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<span class="path"><a href="index.html">FOSSEE Signal Processing Toolbox</a> >> <a href="section_cc2bc01c47967d47fcf3507a91d572ba.html">FOSSEE Signal Processing Toolbox</a> > bilinear</span>
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<div class="refnamediv"><h1 class="refname">bilinear</h1>
<p class="refpurpose">Transform a s-plane filter specification into a z-plane specification</p></div>
<div class="refsynopsisdiv"><h3 class="title">Calling Sequence</h3>
<div class="synopsis"><pre><span class="default">[</span><span class="default">ZB</span><span class="default">, </span><span class="default">ZA</span><span class="default">] = </span><span class="functionid">bilinear</span><span class="default"> (</span><span class="default">SB</span><span class="default">, </span><span class="default">SA</span><span class="default">, </span><span class="default">T</span><span class="default">)</span>
<span class="default">[</span><span class="default">ZB</span><span class="default">, </span><span class="default">ZA</span><span class="default">] = </span><span class="functionid">bilinear</span><span class="default"> (</span><span class="default">SZ</span><span class="default">, </span><span class="default">SP</span><span class="default">, </span><span class="default">SG</span><span class="default">, </span><span class="default">T</span><span class="default">)</span>
<span class="default">[</span><span class="default">ZZ</span><span class="default">, </span><span class="default">ZP</span><span class="default">, </span><span class="default">ZG</span><span class="default">] = </span><span class="functionid">bilinear</span><span class="default"> (...)</span></pre></div></div>
<div class="refsection"><h3 class="title">Description</h3>
<p class="para">Transform a s-plane filter specification into a z-plane specification. Filters can be specified in either zero-pole-gain or transfer function form. The input form does not have to match the output form. 1/T is the sampling frequency represented in the z plane.</p>
<p class="para">Note: this differs from the bilinear function in the signal processing toolbox, which uses 1/T rather than T.</p>
<p class="para">Theory: Given a piecewise flat filter design, you can transform it from the s-plane to the z-plane while maintaining the band edges by means of the bilinear transform. This maps the left hand side of the s-plane into the interior of the unit circle. The mapping is highly non-linear, so you must design your filter with band edges in the s-plane positioned at 2/T tan(w*T/2) so that they will be positioned at w after the bilinear transform is complete.</p></div>
<div class="refsection"><h3 class="title">Examples</h3>
<div class="programlisting"><table border="0" width="100%"><tr><td width="98%"><pre class="scilabcode"><span class="scilabopenclose">[</span><span class="scilabid">ZB</span><span class="scilabdefault">,</span><span class="scilabid">ZA</span><span class="scilabopenclose">]</span><span class="scilaboperator">=</span><span class="scilabid">bilinear</span><span class="scilabopenclose">(</span><span class="scilabopenclose">[</span><span class="scilabnumber">1</span><span class="scilabopenclose">]</span><span class="scilabdefault">,</span><span class="scilabopenclose">[</span><span class="scilabnumber">2</span><span class="scilabdefault">,</span><span class="scilabnumber">3</span><span class="scilabopenclose">]</span><span class="scilabdefault">,</span><span class="scilabnumber">3</span><span class="scilabopenclose">)</span></pre></td><td valign="top"><a href="scilab://scilab.execexample/"><img src="ScilabExecute.png" border="0"/></a></td><td valign="top"><a href="scilab://scilab.editexample/"><img src="ScilabEdit.png" border="0"/></a></td><td></td></tr></table></div></div>
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