<?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.Apply a 1-D digital filter to the data X.</refpurpose>
  </refnamediv>


<refsynopsisdiv>
   <title>Syntax</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&lt;=n&lt;=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&lt;=n&lt;=length(x)
   </para>
   <para>
k=1                 k=0
   </para>
   <para>
where c = a/a(1) and d = b/a(1).
   </para>
   <para>
</para>
</refsection>

<refsection>
   <title>Examples</title>
   <programlisting role="example"><![CDATA[
filter([1,2,3], [3,4,5], [5,6,7])

   ]]></programlisting>
</refsection>
</refentry>
