diff options
Diffstat (limited to 'help/en_US/sftrans.xml')
| -rw-r--r-- | help/en_US/sftrans.xml | 100 |
1 files changed, 100 insertions, 0 deletions
diff --git a/help/en_US/sftrans.xml b/help/en_US/sftrans.xml new file mode 100644 index 0000000..56aee48 --- /dev/null +++ b/help/en_US/sftrans.xml @@ -0,0 +1,100 @@ +<?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> |