text: <!DOCTYPE HTML PUBLIC "-//IETF//DTD HTML 2.2//EN">
  <!--Converted with LaTeX2HTML 96.1-h (September 30, 1996) by Nikos Drakos (nikos@cbl.leeds.ac.uk), CBLU, University of Leeds -->
  <HTML>
  <HEAD>
  <TITLE>Nonlinear noise reduction in a data stream</TITLE>
  <META NAME="description" CONTENT="Nonlinear noise reduction in a data stream">
  <META NAME="keywords" CONTENT="TiseanHTML">
  <META NAME="resource-type" CONTENT="document">
  <META NAME="distribution" CONTENT="global">
  <LINK REL=STYLESHEET HREF="TiseanHTML.css">
  </HEAD>
  <BODY bgcolor=ffffff LANG="EN" >
   <A NAME="tex2html324" HREF="node26.html"><IMG WIDTH=37 HEIGHT=24 ALIGN=BOTTOM ALT="next" SRC="icons/next_motif.gif"></A> <A NAME="tex2html322" HREF="node22.html"><IMG WIDTH=26 HEIGHT=24 ALIGN=BOTTOM ALT="up" SRC="icons/up_motif.gif"></A> <A NAME="tex2html318" HREF="node24.html"><IMG WIDTH=63 HEIGHT=24 ALIGN=BOTTOM ALT="previous" SRC="icons/previous_motif.gif"></A>   <BR>
  <B> Next:</B> <A NAME="tex2html325" HREF="node26.html">Lyapunov exponents</A>
  <B>Up:</B> <A NAME="tex2html323" HREF="node22.html">Nonlinear noise reduction</A>
  <B> Previous:</B> <A NAME="tex2html319" HREF="node24.html">Locally projective nonlinear noise </A>
  <BR> <P>
  <H2><A NAME="SECTION00063000000000000000">Nonlinear noise reduction in a data stream</A></H2>
  <P>
  <A NAME="subsecnoise_stream">&#160;</A>
  In Ref.&nbsp;[<A HREF="citation.html#Filter">65</A>], a number of modifications of the above procedure have
  been discussed which enable the use of nonlinear projective filtering in a data
  stream. In this case, only points in the past are available for the formation
  of neighborhoods. Therefore the neighbor search strategy has to be modified.
  Since the algorithm is described in detail in Ref.&nbsp;[<A HREF="citation.html#Filter">65</A>], we only give
  an example of its use here. Figure&nbsp;<A HREF="node25.html#figmcgnoise"><IMG  ALIGN=BOTTOM ALT="gif" SRC="icons/cross_ref_motif.gif"></A> shows the result of
  nonlinear noise reduction on a magneto-cardiogram (see Figs.&nbsp;<A HREF="node6.html#figmcgd"><IMG  ALIGN=BOTTOM ALT="gif" SRC="icons/cross_ref_motif.gif"></A> 
  and&nbsp;<A HREF="node10.html#figmcg_pc"><IMG  ALIGN=BOTTOM ALT="gif"
  SRC="icons/cross_ref_motif.gif"></A>) with the program
  <tt>noise</tt> (no longer part of TISEAN). The same program has also been
  used successfully for the extraction of the fetal ECG&nbsp;[<A HREF="citation.html#fetal2">66</A>].
  <P>
  <P><blockquote><A NAME="5428">&#160;</A><IMG WIDTH=337 HEIGHT=279 ALIGN=BOTTOM ALT="figure1311" SRC="img100.gif"><BR>
  <STRONG>Figure:</STRONG> <A NAME="figmcgnoise">&#160;</A>
     Real time nonlinear projective filtering of a magneto-cardiogram time
     series. The top panel shows the unfiltered data. Bottom: Two iterations were
     done using projections from <I>m</I>=10 down to <I>q</I>=2 dimensions (delay
     0.01&nbsp;s). Neighborhoods were limited to a radius of 0.1 units (0.05 in the
     second iteration) and to maximally 200 points. Neighbors were only sought
     up to 5&nbsp;s back in time. Thus the first 5&nbsp;s of data are not filtered
     optimally and are not shown here. Since the output of each iteration leaps
     behind its input by one delay window the last 0.2&nbsp;s cannot be processed
     given the data in the upper panel.<BR>
  </blockquote><P><HR><A NAME="tex2html324" HREF="node26.html"><IMG WIDTH=37 HEIGHT=24 ALIGN=BOTTOM ALT="next" SRC="icons/next_motif.gif"></A> <A NAME="tex2html322" HREF="node22.html"><IMG WIDTH=26 HEIGHT=24 ALIGN=BOTTOM ALT="up" SRC="icons/up_motif.gif"></A> <A NAME="tex2html318" HREF="node24.html"><IMG WIDTH=63 HEIGHT=24 ALIGN=BOTTOM ALT="previous" SRC="icons/previous_motif.gif"></A>   <BR>
  <B> Next:</B> <A NAME="tex2html325" HREF="node26.html">Lyapunov exponents</A>
  <B>Up:</B> <A NAME="tex2html323" HREF="node22.html">Nonlinear noise reduction</A>
  <B> Previous:</B> <A NAME="tex2html319" HREF="node24.html">Locally projective nonlinear noise </A>
  <P><ADDRESS>
  <I>Thomas Schreiber <BR>
  Wed Jan  6 15:38:27 CET 1999</I>
  </ADDRESS>
  </BODY>
  </HTML>
  