<p>
  Finite Impulse Response filters are those filters present a non-zero finite length response 
  when excited with a very brief (ideally an infinite peak) input signal. A linear causal 
  FIR filter can be described by the following difference equation
</p>
<div align="center">
  <IMG src="images/sigproc_8.png" width="157" height="56" align="middle" border="0">
</div>
<p>
  This operation describe a nonrecursive system, i.e. a system that only depends on current 
  and past samples of the input data stream <tt>x[n]</tt>
</p>
<h2><a name="FIRbuild">Creating a FIR filter in the LTPDA</a></h2>
<p>
  The LTPDA Toolbox allows the implementation of FIR filters by means of the 
  <a href="class_desc_mfir.html"> mfir class</a>.
</p>
<h2><a name="FIRplist">Creating from a plist</a></h2>
<p>
  The following example creates an order 64 highpass filter with high frequency gain 2. 
  The filter is designed for 1 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>, 64,         ...
    <span class="string">'gain'</span>,  2.0,       ...
    <span class="string">'fs'</span>,    1,        ...
    <span class="string">'fc'</span>,    0.2);
    f = mfir(pl)
</pre></div>

<h2><a name="FIRdiff">Creating from a difference equation</a></h2>
<p>
  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 FIR filter with sampling frequency 
  1 Hz and the following recursive equation:
</p>

<div align="center">
<IMG src="images/sigproc_10.png" width="202" height="28" align="middle" border="0"></div>
</div>

<p><br></p>

<div class="fragment"><pre>
    
    b  = [-0.8 10];
    fs = 1;
    f  = mfir(b,fs)
</pre></div>

<h2><a name="FIRfromAO">Creating from an Analysis Object</a></h2>
<p>
  A FIR filter can be generated based on the magnitude of the input Analysis Object or fsdata object. 
  In the following example a fsdata object is first generated and then passed to the mfir constructor 
  to obtain the equivalent FIR filter.
</p>

<div class="fragment"><pre>
    
    fs  = 10;                      <span class="comment">% sampling frequency</span>
    f   = linspace(0, fs/2, 1000);
    y   = 1./(1+(0.1*2*pi*f).^2);  <span class="comment">% an arbitrary function</span>
    fsd = fsdata(f,y,fs);          <span class="comment">% build the fsdata object</span>
    f = mfir(ao(fsd));
    
</pre></div>
<br>
<p>
  Available methods for this option are: 'frequency-sampling' (uses fir2), 'least-squares' (uses firls) 
  and 'Parks-McClellan' (uses firpm)
</p>
<h2><a name="IIRimport">Importing an existing model</a></h2>
<p>
  The mfir constructor also accepts as an input existing models in different formats:
</p>
<li>
<li><p>LISO files:<p>
  <div class="fragment"><pre>
      f = mfir(<span class="string">'foo_fir.fil'</span>)
  </pre></div>
</li>
<li><p>XML files:</p>
<div class="fragment"><pre>
      f = mfir(<span class="string">'foo_fir.xml'</span>)
</pre></div>
<li><p>MAT files:</p>
  <div class="fragment"><pre>
      f = mfir(<span class="string">'foo_fir.mat'</span>)
  </pre></div>
</li>
<li><p>From repository:</p>
  <div class="fragment"><pre>
      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>, []))
  </pre></div>
</li>
</ul>