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<?xml version="1.0" encoding="UTF-8"?>
<!--
*
* This help file was generated from filter1.sci using help_from_sci().
*
-->
<refentry version="5.0-subset Scilab" xml:id="filter1" 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>filter1</refname>
<refpurpose>Apply a 1-D digital filter to the data X.</refpurpose>
</refnamediv>
<refsynopsisdiv>
<title>Calling Sequence</title>
<synopsis>
Y = filter1(B, A, X)
[Y, SF] = filter1(B, A, X, SI)
[Y, SF] = filter1(B, A, X, [], DIM)
[Y, SF] = filter1(B, A, X, SI, DIM)
</synopsis>
</refsynopsisdiv>
<refsection>
<title>Parameters</title>
<variablelist>
<varlistentry><term>B:</term>
<listitem><para> Matrix or Integer</para></listitem></varlistentry>
<varlistentry><term>A:</term>
<listitem><para> Matrix or Integer</para></listitem></varlistentry>
<varlistentry><term>X:</term>
<listitem><para> Matrix or Integer</para></listitem></varlistentry>
</variablelist>
</refsection>
<refsection>
<title>Description</title>
<para>
'filter' returns the solution to the following linear, time-invariant difference equation:
</para>
<para>
N M
</para>
<para>
SUM a(k+1) y(n-k) = SUM b(k+1) x(n-k) for 1<=n<=length(x)
</para>
<para>
k=0 k=0
</para>
<para>
where N=length(a)-1 and M=length(b)-1. The result is calculated over the first non-singleton dimension of X or over DIM if supplied.
</para>
<para>
An equivalent form of the equation is:
</para>
<para>
N M
</para>
<para>
y(n) = - SUM c(k+1) y(n-k) + SUM d(k+1) x(n-k) for 1<=n<=length(x)
</para>
<para>
k=1 k=0
</para>
<para>
where c = a/a(1) and d = b/a(1).
</para>
</refsection>
<refsection>
<title>Examples</title>
<programlisting role="example"><![CDATA[
filter([1,2,3], [3,4,5], [5,6,7])
ans =
1.6666667 3.1111111 4.4074074
]]></programlisting>
</refsection>
</refentry>
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