<p>
  	Poles and zeros can be combined together to create a pole/zero model. In addition to a list of poles
    and zeros, a gain factor and a delay can be specified such that the resulting model is of the form:
  </p>
  <br>
  <div align="center">
  <img src="images/pzmodel_tf_eqn.png" alt="Pole/zero model TF"  border="3">
  </div>
  <br>
  <p>
	The following sections introduce how to produce and use pole/zero models in the LTPDA environment.
	<ul>
		<li><a href="#direct">Direct form</a></li>
		<li><a href="#plist">Creating from a <tt>plist</tt></a></li>
		<li><a href="#resp">Computing the response of the model</a></li>
	</ul>
  </p>


  <h2><a name="direct">Direct form</a></h2>

  The following code fragment creates a pole/zero model consisting of 2 poles and 2 zeros with a gain
  factor of 10 and a 10ms delay:
  <div class="fragment"><pre>
	>> pzm   = pzmodel(10, {[1 2], 3}, {5, 10}, 0.01)
---- pzmodel 1 ----
    name: None
    gain: 10
   delay: 0.01
  iunits: []
  ounits: []
pole 001: (f=1 Hz,Q=2)
pole 002: (f=3 Hz,Q=NaN)
zero 001: (f=5 Hz,Q=NaN)
zero 002: (f=10 Hz,Q=NaN)
-------------------
  </pre></div>
  <p>
    Notice, you can also pass arrays of <tt>pz</tt> objects to the <tt>pzmodel</tt> constructor, but this 
    should rarely be necessary.
  </p>

  <h2><a name="plist">Creating from a <tt>plist</tt></a></h2>

  <p>
	You can also create a <tt>pzmodel</tt> by passing a parameter list. The following example shows
	this
  </p>

  <div class="fragment"><pre>
	>> pl  = plist(<span class="string">'name'</span>, <span class="string">'test model'</span>, ...
	               <span class="string">'gain'</span>, 10, ...
                   <span class="string">'poles'</span>, {[1 2], 3}, ...
                   <span class="string">'zeros'</span>, {5, 10}, ...
                   <span class="string">'delay'</span>, 0.01, ...
                   <span class="string">'iunits'</span>, 'm', ...
                   <span class="string">'ounits'</span>, 'V^2');
	>> pzm = pzmodel(pl)
	---- pzmodel 1 ----
    name: test model
    gain: 10
   delay: 0.01
  iunits: [m]
  ounits: [V^2]
pole 001: (f=1 Hz,Q=2)
pole 002: (f=3 Hz,Q=NaN)
zero 001: (f=5 Hz,Q=NaN)
zero 002: (f=10 Hz,Q=NaN)
-------------------
  </pre></div>
  <p>
    Here we also specified the input units of the transfer function ('iunits') and the
    output units, ('ounits'). In  this case, the model represents a transfer function 
    from metres to Volts squared.
  </p>

  <h2><a name="resp">Computing the response of the model</a></h2>

  <p>
	The frequency response of the model can generated using the <tt>resp</tt> method of the
	<tt>pzmodel</tt> class. To compute the response of the model created above:
  </p>
  <div class="fragment"><pre>
	>> resp(pzm)
  </pre></div>
  <p>
  Since no output was specified, this command produces the following plot:
  <img src="images/pzmodel_resp.png" alt="Pole/zero model resp" border="3" width="600">
  </p>
  <p>
	You can also specify the frequency band over which to compute the response by passing a <tt>plist</tt>
	to the <tt>resp</tt> method, as follows:
  </p>
  <div class="fragment"><pre>
	>> rpl = plist(<span class="string">'f1'</span>, 0.1, ...
                   <span class="string">'f2'</span>, 1000, ...
                   <span class="string">'nf'</span>, 10000);
	>> a   = resp(pzm, rpl)
	----------- ao 01: resp(test model) -----------
 
       name:  resp(test model)
description:  
       data: (0.1,10.0668830776529-i*0.605439551995965) (0.100092155051679,10.067006787497-i*0.606014805088671) (0.100184395028894,10.0671307268392-i*0.606590636924472) (0.100276720009908,10.0672548961078-i*0.607167048174596) (0.100369130073055,10.0673792957318-i*0.607744039511284) ...
             ----------- fsdata 01 -----------
              
                 fs:  NaN
                  x:  [1 10000], double
                  y:  [1 10000], double
             xunits:  [Hz]
             yunits:  [V^(2)][m^(-1)]
                 t0:  1970-01-01 00:00:00.000
               navs:  NaN
             ---------------------------------
              
       hist:  pzmodel / resp / $Id: pzmodel_model_content.html,v 1.5 2009/02/24 09:44:39 miquel Exp $
  mfilename:  
mdlfilename:  
-----------------------------------------------
  </pre></div>
  <p>
  	In this case, the response is returned as an Analysis Object containing <tt>fsdata</tt>. You can now
	plot the AO using the <tt>iplot</tt> function.
  </p>