0
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff
changeset
+ − 1 <p>
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff
changeset
+ − 2 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
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff
changeset
+ − 3 </p>
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff
changeset
+ − 4 <div align="center">
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff
changeset
+ − 5 <IMG src="images/sigproc_7.png" width="283" height="56" align="middle" border="0">
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff
changeset
+ − 6 </div>
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff
changeset
+ − 7 <p>
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff
changeset
+ − 8 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].
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff
changeset
+ − 9 </p>
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff
changeset
+ − 10 <h2><a name="IIRbuild">Creating a IIR filter in the LTPDA</a></h2>
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff
changeset
+ − 11
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff
changeset
+ − 12 The LTPDA Toolbox allows the implementation of IIR filters by means of the <a href="pzmodel_filter.html"> miir class</a>.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff
changeset
+ − 13
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff
changeset
+ − 14 <h2><a name="IIRplist">Creating from a plist</a></h2>
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff
changeset
+ − 15 <p>
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff
changeset
+ − 16 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.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff
changeset
+ − 17 </p>
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff
changeset
+ − 18 <div class="fragment"><pre>
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff
changeset
+ − 19
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff
changeset
+ − 20 pl = plist(<span class="string">'type'</span>, <span class="string">'highpass'</span>, ...
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff
changeset
+ − 21 <span class="string">'order'</span>, 1, ...
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff
changeset
+ − 22 <span class="string">'gain'</span>, 2.0, ...
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff
changeset
+ − 23 <span class="string">'fs'</span>, 10, ...
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff
changeset
+ − 24 <span class="string">'fc'</span>, 0.2);
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff
changeset
+ − 25 f = miir(pl)
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff
changeset
+ − 26 </pre></div>
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff
changeset
+ − 27
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff
changeset
+ − 28 <h2><a name="IIRpzmodel">Creating from a pzmodel</a></h2>
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff
changeset
+ − 29 <p>
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff
changeset
+ − 30 IIR filters can also be <a href="pzmodel_filter.html"> created from a pzmodel </a>.
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff
changeset
+ − 31 </p>
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff
changeset
+ − 32 <h2><a name="IIRdiff">Creating from a difference equation</a></h2>
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff
changeset
+ − 33 <p>
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff
changeset
+ − 34 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:
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff
changeset
+ − 35 </p>
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff
changeset
+ − 36
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff
changeset
+ − 37 <div align="center">
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff
changeset
+ − 38 <IMG src="images/sigproc_9.png" width="299" height="28" align="middle" border="0">
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff
changeset
+ − 39 </div>
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff
changeset
+ − 40
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff
changeset
+ − 41 <p><br></p>
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff
changeset
+ − 42
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff
changeset
+ − 43 <div class="fragment"><pre>
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff
changeset
+ − 44
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff
changeset
+ − 45 a = [0.5 -0.01];
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff
changeset
+ − 46 b = [1 0.1];
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff
changeset
+ − 47 fs = 1;
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff
changeset
+ − 48 f = miir(a,b,fs)
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff
changeset
+ − 49 </pre></div>
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff
changeset
+ − 50
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff
changeset
+ − 51 <p>
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff
changeset
+ − 52 <br>
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff
changeset
+ − 53 Notice that the convetion used in this function is the one described in the <a href="sigproc_dfilt.html"> Digital filters classification</a> section
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff
changeset
+ − 54 </p>
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff
changeset
+ − 55
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff
changeset
+ − 56 <h2><a name="IIRimport">Importing an existing model</a></h2>
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff
changeset
+ − 57 <p>
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff
changeset
+ − 58 The miir constructor also accepts as an input existing models in different formats:
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff
changeset
+ − 59 </p>
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff
changeset
+ − 60 <li>
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff
changeset
+ − 61 <li><p>LISO files:<p>
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff
changeset
+ − 62 <div class="fragment"><pre>
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff
changeset
+ − 63 f = miir(<span class="string">'foo_iir.fil'</span>)
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff
changeset
+ − 64 </pre></div>
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff
changeset
+ − 65 </li>
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff
changeset
+ − 66 <li><p>XML files:</p>
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff
changeset
+ − 67 <div class="fragment"><pre>
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff
changeset
+ − 68 f = miir(<span class="string">'foo_iir.xml'</span>)
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff
changeset
+ − 69 </pre></div>
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff
changeset
+ − 70 <li><p>MAT files:</p>
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff
changeset
+ − 71 <div class="fragment"><pre>
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff
changeset
+ − 72 f = miir(<span class="string">'foo_iir.mat'</span>)
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff
changeset
+ − 73 </pre></div>
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff
changeset
+ − 74 </li>
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff
changeset
+ − 75 <li><p>From repository:</p>
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff
changeset
+ − 76 <div class="fragment"><pre>
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff
changeset
+ − 77 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>, []))
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff
changeset
+ − 78 </pre></div>
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff
changeset
+ − 79 </li>
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff
changeset
+ − 80 </ul>
Daniele Nicolodi <nicolodi@science.unitn.it>
parents:
diff
changeset
+ − 81