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 * This help file was generated from bilinear.sci using help_from_sci().
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  <refnamediv>
    <refname>bilinear</refname>
    <refpurpose>Transform an s-plane filter (analog) into a z-plane filter (digital) using the bilinear transformation.</refpurpose>
  </refnamediv>


<refsynopsisdiv>
   <title>Syntax</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 the s-domain.</para></listitem>
        </varlistentry>
        <varlistentry>
            <term>Sa:</term>
            <listitem><para> Denominator coefficient vector in the s-domain.</para></listitem>
        </varlistentry>
        <varlistentry>
            <term>Sz:</term>
            <listitem><para> Zeros in the s-plane.</para></listitem>
        </varlistentry>
        <varlistentry>
            <term>Sp:</term>
            <listitem><para> Poles in the s-plane.</para></listitem>
        </varlistentry>
        <varlistentry>
            <term>Sg:</term>
            <listitem><para> Gain in the 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 the z-domain.</para></listitem>
        </varlistentry>
        <varlistentry>
            <term>Za:</term>
            <listitem><para> Denominator coefficient vector in the z-domain.</para></listitem>
        </varlistentry>
        <varlistentry>
            <term>Zz:</term>
            <listitem><para> Zeros in the z-plane.</para></listitem>
        </varlistentry>
        <varlistentry>
            <term>Zp:</term>
            <listitem><para> Poles in the z-plane.</para></listitem>
        </varlistentry>
        <varlistentry>
            <term>Zg:</term>
            <listitem><para> Gain in the z-domain.</para></listitem>
        </varlistentry>
   </variablelist>
</refsection>

<refsection>
   <title>Description</title>
   <para>
This function transforms a filter design from the s-plane to the z-plane while maintaining the band edges using the bilinear transform. The mapping is non-linear, so the filter must be designed with band edges in the s-plane positioned at 2/T tan(w*T/2) to ensure correct positioning in the z-plane.
It does following transformation from s-plane to z-plane
2  z-1
s -&gt; -  --------
T  z+1
   </para>
   <para>
</para>
</refsection>

<refsection>
   <title>Examples</title>
   <programlisting role="example"><![CDATA[
[b, a] = bilinear([1, 2, 3], [4, 5, 6], 1, 1)

   ]]></programlisting>
</refsection>

<refsection role="see also">
   <title>See also</title>
   <simplelist type="inline">
   <member><link linkend="tf2zp">tf2zp</link></member>
   <member><link linkend="postpad">postpad</link></member>
   <member><link linkend="zp2tf">zp2tf</link></member>
   <member><link linkend="prepad">prepad</link></member>
   </simplelist>
</refsection>
</refentry>
