📄 node22.html
字号:
<!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</TITLE><META NAME="description" CONTENT="Nonlinear noise reduction"><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="tex2html293" HREF="node23.html"><IMG WIDTH=37 HEIGHT=24 ALIGN=BOTTOM ALT="next" SRC="icons/next_motif.gif"></A> <A NAME="tex2html291" HREF="TiseanHTML.html"><IMG WIDTH=26 HEIGHT=24 ALIGN=BOTTOM ALT="up" SRC="icons/up_motif.gif"></A> <A NAME="tex2html285" HREF="node21.html"><IMG WIDTH=63 HEIGHT=24 ALIGN=BOTTOM ALT="previous" SRC="icons/previous_motif.gif"></A> <BR><B> Next:</B> <A NAME="tex2html294" HREF="node23.html">Simple nonlinear noise reduction</A><B>Up:</B> <A NAME="tex2html292" HREF="TiseanHTML.html">Practical implementation of nonlinear </A><B> Previous:</B> <A NAME="tex2html286" HREF="node21.html">Global function fits</A><BR> <P><H1><A NAME="SECTION00060000000000000000">Nonlinear noise reduction</A></H1><A NAME="secnoise"> </A>Filtering of signals from nonlinear systems requires the use of specialmethods since the usual spectral or other linear filters may interactunfavorably with the nonlinear structure. Irregular signals from nonlinearsources exhibit genuine broad band spectra and there is no justification toidentify any continuous component in the spectrum as noise. Nonlinear noisereduction does not rely on frequency information in order to define thedistinction between signal and noise. Instead, structure in the reconstructedphase space will be exploited. General serial dependencies among themeasurements <IMG WIDTH=30 HEIGHT=24 ALIGN=MIDDLE ALT="tex2html_wrap_inline6549" SRC="img14.gif"> will cause the delay vectors <IMG WIDTH=30 HEIGHT=24 ALIGN=MIDDLE ALT="tex2html_wrap_inline6675" SRC="img35.gif"> to fill theavailable <I>m</I>-dimensional embedding space in an inhomogeneous way. Linearlycorrelated Gaussian random variables will for example be distributed accordingto an anisotropic multivariate Gaussian distribution. Linear geometricfiltering in phase space seeks to identify the principal directions of thisdistribution and project onto them, see Sec. <A HREF="node12.html#secsvdfilter"><IMG ALIGN=BOTTOM ALT="gif" SRC="icons/cross_ref_motif.gif"></A>. Nonlinearnoise reduction takes into account that nonlinear signals will form curvedstructures in delay space. In particular, noisy <EM>deterministic</EM> signalsform smeared-out lower dimensional manifolds. Nonlinear phase space filteringseeks to identify such structures and project onto them in order to reducenoise.<P>There is a rich literature on nonlinear noise reduction methods. Two articlesof review character are available, one by Kostelich and Schreiber [<A HREF="citation.html#ks">57</A>],and one by Davies [<A HREF="citation.html#Davies">58</A>]. We refer the reader to these articles forfurther references and for the discussion of approaches not described in thepresent article. Here we want to concentrate on two approaches that representthe geometric structure in phase space by local approximation. The first andsimplest does so to constant order, the more sophisticated uses local linearsubspaces plus curvature corrections.<P><BR> <HR><UL><A NAME="CHILD_LINKS"> </A><LI> <A NAME="tex2html295" HREF="node23.html#SECTION00061000000000000000">Simple nonlinear noise reduction</A><LI> <A NAME="tex2html296" HREF="node24.html#SECTION00062000000000000000">Locally projective nonlinear noise reduction</A><LI> <A NAME="tex2html297" HREF="node25.html#SECTION00063000000000000000">Nonlinear noise reduction in a data stream</A></UL><HR><A NAME="tex2html293" HREF="node23.html"><IMG WIDTH=37 HEIGHT=24 ALIGN=BOTTOM ALT="next" SRC="icons/next_motif.gif"></A> <A NAME="tex2html291" HREF="TiseanHTML.html"><IMG WIDTH=26 HEIGHT=24 ALIGN=BOTTOM ALT="up" SRC="icons/up_motif.gif"></A> <A NAME="tex2html285" HREF="node21.html"><IMG WIDTH=63 HEIGHT=24 ALIGN=BOTTOM ALT="previous" SRC="icons/previous_motif.gif"></A> <BR><B> Next:</B> <A NAME="tex2html294" HREF="node23.html">Simple nonlinear noise reduction</A><B>Up:</B> <A NAME="tex2html292" HREF="TiseanHTML.html">Practical implementation of nonlinear </A><B> Previous:</B> <A NAME="tex2html286" HREF="node21.html">Global function fits</A><P><ADDRESS><I>Thomas Schreiber <BR>Wed Jan 6 15:38:27 CET 1999</I></ADDRESS></BODY></HTML>⌨️ 快捷键说明
复制代码
Ctrl + C
搜索代码
Ctrl + F
全屏模式
F11
切换主题
Ctrl + Shift + D
显示快捷键
?
增大字号
Ctrl + =
减小字号
Ctrl + -