希尔伯特黄EMD.zip

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2018版matlab之前版本需要用到的,tftb.2时频分析工具箱,希尔伯特黄变换所用到的\EMD\pack_emd\package_emd\install_emd.m运行文件
EMD.zip
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<html xmlns="http://www.w3.org/1999/xhtml"><head><meta charset="utf-8"><meta name="generator" content="pdf2htmlEX"><meta http-equiv="X-UA-Compatible" content="IE=edge,chrome=1"><link rel="stylesheet" href="https://csdnimg.cn/release/download_crawler_static/css/base.min.css"><link rel="stylesheet" href="https://csdnimg.cn/release/download_crawler_static/css/fancy.min.css"><link rel="stylesheet" href="https://csdnimg.cn/release/download_crawler_static/18705033/raw.css"><script src="https://csdnimg.cn/release/download_crawler_static/js/compatibility.min.js"></script><script src="https://csdnimg.cn/release/download_crawler_static/js/pdf2htmlEX.min.js"></script><script>try{pdf2htmlEX.defaultViewer = new pdf2htmlEX.Viewer({});}catch(e){}</script><title></title></head><body><div id="sidebar" style="display: none"><div id="outline"></div></div><div id="pf1" class="pf w0 h0" data-page-no="1"><div class="pc pc1 w0 h0"><img class="bi x0 y0 w1 h1" alt="" src="https://csdnimg.cn/release/download_crawler_static/18705033/bg1.jpg"><div class="t m0 x1 h2 y1 ff1 fs0 fc0 sc0 ls0 ws0">A<span class="_ _0"> </span>COMPLETE<span class="_ _0"> </span>ENSEMBLE<span class="_ _0"> </span>EMPIRICAL<span class="_ _0"> </span>MODE<span class="_ _0"> </span>DECOMPOSITION</div><div class="t m0 x2 h2 y2 ff1 fs0 fc0 sc0 ls0 ws0">WITH<span class="_ _0"> </span>AD<span class="_ _1"></span>APTIVE<span class="_ _0"> </span>NOISE</div><div class="t m0 x3 h3 y3 ff2 fs0 fc0 sc0 ls0 ws0">Mar</div><div class="t m0 x4 h3 y4 ff2 fs0 fc0 sc0 ls0 ws0">&#180;</div><div class="t m0 x4 h3 y3 ff2 fs0 fc0 sc0 ls0 ws0">&#305;a<span class="_"> </span>E.<span class="_"> </span>T<span class="_ _2"></span>orr<span class="_ _1"></span>es</div><div class="t m0 x5 h4 y5 ff3 fs1 fc0 sc0 ls0 ws0">&#9733;</div><div class="t m0 x6 h3 y3 ff2 fs0 fc0 sc0 ls0 ws0">,<span class="_"> </span>Mar<span class="_ _1"></span>celo<span class="_"> </span>A.<span class="_"> </span>Colominas</div><div class="t m0 x7 h4 y5 ff3 fs1 fc0 sc0 ls0 ws0">&#9733;</div><div class="t m0 x8 h3 y3 ff2 fs0 fc0 sc0 ls0 ws0">,<span class="_"> </span>Gast</div><div class="t m0 x9 h3 y4 ff2 fs0 fc0 sc0 ls0 ws0">&#180;</div><div class="t m0 xa h3 y3 ff2 fs0 fc0 sc0 ls0 ws0">on<span class="_"> </span>Schlotthauer</div><div class="t m0 xb h4 y5 ff3 fs1 fc0 sc0 ls0 ws0">&#9733;</div><div class="t m0 xc h3 y3 ff2 fs0 fc0 sc0 ls0 ws0">,<span class="_"> </span>P<span class="_ _2"></span>atrick<span class="_"> </span>Flandrin</div><div class="t m0 xd h5 y5 ff4 fs1 fc0 sc0 ls0 ws0">&#8225;</div><div class="t m0 xe h4 y6 ff3 fs1 fc0 sc0 ls0 ws0">&#9733;</div><div class="t m0 xf h6 y7 ff5 fs0 fc0 sc0 ls0 ws0">Laboratorio<span class="_"> </span>de<span class="_"> </span>Se</div><div class="t m0 x10 h6 y8 ff5 fs0 fc0 sc0 ls0 ws0">&#732;</div><div class="t m0 x11 h6 y7 ff5 fs0 fc0 sc0 ls0 ws0">nales<span class="_"> </span>y<span class="_"> </span>Din</div><div class="t m0 x12 h6 y8 ff5 fs0 fc0 sc0 ls0 ws0">&#180;</div><div class="t m0 x13 h6 y7 ff5 fs0 fc0 sc0 ls0 ws0">amicas<span class="_"> </span>no<span class="_"> </span>Lineales,<span class="_"> </span>Uni<span class="_ _1"></span>versidad<span class="_"> </span>Nacional<span class="_"> </span>de<span class="_"> </span>Entre<span class="_"> </span>R</div><div class="t m0 x14 h6 y8 ff5 fs0 fc0 sc0 ls0 ws0">&#180;</div><div class="t m0 x14 h6 y7 ff5 fs0 fc0 sc0 ls0 ws0">&#305;os,<span class="_"> </span>Argentina</div><div class="t m0 x15 h5 y9 ff4 fs1 fc0 sc0 ls0 ws0">&#8225;</div><div class="t m0 x16 h6 ya ff5 fs0 fc0 sc0 ls0 ws0">Laboratoire<span class="_"> </span>de<span class="_"> </span>Physique<span class="_"> </span>(UMR<span class="_"> </span>CNRS<span class="_"> </span>5672),</div><div class="t m0 x17 h6 yb ff5 fs0 fc0 sc0 ls0 ws0">`</div><div class="t m0 x18 h6 ya ff5 fs0 fc0 sc0 ls0 ws0">Ecole<span class="_"> </span>Normale<span class="_"> </span>Sup</div><div class="t m0 x19 h6 yc ff5 fs0 fc0 sc0 ls0 ws0">`</div><div class="t m0 x1a h6 ya ff5 fs0 fc0 sc0 ls0 ws0">erieure<span class="_"> </span>de<span class="_"> </span>L<span class="_ _1"></span>yon,<span class="_"> </span>France</div><div class="t m0 x1b h7 yd ff1 fs2 fc0 sc0 ls0 ws0">ABSTRA<span class="_ _1"></span>CT</div><div class="t m0 x1c h8 ye ff5 fs2 fc0 sc0 ls0 ws0">In<span class="_ _3"> </span>this<span class="_ _3"> </span>paper<span class="_ _3"> </span>an<span class="_ _3"> </span>algorithm<span class="_ _3"> </span>based<span class="_ _3"> </span>on<span class="_ _3"> </span>the<span class="_ _3"> </span>ensemble<span class="_ _3"> </span>empirical</div><div class="t m0 x1c h8 yf ff5 fs2 fc0 sc0 ls0 ws0">mode<span class="_ _0"> </span>decomposition<span class="_ _0"> </span>(EEMD)<span class="_"> </span>is<span class="_ _0"> </span>presented.<span class="_ _4"> </span>The<span class="_ _0"> </span>ke<span class="_ _1"></span>y<span class="_ _0"> </span>idea<span class="_ _0"> </span>on</div><div class="t m0 x1c h8 y10 ff5 fs2 fc0 sc0 ls0 ws0">the<span class="_ _0"> </span>EEMD<span class="_ _3"> </span>relies<span class="_ _0"> </span>on<span class="_ _0"> </span>averaging<span class="_ _0"> </span>the<span class="_ _0"> </span>modes<span class="_ _3"> </span>obtained<span class="_ _0"> </span>by<span class="_ _0"> </span>EMD</div><div class="t m0 x1c h8 y11 ff5 fs2 fc0 sc0 ls0 ws0">applied<span class="_"> </span>to<span class="_ _0"> </span>se<span class="_ _1"></span>veral<span class="_"> </span>realizations<span class="_"> </span>of<span class="_ _0"> </span>Gaussian<span class="_"> </span>white<span class="_"> </span>noise<span class="_ _0"> </span>added</div><div class="t m0 x1c h8 y12 ff5 fs2 fc0 sc0 ls0 ws0">to<span class="_"> </span>the<span class="_"> </span>original<span class="_"> </span>signal.<span class="_ _0"> </span>The<span class="_"> </span>resulting<span class="_"> </span>decomposition<span class="_"> </span>solves<span class="_"> </span>the</div><div class="t m0 x1c h8 y13 ff5 fs2 fc0 sc0 ls0 ws0">EMD<span class="_ _5"> </span>mode<span class="_ _5"> </span>mixing<span class="_ _5"> </span>problem,<span class="_"> </span>ho<span class="_ _1"></span>we<span class="_ _1"></span>ver<span class="_ _5"> </span>it<span class="_ _5"> </span>introduces<span class="_ _5"> </span>ne<span class="_ _1"></span>w<span class="_"> </span>ones.</div><div class="t m0 x1c h8 y14 ff5 fs2 fc0 sc0 ls0 ws0">In<span class="_ _3"> </span>the<span class="_ _6"> </span>method<span class="_ _3"> </span>here<span class="_ _6"> </span>proposed,<span class="_ _6"> </span>a<span class="_ _6"> </span>particular<span class="_ _3"> </span>noise<span class="_ _6"> </span>is<span class="_ _3"> </span>added<span class="_ _6"> </span>at</div><div class="t m0 x1c h8 y15 ff5 fs2 fc0 sc0 ls0 ws0">each<span class="_"> </span>stage<span class="_"> </span>of<span class="_"> </span>the<span class="_ _5"> </span>decomposition<span class="_"> </span>and<span class="_"> </span>a<span class="_ _5"> </span>unique<span class="_"> </span>residue<span class="_"> </span>is<span class="_"> </span>com-</div><div class="t m0 x1c h8 y16 ff5 fs2 fc0 sc0 ls0 ws0">puted<span class="_ _3"> </span>to<span class="_ _3"> </span>obtain<span class="_ _3"> </span>each<span class="_ _6"> </span>mode.<span class="_ _7"> </span>The<span class="_ _3"> </span>resulting<span class="_ _3"> </span>decomposition<span class="_ _3"> </span>is</div><div class="t m0 x1c h8 y17 ff5 fs2 fc0 sc0 ls0 ws0">complete,<span class="_"> </span>with<span class="_ _0"> </span>a<span class="_"> </span>numerically<span class="_"> </span>negligible<span class="_"> </span>error<span class="_ _1"></span>.<span class="_ _3"> </span>T<span class="_ _2"></span>wo<span class="_ _0"> </span>e<span class="_ _1"></span>xamples</div><div class="t m0 x1c h8 y18 ff5 fs2 fc0 sc0 ls0 ws0">are<span class="_ _6"> </span>presented:<span class="_ _7"> </span>a<span class="_ _8"> </span>discrete<span class="_ _6"> </span>Dirac<span class="_ _8"> </span>delta<span class="_ _6"> </span>function<span class="_ _8"> </span>and<span class="_ _8"> </span>an<span class="_ _6"> </span>elec-</div><div class="t m0 x1c h8 y19 ff5 fs2 fc0 sc0 ls0 ws0">trocardiogram<span class="_ _0"> </span>signal.<span class="_ _9"> </span>The<span class="_ _0"> </span>results<span class="_ _3"> </span>sho<span class="_ _1"></span>w<span class="_ _3"> </span>that,<span class="_ _0"> </span>compared<span class="_ _3"> </span>with</div><div class="t m0 x1c h8 y1a ff5 fs2 fc0 sc0 ls0 ws0">EEMD,<span class="_ _3"> </span>the<span class="_ _0"> </span>new<span class="_ _0"> </span>method<span class="_ _3"> </span>here<span class="_ _0"> </span>presented<span class="_ _3"> </span>also<span class="_ _3"> </span>pro<span class="_ _1"></span>vides<span class="_ _3"> </span>a<span class="_ _0"> </span>bet-</div><div class="t m0 x1c h8 y1b ff5 fs2 fc0 sc0 ls0 ws0">ter<span class="_ _3"> </span>spectral<span class="_ _3"> </span>separation<span class="_ _3"> </span>of<span class="_ _3"> </span>the<span class="_ _3"> </span>modes<span class="_ _6"> </span>and<span class="_ _3"> </span>a<span class="_ _3"> </span>lesser<span class="_ _3"> </span>number<span class="_ _3"> </span>of</div><div class="t m0 x1c h8 y1c ff5 fs2 fc0 sc0 ls0 ws0">sifting<span class="_"> </span>iterations<span class="_"> </span>is<span class="_"> </span>needed,<span class="_"> </span>reducing<span class="_"> </span>the<span class="_"> </span>computational<span class="_"> </span>cost.</div><div class="t m0 x1d h9 y1d ff6 fs2 fc0 sc0 ls0 ws0">Index<span class="_ _a"> </span>T<span class="_ _2"></span>erms<span class="ff1">&#8212;<span class="_ _6"> </span><span class="ff5">Empirical<span class="_ _a"> </span>Mode<span class="_ _a"> </span>Decomposition,<span class="_ _a"> </span>Biomed-</span></span></div><div class="t m0 x1c h8 y1e ff5 fs2 fc0 sc0 ls0 ws0">ical<span class="_"> </span>Signal<span class="_"> </span>Processing,<span class="_"> </span>Heart<span class="_"> </span>Rate<span class="_"> </span>V<span class="_ _2"></span>ariability</div><div class="t m0 x1e h7 y1f ff1 fs2 fc0 sc0 ls0 ws0">1.<span class="_ _7"> </span>INTR<span class="_ _1"></span>ODUCTION</div><div class="t m0 x1c h8 y20 ff5 fs2 fc0 sc0 ls0 ws0">Empirical<span class="_ _4"> </span>Mode<span class="_ _8"> </span>Decomposition<span class="_ _4"> </span>(EMD)<span class="_ _4"> </span>[1]<span class="_ _4"> </span>is<span class="_ _8"> </span>an<span class="_ _4"> </span>adaptiv<span class="_ _1"></span>e</div><div class="t m0 x1c h8 y21 ff5 fs2 fc0 sc0 ls0 ws0">method<span class="_ _3"> </span>introduced<span class="_ _3"> </span>to<span class="_ _3"> </span>analyze<span class="_ _0"> </span>non-linear<span class="_ _3"> </span>and<span class="_ _3"> </span>non-stationary</div><div class="t m0 x1c h8 y22 ff5 fs2 fc0 sc0 ls0 ws0">signals.<span class="_ _b"> </span>It<span class="_ _6"> </span>consists<span class="_ _6"> </span>in<span class="_ _6"> </span>a<span class="_ _8"> </span>local<span class="_ _6"> </span>and<span class="_ _6"> </span>fully<span class="_ _6"> </span>data-driven<span class="_ _3"> </span>separa-</div><div class="t m0 x1c h8 y23 ff5 fs2 fc0 sc0 ls0 ws0">tion<span class="_ _0"> </span>of<span class="_"> </span>a<span class="_ _0"> </span>signal<span class="_"> </span>in<span class="_ _0"> </span>fas<span class="_ _1"></span>t<span class="_ _0"> </span>and<span class="_"> </span>slow<span class="_"> </span>oscillations.<span class="_ _8"> </span>Howe<span class="_ _1"></span>ver<span class="_ _1"></span>,<span class="_"> </span>EMD</div><div class="t m0 x1c h8 y24 ff5 fs2 fc0 sc0 ls0 ws0">experiences<span class="_ _6"> </span>some<span class="_ _8"> </span>problems,<span class="_ _4"> </span>such<span class="_ _6"> </span>as<span class="_ _8"> </span>the<span class="_ _8"> </span>presence<span class="_ _6"> </span>of<span class="_ _8"> </span>oscil-</div><div class="t m0 x1c h8 y25 ff5 fs2 fc0 sc0 ls0 ws0">lations<span class="_ _6"> </span>of<span class="_ _6"> </span>very<span class="_ _6"> </span>disparate<span class="_ _6"> </span>amplitude<span class="_ _6"> </span>in<span class="_ _8"> </span>a<span class="_ _6"> </span>mode,<span class="_ _8"> </span>or<span class="_ _6"> </span>the<span class="_ _6"> </span>pres-</div><div class="t m0 x1c h8 y26 ff5 fs2 fc0 sc0 ls0 ws0">ence<span class="_"> </span>of<span class="_"> </span>v<span class="_ _1"></span>ery<span class="_"> </span>similar<span class="_"> </span>oscillations<span class="_ _5"> </span>in<span class="_"> </span>dif<span class="_ _1"></span>ferent<span class="_"> </span>modes,<span class="_"> </span>named<span class="_"> </span>as</div><div class="t m0 x1c h8 y27 ff5 fs2 fc0 sc0 ls0 ws0">&#8220;mode<span class="_"> </span>mixing&#8221;.<span class="_ _6"> </span>T<span class="_ _c"></span>o<span class="_"> </span>overcome<span class="_"> </span>these<span class="_"> </span>problems,<span class="_ _0"> </span>a<span class="_"> </span>new<span class="_"> </span>method</div><div class="t m0 x1c h8 y28 ff5 fs2 fc0 sc0 ls0 ws0">was<span class="_ _5"> </span>proposed:<span class="_ _0"> </span>the<span class="_ _5"> </span>Ensemble<span class="_ _5"> </span>Empirical<span class="_"> </span>Mode<span class="_ _a"> </span>Decomposition</div><div class="t m0 x1c h8 y29 ff5 fs2 fc0 sc0 ls0 ws0">(EEMD)<span class="_ _0"> </span>[2].<span class="_ _9"> </span>It<span class="_ _0"> </span>performs<span class="_ _3"> </span>the<span class="_ _0"> </span>EMD<span class="_ _0"> </span>over<span class="_ _0"> </span>an<span class="_ _0"> </span>ensemble<span class="_ _3"> </span>of<span class="_ _0"> </span>the</div><div class="t m0 x1c h8 y2a ff5 fs2 fc0 sc0 ls0 ws0">signal<span class="_ _a"> </span>plus<span class="_ _a"> </span>Gaussian<span class="_ _5"> </span>white<span class="_ _a"> </span>noise.<span class="_ _0"> </span>The<span class="_ _a"> </span>addition<span class="_ _a"> </span>of<span class="_ _5"> </span>white<span class="_ _a"> </span>Gaus-</div><div class="t m0 x1c h8 y2b ff5 fs2 fc0 sc0 ls0 ws0">sian<span class="_"> </span>noise<span class="_"> </span>solv<span class="_ _1"></span>es<span class="_"> </span>the<span class="_"> </span>mode<span class="_ _5"> </span>mixing<span class="_"> </span>problem<span class="_"> </span>by<span class="_ _5"> </span>populating<span class="_"> </span>the</div><div class="t m0 x1c h8 y2c ff5 fs2 fc0 sc0 ls0 ws0">whole<span class="_ _0"> </span>time-frequency<span class="_ _0"> </span>space<span class="_ _3"> </span>to<span class="_ _0"> </span>take<span class="_ _0"> </span>advantage<span class="_ _0"> </span>of<span class="_ _0"> </span>the<span class="_ _3"> </span>dyadic</div><div class="t m0 x1c h8 y2d ff5 fs2 fc0 sc0 ls0 ws0">&#64257;lter<span class="_"> </span>bank<span class="_"> </span>behavior<span class="_"> </span>of<span class="_"> </span>the<span class="_ _0"> </span>EMD<span class="_"> </span>[3];<span class="_"> </span>howe<span class="_ _1"></span>ver<span class="_"> </span>it<span class="_"> </span>creates<span class="_"> </span>some</div><div class="t m0 x1c h8 y2e ff5 fs2 fc0 sc0 ls0 ws0">new<span class="_ _0"> </span>ones.<span class="_ _4"> </span>Indeed,<span class="_ _0"> </span>the<span class="_ _0"> </span>reconstructed<span class="_ _0"> </span>signal<span class="_ _0"> </span>includes<span class="_ _0"> </span>residual</div><div class="t m0 x1c h8 y2f ff5 fs2 fc0 sc0 ls0 ws0">noise<span class="_ _0"> </span>and<span class="_"> </span>different<span class="_"> </span>realizations<span class="_ _0"> </span>of<span class="_"> </span>signal<span class="_ _0"> </span>plus<span class="_"> </span>noise<span class="_ _0"> </span>may<span class="_"> </span>pro-</div><div class="t m0 x1c h8 y30 ff5 fs2 fc0 sc0 ls0 ws0">duce<span class="_ _0"> </span>dif<span class="_ _1"></span>ferent<span class="_ _0"> </span>number<span class="_ _0"> </span>of<span class="_"> </span>modes.<span class="_ _4"> </span>In<span class="_ _0"> </span>order<span class="_"> </span>to<span class="_ _0"> </span>overcome<span class="_"> </span>these</div><div class="t m0 x1d ha y31 ff5 fs1 fc0 sc0 ls0 ws0">Thanks<span class="_ _3"> </span>to<span class="_ _3"> </span>Agencia<span class="_ _6"> </span>Nacional<span class="_ _3"> </span>de<span class="_ _3"> </span>Promoci</div><div class="t m0 x1f ha y32 ff5 fs1 fc0 sc0 ls0 ws0">&#180;</div><div class="t m0 x20 ha y31 ff5 fs1 fc0 sc0 ls0 ws0">on<span class="_ _3"> </span>Cient</div><div class="t m0 x21 ha y32 ff5 fs1 fc0 sc0 ls0 ws0">&#180;</div><div class="t m0 x21 ha y31 ff5 fs1 fc0 sc0 ls0 ws0">&#305;&#64257;ca<span class="_ _3"> </span>y<span class="_ _3"> </span>T<span class="_ _1"></span>ecnol</div><div class="t m0 x22 ha y32 ff5 fs1 fc0 sc0 ls0 ws0">&#180;</div><div class="t m0 x23 ha y31 ff5 fs1 fc0 sc0 ls0 ws0">ogica</div><div class="t m0 x1c ha y33 ff5 fs1 fc0 sc0 ls0 ws0">(ANPCyT),<span class="_ _8"> </span>Consejo<span class="_ _8"> </span>Nacional<span class="_ _8"> </span>de<span class="_ _6"> </span>Investigaciones<span class="_ _6"> </span>Cient</div><div class="t m0 x24 ha y34 ff5 fs1 fc0 sc0 ls0 ws0">&#180;</div><div class="t m0 x24 ha y33 ff5 fs1 fc0 sc0 ls0 ws0">&#305;&#64257;cas<span class="_ _8"> </span>y<span class="_ _8"> </span>T</div><div class="t m0 x25 ha y34 ff5 fs1 fc0 sc0 ls0 ws0">&#180;</div><div class="t m0 x25 ha y33 ff5 fs1 fc0 sc0 ls0 ws0">ecnicas</div><div class="t m0 x1c ha y35 ff5 fs1 fc0 sc0 ls0 ws0">(CONICET)<span class="_"> </span>of<span class="_"> </span>Argentina,<span class="_"> </span>UNER<span class="_"> </span>and<span class="_"> </span>UNL.</div><div class="t m0 x26 h8 yd ff5 fs2 fc0 sc0 ls0 ws0">situations,<span class="_ _0"> </span>in<span class="_"> </span>this<span class="_ _0"> </span>paper<span class="_"> </span>we<span class="_ _0"> </span>propose<span class="_"> </span>a<span class="_"> </span>variation<span class="_"> </span>of<span class="_ _0"> </span>the<span class="_"> </span>EEMD</div><div class="t m0 x26 h8 y36 ff5 fs2 fc0 sc0 ls0 ws0">algorithm<span class="_ _3"> </span>that<span class="_ _0"> </span>provides<span class="_ _0"> </span>an<span class="_ _3"> </span>exact<span class="_ _0"> </span>reconstruction<span class="_ _3"> </span>of<span class="_ _3"> </span>the<span class="_ _0"> </span>origi-</div><div class="t m0 x26 h8 y37 ff5 fs2 fc0 sc0 ls0 ws0">nal<span class="_ _0"> </span>signal<span class="_"> </span>and<span class="_ _0"> </span>a<span class="_"> </span>better<span class="_ _0"> </span>spectral<span class="_"> </span>separation<span class="_ _0"> </span>of<span class="_"> </span>the<span class="_ _0"> </span>modes,<span class="_ _0"> </span>with</div><div class="t m0 x26 h8 y38 ff5 fs2 fc0 sc0 ls0 ws0">a<span class="_"> </span>lower<span class="_"> </span>computational<span class="_"> </span>cost.</div><div class="t m0 x27 h8 y39 ff5 fs2 fc0 sc0 ls0 ws0">The<span class="_ _6"> </span>paper<span class="_ _3"> </span>is<span class="_ _6"> </span>organized<span class="_ _3"> </span>as<span class="_ _6"> </span>follows.<span class="_ _d"> </span>In<span class="_ _6"> </span>Sec.<span class="_ _d"> </span>2<span class="_ _6"> </span>the<span class="_ _3"> </span>main</div><div class="t m0 x26 h8 y3a ff5 fs2 fc0 sc0 ls0 ws0">EEMD<span class="_ _3"> </span>concepts<span class="_ _0"> </span>are<span class="_ _3"> </span>recalled,<span class="_ _6"> </span>the<span class="_ _3"> </span>ne<span class="_ _1"></span>w<span class="_ _3"> </span>method<span class="_ _3"> </span>is<span class="_ _0"> </span>introduced</div><div class="t m0 x26 h8 y3b ff5 fs2 fc0 sc0 ls0 ws0">and<span class="_ _3"> </span>the<span class="_ _3"> </span>data<span class="_ _3"> </span>used<span class="_ _6"> </span>for<span class="_ _3"> </span>the<span class="_ _3"> </span>experiments<span class="_ _3"> </span>is<span class="_ _3"> </span>described.<span class="_ _7"> </span>In<span class="_ _6"> </span>Sec.</div><div class="t m0 x26 h8 y3c ff5 fs2 fc0 sc0 ls0 ws0">3<span class="_ _0"> </span>the<span class="_ _0"> </span>results<span class="_ _0"> </span>obtained<span class="_ _0"> </span>via<span class="_ _0"> </span>the<span class="_ _0"> </span>method<span class="_ _0"> </span>here<span class="_ _0"> </span>proposed<span class="_ _3"> </span>are<span class="_ _0"> </span>pre-</div><div class="t m0 x26 h8 y3d ff5 fs2 fc0 sc0 ls0 ws0">sented<span class="_ _6"> </span>and<span class="_ _6"> </span>compared<span class="_ _6"> </span>with<span class="_ _8"> </span>EEMD.<span class="_ _6"> </span>Finally<span class="_ _c"></span>,<span class="_ _8"> </span>the<span class="_ _8"> </span>conclusions</div><div class="t m0 x26 h8 y3e ff5 fs2 fc0 sc0 ls0 ws0">are<span class="_"> </span>discussed<span class="_"> </span>in<span class="_"> </span>Sec.<span class="_ _0"> </span>4.</div><div class="t m0 x28 h7 y3f ff1 fs2 fc0 sc0 ls0 ws0">2.<span class="_ _7"> </span>MA<span class="_ _2"></span>TERIALS<span class="_ _e"> </span>AND<span class="_ _e"> </span>METHODS</div><div class="t m0 x26 h7 y40 ff1 fs2 fc0 sc0 ls0 ws0">2.1.<span class="_ _7"> </span>Ensemble<span class="_ _5"> </span>Empirical<span class="_ _e"> </span>Mode<span class="_ _e"> </span>Decomposition</div><div class="t m0 x26 hb y41 ff5 fs2 fc0 sc0 ls0 ws0">EMD<span class="_ _8"> </span>[1]<span class="_ _4"> </span>decomposes<span class="_ _4"> </span>a<span class="_ _4"> </span>signal<span class="_ _8"> </span><span class="ff7">&#119909;<span class="ff8">(</span>&#119905;<span class="ff8">)<span class="_ _4"> </span></span></span>into<span class="_ _4"> </span>a<span class="_ _8"> </span>(usually)<span class="_ _4"> </span>small</div><div class="t m0 x26 h8 y42 ff5 fs2 fc0 sc0 ls0 ws0">number<span class="_"> </span>of<span class="_ _e"> </span>Intrinsic<span class="_ _e"> </span>Mode<span class="_ _e"> </span>Functions<span class="_ _e"> </span>(IMFs)<span class="_ _e"> </span>or<span class="_ _0"> </span>modes.<span class="_ _3"> </span>T<span class="_ _c"></span>o<span class="_"> </span>be</div><div class="t m0 x26 h8 y43 ff5 fs2 fc0 sc0 ls0 ws0">considered<span class="_ _a"> </span>as<span class="_ _5"> </span>an<span class="_ _a"> </span>IMF<span class="_ _c"></span>,<span class="_"> </span>a<span class="_ _a"> </span>signal<span class="_ _a"> </span>must<span class="_ _a"> </span>satisfy<span class="_"> </span>tw<span class="_ _1"></span>o<span class="_ _5"> </span>conditions:<span class="_ _e"> </span>(i)</div><div class="t m0 x26 h8 y44 ff5 fs2 fc0 sc0 ls0 ws0">the<span class="_"> </span>number<span class="_"> </span>of<span class="_ _e"> </span>extrema<span class="_"> </span>and<span class="_"> </span>the<span class="_ _e"> </span>number<span class="_ _e"> </span>of<span class="_ _e"> </span>zero<span class="_ _e"> </span>crossing<span class="_"> </span>must</div><div class="t m0 x26 h8 y45 ff5 fs2 fc0 sc0 ls0 ws0">be<span class="_ _0"> </span>equal<span class="_ _0"> </span>or<span class="_ _0"> </span>dif<span class="_ _1"></span>fer<span class="_ _0"> </span>at<span class="_ _0"> </span>most<span class="_ _0"> </span>by<span class="_ _0"> </span>one;<span class="_ _3"> </span>and<span class="_ _0"> </span>(ii)<span class="_ _0"> </span>the<span class="_ _0"> </span>mean<span class="_ _0"> </span>v<span class="_ _1"></span>alue<span class="_ _0"> </span>of</div><div class="t m0 x26 h8 y46 ff5 fs2 fc0 sc0 ls0 ws0">the<span class="_"> </span>upper<span class="_"> </span>and<span class="_"> </span>lower<span class="_"> </span>en<span class="_ _c"></span>velope<span class="_"> </span>is<span class="_"> </span>zero<span class="_"> </span>ev<span class="_ _1"></span>erywhere.</div><div class="t m0 x27 h8 y47 ff5 fs2 fc0 sc0 ls0 ws0">EEMD<span class="_ _e"> </span>de&#64257;nes<span class="_ _0"> </span>the<span class="_ _e"> </span>&#8220;<span class="ff2">true</span>&#8221;<span class="_ _0"> </span>IMF<span class="_ _e"> </span>components<span class="_ _0"> </span>(here<span class="_ _e"> </span>notated</div><div class="t m0 x26 h8 y48 ff5 fs2 fc0 sc0 ls0 ws0">as</div><div class="t m0 x29 hb y49 ff7 fs2 fc0 sc0 ls0 ws0">&#119868;<span class="_ _f"></span>&#119872;<span class="_ _10"></span>&#119865;<span class="_ _4"> </span><span class="ff5">in<span class="_ _3"> </span>what<span class="_ _0"> </span>follows)<span class="_ _0"> </span>as<span class="_ _3"> </span>the<span class="_ _0"> </span>mean<span class="_ _3"> </span>of<span class="_ _0"> </span>the<span class="_ _3"> </span>corresponding</span></div><div class="t m0 x26 h8 y4a ff5 fs2 fc0 sc0 ls0 ws0">IMFs<span class="_ _3"> </span>obtained<span class="_ _6"> </span>via<span class="_ _6"> </span>EMD<span class="_ _6"> </span>ov<span class="_ _1"></span>er<span class="_ _6"> </span>an<span class="_ _6"> </span>ensemble<span class="_ _3"> </span>of<span class="_ _6"> </span>trials,<span class="_ _8"> </span>gener-</div><div class="t m0 x26 h8 y4b ff5 fs2 fc0 sc0 ls0 ws0">ated<span class="_ _3"> </span>by<span class="_ _0"> </span>adding<span class="_ _3"> </span>different<span class="_ _0"> </span>realizations<span class="_ _3"> </span>of<span class="_ _3"> </span>white<span class="_ _3"> </span>noise<span class="_ _0"> </span>of<span class="_ _3"> </span>&#64257;nite</div><div class="t m0 x26 hb y4c ff5 fs2 fc0 sc0 ls0 ws0">variance<span class="_"> </span>to<span class="_"> </span>the<span class="_ _0"> </span>original<span class="_"> </span>signal<span class="_ _0"> </span><span class="ff7">&#119909;<span class="ff8">[</span>&#119899;<span class="ff8">]</span></span>.<span class="_ _6"> </span>EEMD<span class="_ _e"> </span>algorithm<span class="_ _0"> </span>can<span class="_"> </span>be</div><div class="t m0 x26 h8 y4d ff5 fs2 fc0 sc0 ls0 ws0">described<span class="_"> </span>as:</div><div class="t m0 x2a hb y4e ff5 fs2 fc0 sc0 ls0 ws0">1.<span class="_ _11"> </span>generate<span class="_ _4"> </span><span class="ff7">&#119909;</span></div><div class="t m0 x2b hc y4f ff9 fs3 fc0 sc0 ls0 ws0">&#119894;</div><div class="t m0 x2c hb y4e ff8 fs2 fc0 sc0 ls0 ws0">[<span class="ff7">&#119899;</span>]<span class="_ _d"> </span>=<span class="_ _d"> </span><span class="ff7">&#119909;</span>[<span class="ff7">&#119899;</span>]<span class="_ _6"> </span>+<span class="_ _6"> </span><span class="ff7">&#119908;</span></div><div class="t m0 x2d hc y4f ff9 fs3 fc0 sc0 ls0 ws0">&#119894;</div><div class="t m0 x2e hb y4e ff8 fs2 fc0 sc0 ls0 ws0">[<span class="ff7">&#119899;</span>]<span class="ff5">,<span class="_ _11"> </span>where<span class="_ _4"> </span><span class="ff7">&#119908;</span></span></div><div class="t m0 x2f hc y4f ff9 fs3 fc0 sc0 ls0 ws0">&#119894;</div><div class="t m0 x30 hb y4e ff8 fs2 fc0 sc0 ls0 ws0">[<span class="ff7">&#119899;</span>]<span class="_ _4"> </span><span class="ff5">(<span class="ff7">&#119894;<span class="_"> </span></span></span>=</div><div class="t m0 x31 hb y50 ff8 fs2 fc0 sc0 ls0 ws0">1<span class="ff7">,<span class="_ _a"> </span>.<span class="_ _12"> </span>.<span class="_ _12"> </span>.<span class="_ _a"> </span>,<span class="_ _12"> </span>&#119868;<span class="_ _f"></span><span class="ff5">)<span class="_ _8"> </span>are<span class="_ _8"> </span>different<span class="_ _6"> </span>realizations<span class="_ _8"> </span>of<span class="_ _8"> </span>white<span class="_ _8"> </span>Gaussian</span></span></div><div class="t m0 x31 h8 y51 ff5 fs2 fc0 sc0 ls0 ws0">noise,</div><div class="t m0 x2a hb y52 ff5 fs2 fc0 sc0 ls0 ws0">2.<span class="_ _11"> </span>each<span class="_"> </span><span class="ff7">&#119909;</span></div><div class="t m0 x32 hc y53 ff9 fs3 fc0 sc0 ls0 ws0">&#119894;</div><div class="t m0 x33 hb y52 ff8 fs2 fc0 sc0 ls0 ws0">[<span class="ff7">&#119899;</span>]<span class="_ _5"> </span><span class="ff5">(<span class="ff7">&#119894;<span class="_ _0"> </span></span></span>=<span class="_ _e"> </span>1<span class="ff7">,<span class="_ _a"> </span>.<span class="_ _12"> </span>.<span class="_ _a"> </span>.<span class="_ _12"> </span>,<span class="_ _a"> </span>&#119868;<span class="_ _f"></span><span class="ff5">)<span class="_"> </span>is<span class="_"> </span>fully<span class="_"> </span>decomposed<span class="_ _5"> </span>by<span class="_"> </span>EMD</span></span></div><div class="t m0 x31 hb y54 ff5 fs2 fc0 sc0 ls0 ws0">getting<span class="_"> </span>their<span class="_"> </span>modes<span class="_"> </span><span class="ff7">&#119868;<span class="_ _f"></span>&#119872;<span class="_ _10"></span>&#119865;</span></div><div class="t m0 x34 hc y55 ff9 fs3 fc0 sc0 ls0 ws0">&#119894;</div><div class="t m0 x35 hc y56 ff9 fs3 fc0 sc0 ls0 ws0">&#119896;</div><div class="t m0 x36 hb y54 ff8 fs2 fc0 sc0 ls0 ws0">[<span class="ff7">&#119899;</span>]<span class="ff5">,<span class="_"> </span>where<span class="_"> </span><span class="ff7">&#119896;<span class="_ _0"> </span></span></span>=<span class="_ _0"> </span>1<span class="ff7">,<span class="_ _a"> </span>.<span class="_ _12"> </span>.<span class="_ _a"> </span>.<span class="_ _12"> </span>,<span class="_ _a"> </span>&#119870;<span class="_ _0"> </span><span class="ff5">in-</span></span></div><div class="t m0 x31 h8 y57 ff5 fs2 fc0 sc0 ls0 ws0">dicates<span class="_"> </span>the<span class="_"> </span>modes,</div><div class="t m0 x2a hb y58 ff5 fs2 fc0 sc0 ls0 ws0">3.<span class="_ _11"> </span>assign<span class="_ _6"> </span><span class="ff7">&#119868;<span class="_ _f"></span>&#119872;<span class="_ _10"> </span>&#119865;</span></div><div class="t m0 x37 hc y59 ff9 fs3 fc0 sc0 ls0 ws0">&#119896;</div><div class="t m0 x38 hb y58 ff5 fs2 fc0 sc0 ls0 ws0">as<span class="_ _6"> </span>the<span class="_ _8"> </span><span class="ff7">&#119896;<span class="_ _13"></span></span>-th<span class="_ _6"> </span>mode<span class="_ _8"> </span>of<span class="_ _6"> </span><span class="ff7">&#119909;<span class="ff8">[</span>&#119899;<span class="ff8">]</span>,<span class="_ _8"> </span></span>obtained<span class="_ _6"> </span>as</div><div class="t m0 x31 hb y5a ff5 fs2 fc0 sc0 ls0 ws0">the<span class="_ _e"> </span>average<span class="_"> </span>of<span class="_ _e"> </span>the<span class="_ _0"> </span>corresponding<span class="_ _e"> </span><span class="ff7">&#119868;<span class="_ _f"></span>&#119872;<span class="_ _10"> </span>&#119865;</span></div><div class="t m0 x39 hc y5b ff9 fs3 fc0 sc0 ls0 ws0">&#119894;</div><div class="t m0 x3a hc y5c ff9 fs3 fc0 sc0 ls0 ws0">&#119896;</div><div class="t m0 x3b hb y5a ff5 fs2 fc0 sc0 ls0 ws0">:<span class="_ _3"> </span><span class="ff7">&#119868;<span class="_ _f"></span>&#119872;<span class="_ _10"> </span>&#119865;</span></div><div class="t m0 x3c hc y5d ff9 fs3 fc0 sc0 ls0 ws0">&#119896;</div><div class="t m0 x3d hb y5a ff8 fs2 fc0 sc0 ls0 ws0">[<span class="ff7">&#119899;</span>]<span class="_ _3"> </span>=</div><div class="t m0 x3e hd y5e ffa fs3 fc0 sc0 ls0 ws0">1</div><div class="t m0 x3e hc y5f ff9 fs3 fc0 sc0 ls0 ws0">&#119868;</div><div class="t m0 x3f he y60 ffb fs2 fc0 sc0 ls0 ws0">&#58960;</div><div class="t m0 x40 hc y61 ff9 fs3 fc0 sc0 ls0 ws0">&#119868;</div><div class="t m0 x40 hd y62 ff9 fs3 fc0 sc0 ls0 ws0">&#119894;<span class="ffa">=1</span></div><div class="t m0 x41 hb y63 ff7 fs2 fc0 sc0 ls0 ws0">&#119868;<span class="_ _f"></span>&#119872;<span class="_ _10"></span>&#119865;</div><div class="t m0 x42 hc y64 ff9 fs3 fc0 sc0 ls0 ws0">&#119894;</div><div class="t m0 x43 hc y65 ff9 fs3 fc0 sc0 ls0 ws0">&#119896;</div><div class="t m0 x38 hb y63 ff8 fs2 fc0 sc0 ls0 ws0">[<span class="ff7">&#119899;</span>]<span class="ff7">.</span></div><div class="t m0 x26 h7 y66 ff1 fs2 fc0 sc0 ls0 ws0">2.2.<span class="_ _7"> </span>Our<span class="_ _5"> </span>Method</div><div class="t m0 x26 hb y67 ff5 fs2 fc0 sc0 ls0 ws0">Observe<span class="_ _3"> </span>that<span class="_ _3"> </span>in<span class="_ _0"> </span>EEMD,<span class="_ _3"> </span>each<span class="_ _3"> </span><span class="ff7">&#119909;</span></div><div class="t m0 x44 hc y68 ff9 fs3 fc0 sc0 ls0 ws0">&#119894;</div><div class="t m0 x45 hb y67 ff8 fs2 fc0 sc0 ls0 ws0">[<span class="ff7">&#119899;</span>]<span class="_ _3"> </span><span class="ff5">is<span class="_ _3"> </span>decomposed<span class="_ _3"> </span>indepen-</span></div><div class="t m0 x26 h8 y69 ff5 fs2 fc0 sc0 ls0 ws0">dently<span class="_ _11"> </span>from<span class="_ _11"> </span>the<span class="_ _11"> </span>other<span class="_ _4"> </span>realizations<span class="_ _11"> </span>and<span class="_ _11"> </span>so<span class="_ _11"> </span>for<span class="_ _11"> </span>each<span class="_ _11"> </span>one<span class="_ _4"> </span>a</div><div class="t m0 x26 hb y35 ff5 fs2 fc0 sc0 ls0 ws0">residue<span class="_"> </span><span class="ff7">&#119903;</span></div><div class="t m0 x46 hc y6a ff9 fs3 fc0 sc0 ls0 ws0">&#119894;</div><div class="t m0 x46 hc y6b ff9 fs3 fc0 sc0 ls0 ws0">&#119896;</div><div class="t m0 x47 hb y35 ff8 fs2 fc0 sc0 ls0 ws0">[<span class="ff7">&#119899;</span>]<span class="_ _e"> </span>=<span class="_ _0"> </span><span class="ff7">&#119903;</span></div><div class="t m0 x48 hc y6a ff9 fs3 fc0 sc0 ls0 ws0">&#119894;</div><div class="t m0 x48 hd y6b ff9 fs3 fc0 sc0 ls0 ws0">&#119896;<span class="ffc">&#8722;<span class="ffa">1</span></span></div><div class="t m0 x49 hf y35 ff8 fs2 fc0 sc0 ls0 ws0">[<span class="ff7">&#119899;</span>]<span class="_ _5"> </span><span class="ffd">&#8722;<span class="_ _5"> </span><span class="ff7">&#119868;<span class="_ _f"></span>&#119872;<span class="_ _10"></span>&#119865;</span></span></div><div class="t m0 x4a hc y6a ff9 fs3 fc0 sc0 ls0 ws0">&#119894;</div><div class="t m0 x45 hc y6b ff9 fs3 fc0 sc0 ls0 ws0">&#119896;</div><div class="t m0 x4b hb y35 ff8 fs2 fc0 sc0 ls0 ws0">[<span class="ff7">&#119899;</span>]<span class="_ _e"> </span><span class="ff5">is<span class="_"> </span>obtained.</span></div></div><div class="pi" data-data='{"ctm":[1.568627,0.000000,0.000000,1.568627,0.000000,0.000000]}'></div></div></body></html>
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