Mercurial > hg > ltpda
diff m-toolbox/html_help/help/ug/pzmodel_model.html @ 0:f0afece42f48
Import.
| author | Daniele Nicolodi <nicolodi@science.unitn.it> |
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| date | Wed, 23 Nov 2011 19:22:13 +0100 |
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--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/m-toolbox/html_help/help/ug/pzmodel_model.html Wed Nov 23 19:22:13 2011 +0100 @@ -0,0 +1,190 @@ +<!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>