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<?xml version="1.0" encoding="UTF-8"?>
<!--
*
* This help file was generated from bilinear.sci using help_from_sci().
*
-->
<refentry version="5.0-subset Scilab" xml:id="bilinear" xml:lang="en"
xmlns="http://docbook.org/ns/docbook"
xmlns:xlink="http://www.w3.org/1999/xlink"
xmlns:svg="http://www.w3.org/2000/svg"
xmlns:ns3="http://www.w3.org/1999/xhtml"
xmlns:mml="http://www.w3.org/1998/Math/MathML"
xmlns:scilab="http://www.scilab.org"
xmlns:db="http://docbook.org/ns/docbook">
<refnamediv>
<refname>bilinear</refname>
<refpurpose>Transforms a s-plane filter (Analog) into a z-plane filter (Digital) using Bilinear transformation</refpurpose>
</refnamediv>
<refsynopsisdiv>
<title>Calling Sequence</title>
<synopsis>
[Zb, Za] = bilinear(Sb, Sa, T)
[Zb, Zb] = bilinear(Sz, Sp, Sg, T)
[Zz, Zp, Zg] = bilinear(...)
</synopsis>
</refsynopsisdiv>
<refsection>
<title>Parameters</title>
<variablelist>
<varlistentry><term>Sb:</term>
<listitem><para> Numerator coefficient vector in s-domain. </para></listitem></varlistentry>
<varlistentry><term>Sa:</term>
<listitem><para> Denumerator coefficient vector s-domain.</para></listitem></varlistentry>
<varlistentry><term>Sz:</term>
<listitem><para> zeros in s-plane.</para></listitem></varlistentry>
<varlistentry><term>Sp:</term>
<listitem><para> poles in s-plane.</para></listitem></varlistentry>
<varlistentry><term>Sg:</term>
<listitem><para> gain in s-domain.</para></listitem></varlistentry>
<varlistentry><term>T:</term>
<listitem><para> Sampling period (double).</para></listitem></varlistentry>
<varlistentry><term>Zb:</term>
<listitem><para> Numerator coefficient vector in z-domain.</para></listitem></varlistentry>
<varlistentry><term>Za:</term>
<listitem><para> Denumerator coefficient vector z-domain.</para></listitem></varlistentry>
<varlistentry><term>Zz:</term>
<listitem><para> zeros in z-plane.</para></listitem></varlistentry>
<varlistentry><term>Zp:</term>
<listitem><para> poles in z-plane.</para></listitem></varlistentry>
<varlistentry><term>Zg:</term>
<listitem><para> gain in z-domain.</para></listitem></varlistentry>
</variablelist>
</refsection>
<refsection>
<title>Description</title>
<para>
a filter design can be transformed 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 in z-plane. 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.
</para>
<para>
It does following transformation from s-plane to z-plane
</para>
<para>
<latex>
\begin{eqnarray}
s --> \frac{2} {T} \frac {z - 1} {z + 1}
\end{eqnarray}
</latex>
</para>
</refsection>
<refsection>
<title>Examples</title>
<programlisting role="example"><![CDATA[
Sz = [1 2 3]
Sp = [4 5 6]
Sg = 1;
T = 1;
[Zb,Za] = bilinear (Sz, Sp, Sg, T)
]]></programlisting>
</refsection>
<refsection>
<title>Modified by :</title>
<simplelist type="vert">
<member>Sonu Sharma, RGIT Mumbai (fellow at FOSSEE, IIT Bombay)</member>
</simplelist>
</refsection>
</refentry>
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