line source
+ −
+ − <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>