox)</title>
12 <link rel="stylesheet" href="docstyle.css" type="text/css">
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14 <meta name="description" content=
15 "Presents an overview of the features, system requirements, and starting the toolbox.">
16 </head>
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_iir.html"><img src="b_prev.gif" border="0" align=
30 "bottom" alt="IIR Filters"></a>&nbsp;&nbsp;&nbsp;<a href=
31 "sigproc_filterbanks.html"><img src="b_next.gif" border="0" align=
32 "bottom" alt="Filter banks"></a></td>
33 </tr>
34 </table>
35
36 <h1 class="title"><a name="f3-12899" id="f3-12899"></a>FIR Filters</h1>
37 <hr>
38
39 <p>
40 <p>
41 Finite Impulse Response filters are those filters present a non-zero finite length response
42 when excited with a very brief (ideally an infinite peak) input signal. A linear causal
43 FIR filter can be described by the following difference equation
44 </p>
45 <div align="center">
46 <IMG src="images/sigproc_8.png" width="157" height="56" align="middle" border="0">
47 </div>
48 <p>
49 This operation describe a nonrecursive system, i.e. a system that only depends on current
50 and past samples of the input data stream <tt>x[n]</tt>
51 </p>
52 <h2><a name="FIRbuild">Creating a FIR filter in the LTPDA</a></h2>
53 <p>
54 The LTPDA Toolbox allows the implementation of FIR filters by means of the
55 <a href="class_desc_mfir.html"> mfir class</a>.
56 </p>
57 <h2><a name="FIRplist">Creating from a plist</a></h2>
58 <p>
59 The following example creates an order 64 highpass filter with high frequency gain 2.
60 The filter is designed for 1 Hz sampled data and has a cut-off frequency of 0.2 Hz.
61 </p>
62 <div class="fragment"><pre>
63
64 pl = plist(<span class="string">'type'</span>, <span class="string">'highpass'</span>, ...
65 <span class="string">'order'</span>, 64, ...
66 <span class="string">'gain'</span>, 2.0, ...
67 <span class="string">'fs'</span>, 1, ...
68 <span class="string">'fc'</span>, 0.2);
69 f = mfir(pl)
70 </pre></div>
71
72 <h2><a name="FIRdiff">Creating from a difference equation</a></h2>
73 <p>
74 The filter can be defined in terms of two vectors specifying the coefficients of the filter
75 and the sampling frequency. The following example creates a FIR filter with sampling frequency
76 1 Hz and the following recursive equation:
77 </p>
78
79 <div align="center">
80 <IMG src="images/sigproc_10.png" width="202" height="28" align="middle" border="0"></div>
81 </div>
82
83 <p><br></p>
84
85 <div class="fragment"><pre>
86
87 b = [-0.8 10];
88 fs = 1;
89 f = mfir(b,fs)
90 </pre></div>
91
92 <h2><a name="FIRfromAO">Creating from an Analysis Object</a></h2>
93 <p>
94 A FIR filter can be generated based on the magnitude of the input Analysis Object or fsdata object.
95 In the following example a fsdata object is first generated and then passed to the mfir constructor
96 to obtain the equivalent FIR filter.
97 </p>
98
99 <div class="fragment"><pre>
100
101 fs = 10; <span class="comment">% sampling frequency</span>
102 f = linspace(0, fs/2, 1000);
103 y = 1./(1+(0.1*2*pi*f).^2); <span class="comment">% an arbitrary function</span>
104 fsd = fsdata(f,y,fs); <span class="comment">% build the fsdata object</span>
105 f = mfir(ao(fsd));
106
107 </pre></div>
108 <br>
109 <p>
110 Available methods for this option are: 'frequency-sampling' (uses fir2), 'least-squares' (uses firls)
111 and 'Parks-McClellan' (uses firpm)
112 </p>
113 <h2><a name="IIRimport">Importing an existing model</a></h2>
114 <p>
115 The mfir constructor also accepts as an input existing models in different formats:
116 </p>
117 <li>
118 <li><p>LISO files:<p>
119 <div class="fragment"><pre>
120 f = mfir(<span class="string">'foo_fir.fil'</span>)
121 </pre></div>
122 </li>
123 <li><p>XML files:</p>
124 <div class="fragment"><pre>
125 f = mfir(<span class="string">'foo_fir.xml'</span>)
126 </pre></div>
127 <li><p>MAT files:</p>
128 <div class="fragment"><pre>
129 f = mfir(<span class="string">'foo_fir.mat'</span>)
130 </pre></div>
131 </li>
132 <li><p>From repository:</p>
133 <div class="fragment"><pre>
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>, []))
135 </pre></div>
136 </li>
137 </ul>
138
139 </p>
140
141 <br>
142 <br>
143 <table class="nav" summary="Navigation aid" border="0" width=
144 "100%" cellpadding="0" cellspacing="0">
145 <tr valign="top">
146 <td align="left" width="20"><a href="sigproc_iir.html"><img src=
147 "b_prev.gif" border="0" align="bottom" alt=
148 "IIR Filters"></a>&nbsp;</td>
149
150 <td align="left">IIR Filters</td>
151
152 <td>&nbsp;</td>
153
154 <td align="right">Filter banks</td>
155
156 <td align="right" width="20"><a href=
157 "sigproc_filterbanks.html"><img src="b_next.gif" border="0" align=
158 "bottom" alt="Filter banks"></a></td>
159 </tr>
160 </table><br>
161
162 <p class="copy">&copy;LTP Team</p>
163 </body>
164 </html>