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<?xml version="1.0" encoding="UTF-8"?>
<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="en" xml:id="cepstrum">
<refnamediv>
<refname>cepstrum</refname>
<refpurpose>cepstrum calculation</refpurpose>
</refnamediv>
<refsynopsisdiv>
<title>Syntax</title>
<synopsis>fresp = cepstrum(w,mag)</synopsis>
</refsynopsisdiv>
<refsection>
<title>Arguments</title>
<variablelist>
<varlistentry>
<term>w</term>
<listitem>
<para>positive real vector of frequencies (rad/sec)</para>
</listitem>
</varlistentry>
<varlistentry>
<term>mag</term>
<listitem>
<para>
real vector of magnitudes (same size as <literal>w</literal>)
</para>
</listitem>
</varlistentry>
<varlistentry>
<term>fresp</term>
<listitem>
<para>complex vector</para>
</listitem>
</varlistentry>
</variablelist>
</refsection>
<refsection>
<title>Description</title>
<para>
<literal>fresp = cepstrum(w,mag)</literal> returns a frequency response <literal>fresp(i)</literal>
whose magnitude at frequency <literal>w(i)</literal> equals <literal>mag(i)</literal> and such
that the phase of <literal>freq</literal> corresponds to a stable and minimum phase
system. <literal>w</literal> needs not to be sorted, but minimal entry should not be
close to zero and all the entries of <literal>w</literal> should be different.
</para>
</refsection>
<refsection>
<title>Examples</title>
<programlisting role="example"><![CDATA[
w=0.1:0.1:5;mag=1+abs(sin(w));
fresp=cepstrum(w,mag);
plot2d([w',w'],[mag(:),abs(fresp)])
]]></programlisting>
<scilab:image>
w=0.1:0.1:5;mag=1+abs(sin(w));
fresp=cepstrum(w,mag);
plot2d([w',w'],[mag(:),abs(fresp)])
</scilab:image>
</refsection>
<refsection role="see also">
<title>See also</title>
<simplelist type="inline">
<member>
<link linkend="frfit">frfit</link>
</member>
</simplelist>
</refsection>
</refentry>
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