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| author | Daniele Nicolodi <nicolodi@science.unitn.it> |
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| date | Wed, 23 Nov 2011 19:22:13 +0100 |
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<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN" "http://www.w3.org/TR/1999/REC-html401-19991224/loose.dtd"> <html lang="en"> <head> <meta name="generator" content= "HTML Tidy for Mac OS X (vers 1st December 2004), see www.w3.org"> <meta http-equiv="Content-Type" content= "text/html; charset=us-ascii"> <title>Building a model (LTPDA Toolbox)</title> <link rel="stylesheet" href="docstyle.css" type="text/css"> <meta name="generator" content="DocBook XSL Stylesheets V1.52.2"> <meta name="description" content= "Presents an overview of the features, system requirements, and starting the toolbox."> </head> <body> <a name="top_of_page" id="top_of_page"></a> <p style="font-size:1px;"> </p> <table class="nav" summary="Navigation aid" border="0" width= "100%" cellpadding="0" cellspacing="0"> <tr> <td valign="baseline"><b>LTPDA Toolbox</b></td><td><a href="../helptoc.html">contents</a></td> <td valign="baseline" align="right"><a href= "pzmodel.html"><img src="b_prev.gif" border="0" align= "bottom" alt="Pole/Zero representation"></a> <a href= "pzmodel_gui.html"><img src="b_next.gif" border="0" align= "bottom" alt="Model helper GUI"></a></td> </tr> </table> <h1 class="title"><a name="f3-12899" id="f3-12899"></a>Building a model</h1> <hr> <p> <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> </p> <br> <br> <table class="nav" summary="Navigation aid" border="0" width= "100%" cellpadding="0" cellspacing="0"> <tr valign="top"> <td align="left" width="20"><a href="pzmodel.html"><img src= "b_prev.gif" border="0" align="bottom" alt= "Pole/Zero representation"></a> </td> <td align="left">Pole/Zero representation</td> <td> </td> <td align="right">Model helper GUI</td> <td align="right" width="20"><a href= "pzmodel_gui.html"><img src="b_next.gif" border="0" align= "bottom" alt="Model helper GUI"></a></td> </tr> </table><br> <p class="copy">©LTP Team</p> </body> </html>