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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>Transform a s-plane filter specification into a z-plane specification</refpurpose>
</refnamediv>
<refsynopsisdiv>
<title>Calling Sequence</title>
<synopsis>
[ZB, ZA] = bilinear (SB, SA, T)
[ZB, ZA] = bilinear (SZ, SP, SG, T)
[ZZ, ZP, ZG] = bilinear (...)
</synopsis>
</refsynopsisdiv>
<refsection>
<title>Description</title>
<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.
</para>
<para>
Note: this differs from the bilinear function in the signal processing toolbox, which uses 1/T rather than T.
</para>
<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.
</para>
</refsection>
<refsection>
<title>Examples</title>
<programlisting role="example"><![CDATA[
[ZB,ZA]=bilinear([1],[2,3],3)
]]></programlisting>
</refsection>
</refentry>
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