<p>
  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
</p>
<div align="center">
  <IMG src="images/sigproc_7.png" width="283" height="56" align="middle" border="0">
</div>
<p>
  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]. 
</p>
<h2><a name="IIRbuild">Creating a IIR filter in the LTPDA</a></h2>

The LTPDA Toolbox allows the implementation of IIR filters by means of the <a href="pzmodel_filter.html"> miir class</a>. 

<h2><a name="IIRplist">Creating from a plist</a></h2>
<p>
  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.
</p>
<div class="fragment"><pre>
    
    pl = plist(<span class="string">'type'</span>, <span class="string">'highpass'</span>, ...
      <span class="string">'order'</span>, 1,         ...
      <span class="string">'gain'</span>,  2.0,       ...
      <span class="string">'fs'</span>,    10,        ...
      <span class="string">'fc'</span>,    0.2);
    f = miir(pl)
</pre></div>

<h2><a name="IIRpzmodel">Creating from a pzmodel</a></h2>
<p>
  IIR filters can also be <a href="pzmodel_filter.html"> created from a pzmodel </a>.
</p>
<h2><a name="IIRdiff">Creating from a difference equation</a></h2>
<p>
  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:
</p>

<div align="center">
  <IMG src="images/sigproc_9.png" width="299" height="28" align="middle" border="0">
</div>

<p><br></p>

<div class="fragment"><pre>
    
    a = [0.5 -0.01];
    b = [1 0.1];
    fs = 1;
    f = miir(a,b,fs)
</pre></div>

<p>
  <br>
  Notice that the convetion used in this function is the one described in the <a href="sigproc_dfilt.html"> Digital filters classification</a> section 
</p>

<h2><a name="IIRimport">Importing an existing model</a></h2>
<p>
  The miir constructor also accepts as an input existing models in different formats:
</p>
<li>
<li><p>LISO files:<p>
  <div class="fragment"><pre>
      f = miir(<span class="string">'foo_iir.fil'</span>)
  </pre></div>
</li>
<li><p>XML files:</p>
<div class="fragment"><pre>
    f = miir(<span class="string">'foo_iir.xml'</span>)
</pre></div>
<li><p>MAT files:</p>
  <div class="fragment"><pre>
      f = miir(<span class="string">'foo_iir.mat'</span>)
  </pre></div>
</li>
<li><p>From repository:</p>
  <div class="fragment"><pre>
      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>, []))
  </pre></div>
</li>
</ul>