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<HTML>
<HEAD>
<TITLE>FILTER command</TITLE>
</HEAD>
<BODY BGCOLOR="#FFFFFF" TEXT="#000000">
<P><font size="+3" color="green"><B>FILTER command</B></font></P>
<TABLE border="1" cols="2" frame="box" rules="all" width="572">
<TR>
<TD width="15%" valign="top"><B>Syntax</B>:</TD>
<TD width="85%" valign="top"><CODE>
FILTER\MEDIAN x f npt<br />
FILTER\MEAN x f npt<br />
FILTER\-RECURSIVE x f c<br />
FILTER\RECURSIVE x f c d</CODE>
</TD></TR>
<TR>
<TD valign="top"><B>Qualifiers</B>:</TD>
<TD valign="top"><CODE>\MEDIAN, \MEAN, \RECURSIVE</CODE></TD></TR>
<TR>
<TD valign="top"><B>Defaults</B>:</TD>
<TD valign="top"><CODE>\-RECURSIVE</CODE></TD></TR>
<TR>
<TD valign="top"><B>Examples</B>:</TD>
<TD valign="top"><CODE>
FILTER\MEDIAN X XF 5<br />
FILTER\-RECURSIVE X XF [1;-2;1]<br />
FILTER\MEAN X XF -5<br />
FILTER\RECURSIVE X XF [.3584;1.2832;.3584;0;0] [0;1]</CODE>
</TD></TR>
</TABLE>
<P>
A digital filter is a linear combination of the input data,
<IMG SRC="x.gif">, and possibly the output data, <IMG SRC="f.gif">. The
input data is assumed to be <em>equally spaced</em> samples of some
continuously varying quantity; and any error or noise is in the measurements. In this
implementation of filters, the input data is assumed to have unit spacing, so a scale
factor may have to be applied to produce the correctly scaled output data.</P>
<P>
The simplest kinds of filters are the nonrecursive filters defined by the
convolution formula:</P>
<P>
<center><IMG SRC="fneq.gif"></center></P>
<P>
The coefficients <IMG SRC="ck.gif"> are
the constants of the filter, the <IMG SRC="xn-k.gif"> are the input
data, and the <IMG SRC="fn.gif"> are the outputs. When values of the output as well as the data
values are used to compute the output values, the filter is called a recursive filter. It is
usual to limit the range of nonzero coefficients to current and past values
of the data <IMG SRC="xn.gif"> and to only past values of the output
<IMG SRC="fn.gif">. This type of filter is called causal recursive and can be defined by the
convolution formula:</P>
<P>
<center><IMG SRC="fneq2.gif"></center></P>
<P>
Nonrecursive or recursive filters using constant coefficients
<IMG SRC="ck.gif"> and <IMG SRC="dk.gif"> are called time-invariant filters.</P>
<P>
It can be shown that the sum of the squares of the filter
coefficients measures the noise amplification of the filtering process. Thus,
the variance, <IMG SRC="sigma2.gif">, will be
amplified by <IMG SRC="sumsigma.gif">.</P>
<P>
<a href="median.htm"><font size="+1" color="olive">Median filters</font></a><br />
<a href="mean.htm"><font size="+1" color="olive">Mean filters</font></a><br />
<a href="nonrecursive.htm"><font size="+1" color="olive">Nonrecursive filters</font></a><br />
<a href="recursive.htm"><font size="+1" color="olive">Recursive filters</font></a><br />
<a href="examples.htm"><font size="+1" color="olive">Examples</font></a></P>
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