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<?xml version="1.0" encoding="UTF-8"?>
<!--
*
* This help file was generated from sftrans.sci using help_from_sci().
*
-->
<refentry version="5.0-subset Scilab" xml:id="sftrans" 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>sftrans</refname>
<refpurpose>Transform band edges of a generic lowpass filter (cutoff at W=1) represented in splane zero-pole-gain form.</refpurpose>
</refnamediv>
<refsynopsisdiv>
<title>Calling Sequence</title>
<synopsis>
[Sz, Sp, Sg] = sftrans (Sz, Sp, Sg, W, stop)
[Sz, Sp] = sftrans (Sz, Sp, Sg, W, stop)
[Sz] = sftrans (Sz, Sp, Sg, W, stop)
</synopsis>
</refsynopsisdiv>
<refsection>
<title>Parameters</title>
<variablelist>
<varlistentry><term>Sz:</term>
<listitem><para> Zeros.</para></listitem></varlistentry>
<varlistentry><term>Sp:</term>
<listitem><para> Poles.</para></listitem></varlistentry>
<varlistentry><term>Sg:</term>
<listitem><para> Gain.</para></listitem></varlistentry>
<varlistentry><term>W:</term>
<listitem><para> Edge of target filter.</para></listitem></varlistentry>
<varlistentry><term>stop:</term>
<listitem><para> True for high pass and band stop filters or false for low pass and band pass filters.</para></listitem></varlistentry>
</variablelist>
</refsection>
<refsection>
<title>Description</title>
<para>
This is an Octave function.
Theory: Given a low pass filter represented by poles and zeros in the splane, you can convert it to a low pass, high pass, band pass or band stop by transforming each of the poles and zeros
individually. The following table summarizes the transformation:
</para>
<para>
Transform Zero at x Pole at x
---------------- ------------------------- ------------------------
Low Pass zero: Fc x/C pole: Fc x/C
S -> C S/Fc gain: C/Fc gain: Fc/C
---------------- ------------------------- ------------------------
High Pass zero: Fc C/x pole: Fc C/x
S -> C Fc/S pole: 0 zero: 0
gain: -x gain: -1/x
---------------- ------------------------- ------------------------
Band Pass zero: b +- sqrt(b^2-FhFl) pole: b +- sqrt(b^2-FhFl)
S^2+FhFl pole: 0 zero: 0
S -> C -------- gain: C/(Fh-Fl) gain: (Fh-Fl)/C
S(Fh-Fl) b=x/C (Fh-Fl)/2 b=x/C (Fh-Fl)/2
---------------- ------------------------- ------------------------
Band Stop zero: b +- sqrt(b^2-FhFl) pole: b +- sqrt(b^2-FhFl)
S(Fh-Fl) pole: +-sqrt(-FhFl) zero: +-sqrt(-FhFl)
S -> C -------- gain: -x gain: -1/x
S^2+FhFl b=C/x (Fh-Fl)/2 b=C/x (Fh-Fl)/2
---------------- ------------------------- ------------------------
Bilinear zero: (2+xT)/(2-xT) pole: (2+xT)/(2-xT)
2 z-1 pole: -1 zero: -1
S -> - --- gain: (2-xT)/T gain: (2-xT)/T
T z+1
---------------- ------------------------- ------------------------
</para>
<para>
where C is the cutoff frequency of the initial lowpass filter, Fc is the edge of the target low/high pass filter and [Fl,Fh] are the edges of the target band pass/stop filter. With abundant tedious
algebra, you can derive the above formulae yourself by substituting the transform for S into H(S)=S-x for a zero at x or H(S)=1/(S-x) for a pole at x, and converting the result into the form:
</para>
<para>
H(S)=g prod(S-Xi)/prod(S-Xj)
</para>
</refsection>
<refsection>
<title>Examples</title>
<programlisting role="example"><![CDATA[
[Sz, Sp, Sg] = sftrans (5, 10, 15, 20, 30)
Sz = 4
Sp = 2
Sg = 7.5000
]]></programlisting>
</refsection>
</refentry>
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