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利用分数低阶循环统计量进行循环平稳分析。对于非信号处理的雪珍很有帮助
Fractional Lower Order Cyclic Statistics.rar
  • Exploitation of Cyclostationarity Using Fractional Lower-Order Cyclic Statistics.pdf
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内容介绍
<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://static.pudn.com/base/css/base.min.css"> <link rel="stylesheet" href="https://static.pudn.com/base/css/fancy.min.css"> <link rel="stylesheet" href="https://static.pudn.com/prod/directory_preview_static/62541b526caf596192b782ab/raw.css"> <script src="https://static.pudn.com/base/js/compatibility.min.js"></script> <script src="https://static.pudn.com/base/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://static.pudn.com/prod/directory_preview_static/62541b526caf596192b782ab/bg1.jpg"><div class="t m0 x1 h2 y1 ff1 fs0 fc0 sc0 ls0 ws0">Exploi<span class="_ _0"></span>tation of Cyclos<span class="_ _0"></span>tationari<span class="_ _0"></span>ty Using Fr<span class="_ _0"></span><span class="ls1 ws1">actio<span class="_ _1"></span>nal Lower-O<span class="_ _1"></span>rder Cy<span class="_ _1"></span>clic Stati<span class="_ _1"></span>stics<span class="_ _1"></span> </span></div><div class="t m0 x2 h3 y2 ff1 fs1 fc0 sc0 ls2 ws2"> </div><div class="t m0 x3 h4 y3 ff1 fs2 fc0 sc0 ls2 ws2">Yang Liu</div><div class="t m0 x4 h5 y4 ff1 fs3 fc0 sc0 ls2 ws2">1,2</div><div class="t m0 x5 h4 y3 ff1 fs2 fc0 sc0 ls2 ws2"> </div><div class="t m0 x6 h3 y5 ff1 fs1 fc0 sc0 ls3 ws3">1. Faculty of Electronic <span class="ls4 ws4">Inf<span class="_ _1"></span>ormation and electrical </span></div><div class="t m0 x7 h3 y6 ff1 fs1 fc0 sc0 ls5 ws2">engine<span class="_ _0"></span>eri<span class="_ _0"></span>ng </div><div class="t m0 x8 h3 y7 ff1 fs1 fc0 sc0 ls6 ws5"> Dalian University of Technolo<span class="_ _0"></span>gy </div><div class="t m0 x9 h3 y8 ff1 fs1 fc0 sc0 ls7 ws5">Dalian, China </div><div class="t m0 xa h3 y9 ff1 fs1 fc0 sc0 ls8 ws6"> yangli<span class="_ _0"></span>uimu<span class="_ _0"></span>@g<span class="_ _0"></span>mail.<span class="_ _0"></span>co<span class="_ _0"></span>m </div><div class="t m0 xb h4 y3 ff1 fs2 fc0 sc0 ls9 ws7">Tian-Shuang<span class="_ _1"></span> Qiu</div><div class="t m0 xc h5 y4 ff1 fs3 fc0 sc0 ls2 ws2">1</div><div class="t m0 xd h4 y3 ff1 fs2 fc0 sc0 ls2 ws2"> </div><div class="t m0 xe h3 y5 ff1 fs1 fc0 sc0 lsa ws8">2. College of electron<span class="_ _1"></span>ic and Information engineering </div><div class="t m0 xf h3 y6 ff1 fs1 fc0 sc0 lsb ws9">Inner Mongolia University </div><div class="t m0 x10 h3 y7 ff1 fs1 fc0 sc0 ls5 wsa">Huhho<span class="_ _0"></span>t, C<span class="_ _0"></span>hina<span class="_ _0"></span> </div><div class="t m0 x2 h3 ya ff1 fs1 fc0 sc0 ls2 ws2"> </div><div class="t m0 x2 h3 yb ff1 fs1 fc0 sc0 ls2 ws2"> </div><div class="t m0 x11 h6 yc ff2 fs4 fc0 sc0 lsc ws2">Abstract<span class="ff3 lsd wsb">&#8212;M<span class="_ _0"></span>any signals e<span class="_ _0"></span>ncountere<span class="_ _0"></span>d in w<span class="_ _0"></span>ireless co<span class="_ _0"></span>mmunicatio<span class="_ _0"></span>n, </span></div><div class="t m0 x11 h6 yd ff3 fs4 fc0 sc0 lse wsc">telemetry, radar and sonar syste<span class="_ _0"></span>ms exhibit a cyclostationarity (or </div><div class="t m0 x11 h6 ye ff3 fs4 fc0 sc0 lsf wsd">spectral correl<span class="_ _0"></span>atio<span class="_ _0"></span>n) property, as a result of perio<span class="_ _0"></span>dically carri<span class="_ _0"></span>er </div><div class="t m0 x11 h6 yf ff3 fs4 fc0 sc0 ls10 wse">modul<span class="_ _0"></span>ati<span class="_ _0"></span>ng, <span class="_ _0"></span>multi<span class="_ _0"></span>plex<span class="_ _0"></span>ing<span class="_ _0"></span> and <span class="_ _0"></span>codi<span class="_ _0"></span>ng ope<span class="_ _0"></span>rati<span class="_ _0"></span>ons.<span class="_ _0"></span> By<span class="_ _0"></span> ex<span class="_ _0"></span>ploiti<span class="_ _0"></span>ng </div><div class="t m0 x11 h6 y10 ff3 fs4 fc0 sc0 lsf wsf">cyclostatio<span class="_ _0"></span>narity,<span class="_ _0"></span> i.e., eval<span class="_ _0"></span>uating the cy<span class="_ _0"></span>clic correlati<span class="_ _0"></span>on or cyc<span class="_ _0"></span>lic </div><div class="t m0 x11 h6 y11 ff3 fs4 fc0 sc0 ls11 ws10">spectru<span class="_ _0"></span>m<span class="_ _1"></span> of the recei<span class="_ _0"></span>ved signal<span class="_ _0"></span>s at certain cycle freque<span class="_ _0"></span>ncy, we </div><div class="t m0 x11 h6 y12 ff3 fs4 fc0 sc0 ls12 ws11">can extract the <span class="_ _0"></span>measures of<span class="_ _0"></span> the signals w<span class="_ _0"></span>ith different c<span class="_ _0"></span>ycle </div><div class="t m0 x11 h6 y13 ff3 fs4 fc0 sc0 ls10 ws12">freq<span class="_ _0"></span>uency<span class="_ _0"></span>. T<span class="_ _0"></span>hus, t<span class="_ _0"></span>he<span class="_ _0"></span> sig<span class="_ _0"></span>nal pr<span class="_ _0"></span>oce<span class="_ _0"></span>ssi<span class="_ _0"></span>ng alg<span class="_ _0"></span>orit<span class="_ _0"></span>hms w<span class="_ _0"></span>hi<span class="_ _0"></span>ch b<span class="_ _0"></span>ased <span class="_ _0"></span>on </div><div class="t m0 x11 h6 y14 ff3 fs4 fc0 sc0 ls13 ws13">cyclic statisti<span class="_ _0"></span>cs are hig<span class="_ _0"></span>hly toler<span class="_ _0"></span>ant to t<span class="_ _0"></span>he interfere<span class="_ _0"></span>nce and <span class="_ _0"></span>noise. </div><div class="t m0 x11 h6 y15 ff3 fs4 fc0 sc0 ls14 ws14">How<span class="_ _0"></span>ever, most of the cy<span class="_ _0"></span>closta<span class="_ _0"></span>tionarit<span class="_ _0"></span>y based <span class="_ _0"></span>methods ass<span class="_ _0"></span>ume </div><div class="t m0 x11 h6 y16 ff3 fs4 fc0 sc0 ls15 ws15">that the noise is G<span class="_ _0"></span>aussian noise.<span class="_ _0"></span> Hence, their <span class="_ _0"></span>perfor<span class="_ _0"></span>mance can be </div><div class="t m0 x11 h6 y17 ff3 fs4 fc0 sc0 ls16 ws16">degraded in real a<span class="_ _0"></span>pplications<span class="_ _0"></span> where the noises contai<span class="_ _0"></span>n non-</div><div class="t m0 x11 h6 y18 ff3 fs4 fc0 sc0 ls16 ws17">Gaussian i<span class="_ _0"></span>mpulsive component<span class="_ _0"></span>s. In this paper, we propose a n<span class="_ _0"></span>ew </div><div class="t m0 x11 h6 y19 ff3 fs4 fc0 sc0 ls17 ws18">approa<span class="_ _0"></span>ch for ex<span class="_ _0"></span>ploiti<span class="_ _0"></span>ng cycl<span class="_ _0"></span>ostatio<span class="_ _0"></span>narity of<span class="_ _0"></span> signals i<span class="_ _0"></span>n alpha-</div><div class="t m0 x11 h6 y1a ff3 fs4 fc0 sc0 ls18 ws19">stable impu<span class="_ _1"></span>lsive noise. Sim<span class="_ _1"></span>ulation r<span class="_ _1"></span>esults indicate<span class="_ _1"></span> a significantly </div><div class="t m0 x11 h6 y1b ff3 fs4 fc0 sc0 ls19 ws1a">better perfor<span class="_ _0"></span>mance for the new<span class="_ _0"></span> statistics in so<span class="_ _0"></span>me environ<span class="_ _0"></span>ments. </div><div class="t m0 x12 h7 y1c ff2 fs4 fc0 sc0 ls1a ws1b">Keywords-fract<span class="_ _0"></span>ional lower-ord<span class="_ _0"></span>er statistics; cyclost<span class="_ _0"></span>ationarity; </div><div class="t m0 x11 h7 y1d ff2 fs4 fc0 sc0 ls1b ws1c">cyclic c<span class="_ _1"></span>orrelation; cyclic spec<span class="_ _1"></span>trum </div><div class="t m0 x13 h3 y1e ff1 fs1 fc0 sc0 ls1c ws2">I.<span class="ff4 ls2"> <span class="_ _2"> </span><span class="ff1 fs5"> <span class="fs1">I</span><span class="ls1d">NTRODUCTION</span><span class="fs1"> </span></span></span></div><div class="t m0 x12 h3 y1f ff1 fs1 fc0 sc0 ls1e ws1d">Many conve<span class="_ _0"></span>ntional<span class="_ _0"></span> array signal pro<span class="_ _0"></span>cessing method<span class="_ _0"></span>s </div><div class="t m0 x11 h3 y20 ff1 fs1 fc0 sc0 ls1f ws1e">assume is th<span class="_ _0"></span>at the sour<span class="_ _0"></span>ce signals<span class="_ _0"></span> under consid<span class="_ _0"></span>eratio<span class="_ _0"></span>n are </div><div class="t m0 x11 h3 y21 ff1 fs1 fc0 sc0 ls20 ws1f">statistically<span class="_ _1"></span> stati<span class="_ _1"></span>onary<span class="_ _1"></span>, and<span class="_ _1"></span> that th<span class="_ _1"></span>eir tem<span class="_ _1"></span>poral<span class="_ _1"></span> samples<span class="_ _1"></span> are </div><div class="t m0 x11 h3 y22 ff1 fs1 fc0 sc0 ls21 ws20">uncorr<span class="_ _0"></span>elated. But<span class="_ _0"></span> for many man-mad<span class="_ _0"></span>e signal<span class="_ _0"></span>s encounter<span class="_ _0"></span>ed in </div><div class="t m0 x11 h3 y23 ff1 fs1 fc0 sc0 ls22 ws21">communicat<span class="_ _0"></span>ion systems, some p<span class="_ _0"></span>arameters do var<span class="_ _0"></span>y periodically </div><div class="t m0 x11 h3 y24 ff1 fs1 fc0 sc0 ls23 ws22">with time due to vario<span class="_ _0"></span>us periodic operat<span class="_ _0"></span>ions, such as sampling, </div><div class="t m0 x11 h3 y25 ff1 fs1 fc0 sc0 ls24 ws23">scanning,<span class="_ _1"></span> modulat<span class="_ _1"></span>ing, m<span class="_ _1"></span>ultiplexin<span class="_ _1"></span>g, a<span class="_ _1"></span>re appro<span class="_ _1"></span>priately m<span class="_ _1"></span>odeled </div><div class="t m0 x11 h3 y26 ff1 fs1 fc0 sc0 ls25 ws24">as cy<span class="_ _1"></span>clostationa<span class="_ _1"></span>ry signals <span class="_ _1"></span>[1-2]. S<span class="_ _1"></span>o far,<span class="_ _1"></span> the cy<span class="_ _1"></span>clostationa<span class="_ _1"></span>rity </div><div class="t m0 x11 h3 y27 ff1 fs1 fc0 sc0 ls1c ws25">prope<span class="_ _1"></span>rty<span class="_ _1"></span> has <span class="_ _1"></span>been w<span class="_ _1"></span>idely<span class="_ _1"></span> us<span class="_ _1"></span>ed to i<span class="_ _1"></span>mpr<span class="_ _1"></span>ove p<span class="_ _1"></span>erfo<span class="_ _1"></span>rman<span class="_ _1"></span>ce of </div><div class="t m0 x11 h3 y28 ff1 fs1 fc0 sc0 ls26 ws26">signal proce<span class="_ _0"></span>ssing tasks in communicat<span class="_ _0"></span>ion, telemetr<span class="_ _0"></span>y, and radar </div><div class="t m0 x11 h3 y29 ff1 fs1 fc0 sc0 ls27 ws27">sys<span class="_ _1"></span>tems [3-5<span class="_ _1"></span>]. By<span class="_ _1"></span> virtue <span class="_ _1"></span>of the f<span class="_ _1"></span>act th<span class="_ _1"></span>at these<span class="_ _1"></span> algor<span class="_ _1"></span>ithms </div><div class="t m0 x11 h3 y2a ff1 fs1 fc0 sc0 ls24 ws28">exhibit th<span class="_ _1"></span>eir sig<span class="_ _1"></span>nal selectiv<span class="_ _1"></span>ity<span class="_ _1"></span> regardless of th<span class="_ _1"></span>e extent<span class="_ _1"></span> of </div><div class="t m0 x11 h3 y2b ff1 fs1 fc0 sc0 ls28 ws29">temporal<span class="_ _1"></span>, spect<span class="_ _1"></span>ral, <span class="_ _1"></span>or spatia<span class="_ _1"></span>l overla<span class="_ _1"></span>p amon<span class="_ _1"></span>g receiv<span class="_ _1"></span>ed signa<span class="_ _1"></span>ls. </div><div class="t m0 x11 h3 y2c ff1 fs1 fc0 sc0 ls24 ws2a">Unfortuna<span class="_ _1"></span>tely, m<span class="_ _1"></span>ost of th<span class="_ _1"></span>ese cyclost<span class="_ _1"></span>ationarity<span class="_ _1"></span>-exploiti<span class="_ _1"></span>ng </div><div class="t m0 x11 h3 y2d ff1 fs1 fc0 sc0 ls23 ws2b">method<span class="_ _0"></span>s are prop<span class="_ _0"></span>osed under<span class="_ _0"></span> assumptio<span class="_ _0"></span>n of Gaussian </div><div class="t m0 x11 h3 y2e ff1 fs1 fc0 sc0 ls29 ws2c">distri<span class="_ _1"></span>buti<span class="_ _1"></span>on nois<span class="_ _1"></span>e. Bu<span class="_ _1"></span>t there <span class="_ _1"></span>are m<span class="_ _1"></span>any ph<span class="_ _1"></span>enom<span class="_ _1"></span>ena in sig<span class="_ _1"></span>nal </div><div class="t m0 x11 h3 y2f ff1 fs1 fc0 sc0 ls23 ws2d">proce<span class="_ _0"></span>ssing that are decid<span class="_ _0"></span>edly non-G<span class="_ _0"></span>aussian. Many noi<span class="_ _0"></span>ses in </div><div class="t m0 x11 h3 y30 ff1 fs1 fc0 sc0 ls2a ws2e">practice<span class="_ _1"></span> such as<span class="_ _1"></span> low<span class="_ _1"></span> frequen<span class="_ _1"></span>cy atm<span class="_ _1"></span>ospheric n<span class="_ _1"></span>oise, m<span class="_ _1"></span>ultiuser </div><div class="t m0 x11 h3 y31 ff1 fs1 fc0 sc0 ls24 ws2f">interfer<span class="_ _1"></span>ence, car<span class="_ _1"></span> ignitions,<span class="_ _1"></span> and other<span class="_ _1"></span> types of natur<span class="_ _1"></span>ally </div><div class="t m0 x11 h3 y32 ff1 fs1 fc0 sc0 ls2b ws30">occurring<span class="_ _1"></span> or m<span class="_ _1"></span>an-m<span class="_ _1"></span>ade noise <span class="_ _1"></span>that m<span class="_ _1"></span>ay ex<span class="_ _1"></span>hibit hig<span class="_ _1"></span>h am<span class="_ _1"></span>plitudes </div><div class="t m0 x11 h3 y33 ff1 fs1 fc0 sc0 ls2b ws31">for sm<span class="_ _1"></span>all durati<span class="_ _1"></span>on time int<span class="_ _1"></span>erva<span class="_ _1"></span>ls [6-7]. <span class="_ _1"></span> </div><div class="t m0 x12 h3 y34 ff1 fs1 fc0 sc0 ls2c ws32">Studies and experimental<span class="_ _0"></span> measurements ha<span class="_ _0"></span>ve show<span class="_ _1"></span>n that </div><div class="t m0 x11 h3 y35 ff1 fs1 fc0 sc0 ls25 ws33">alpha-sta<span class="_ _1"></span>ble distri<span class="_ _1"></span>bution<span class="_ _1"></span> is m<span class="_ _1"></span>ore suitable<span class="_ _1"></span> for m<span class="_ _1"></span>odeling n<span class="_ _1"></span>oise of<span class="_ _1"></span> </div><div class="t m0 x11 h3 y36 ff1 fs1 fc0 sc0 ls2b ws34">impulsive n<span class="_ _1"></span>ature than <span class="_ _1"></span>Gaussian<span class="_ _1"></span> distri<span class="_ _1"></span>bution. How<span class="_ _1"></span>ever, <span class="_ _1"></span>as </div><div class="t m0 x11 h3 y37 ff1 fs1 fc0 sc0 ls2d ws35">stable distr<span class="_ _0"></span>ibution does not have finite seco<span class="_ _0"></span>nd-order mome<span class="_ _0"></span>nts </div><div class="t m0 x11 h8 y38 ff1 fs1 fc0 sc0 ls21 ws36">(exce<span class="_ _0"></span>pt for <span class="ff5 ls2 ws2">&#945;</span><span class="ls2e ws37">=2), conventional<span class="_ _0"></span> signal-selec<span class="_ _0"></span>tive algorit<span class="_ _0"></span>hms </span></div><div class="t m0 x14 h3 y39 ff1 fs1 fc0 sc0 ls2f ws38">base<span class="_ _0"></span>d on the seco<span class="_ _0"></span>nd-ord<span class="_ _0"></span>er cyclos<span class="_ _0"></span>tat<span class="_ _0"></span>ionari<span class="_ _0"></span>ty can be severa<span class="_ _0"></span>lly </div><div class="t m0 x14 h3 y3a ff1 fs1 fc0 sc0 ls30 ws39">weak<span class="_ _1"></span>ened in st<span class="_ _1"></span>able dist<span class="_ _1"></span>ributio<span class="_ _1"></span>n impulsiv<span class="_ _1"></span>e noise.<span class="_ _1"></span> Although<span class="_ _1"></span> the </div><div class="t m0 x14 h3 y3b ff1 fs1 fc0 sc0 ls31 ws3a">fract<span class="_ _1"></span>iona<span class="_ _1"></span>l l<span class="_ _1"></span>ower-<span class="_ _1"></span>orde<span class="_ _1"></span>r sta<span class="_ _1"></span>tist<span class="_ _1"></span>ics<span class="_ _1"></span> (FL<span class="_ _1"></span>OS) <span class="_ _1"></span>base<span class="_ _1"></span>d met<span class="_ _1"></span>hods<span class="_ _1"></span> are<span class="_ _1"></span> </div><div class="t m0 x14 h3 y3c ff1 fs1 fc0 sc0 ls25 ws3b">robust t<span class="_ _1"></span>o both Gau<span class="_ _1"></span>ssian an<span class="_ _1"></span>d impulsive<span class="_ _1"></span> noises [<span class="_ _1"></span>6], th<span class="_ _1"></span>e </div><div class="t m0 x14 h3 y3d ff1 fs1 fc0 sc0 ls32 ws3c">interfe<span class="_ _1"></span>ring sig<span class="_ _1"></span>nals wh<span class="_ _1"></span>ich occu<span class="_ _1"></span>py the sam<span class="_ _1"></span>e spectr<span class="_ _1"></span>al ban<span class="_ _1"></span>d as t<span class="_ _1"></span>he </div><div class="t m0 x14 h3 y3e ff1 fs1 fc0 sc0 ls33 ws3d">sign<span class="_ _1"></span>al of interest<span class="_ _1"></span> can degr<span class="_ _1"></span>ade the perf<span class="_ _1"></span>orm<span class="_ _1"></span>ance of these<span class="_ _1"></span> </div><div class="t m0 x14 h3 y3f ff1 fs1 fc0 sc0 ls34 ws3e">me<span class="_ _1"></span>thods.<span class="_ _1"></span> </div><div class="t m0 x15 h3 y40 ff1 fs1 fc0 sc0 ls35 ws3f"> <span class="_ _3"></span>In th<span class="_ _1"></span>is w<span class="_ _1"></span>ork, w<span class="_ _1"></span>e analy<span class="_ _1"></span>ze the <span class="_ _1"></span>effects <span class="_ _1"></span>of im<span class="_ _1"></span>pulsiv<span class="_ _1"></span>e noise<span class="_ _1"></span> on </div><div class="t m0 x14 h3 y41 ff1 fs1 fc0 sc0 ls36 ws40">conve<span class="_ _0"></span>ntional seco<span class="_ _0"></span>nd-orde<span class="_ _0"></span>r cyclic statist<span class="_ _0"></span>ics. By fusing fract<span class="_ _0"></span>ional </div><div class="t m0 x14 h3 y42 ff1 fs1 fc0 sc0 ls37 ws41">lower<span class="_ _0"></span> order theor<span class="_ _0"></span>y and spectral corre<span class="_ _0"></span>lation the<span class="_ _0"></span>ory, we derive<span class="_ _0"></span> </div><div class="t m0 x14 h3 y43 ff1 fs1 fc0 sc0 ls38 ws42">two types of FL<span class="_ _1"></span>OS based cyclic<span class="_ _1"></span> statistics<span class="_ _1"></span> that are r<span class="_ _1"></span>obust to </div><div class="t m0 x14 h3 y44 ff1 fs1 fc0 sc0 ls39 ws43">impu<span class="_ _1"></span>lsive noise <span class="_ _1"></span>and exh<span class="_ _1"></span>ibit<span class="_ _1"></span> the sp<span class="_ _1"></span>ectral <span class="_ _1"></span>correlati<span class="_ _1"></span>on pr<span class="_ _1"></span>operty<span class="_ _1"></span>. </div><div class="t m0 x14 h3 y45 ff1 fs1 fc0 sc0 ls3 ws44">These n<span class="_ _1"></span>ew f<span class="_ _1"></span>racti<span class="_ _1"></span>onal l<span class="_ _1"></span>ower <span class="_ _1"></span>order cy<span class="_ _1"></span>cli<span class="_ _1"></span>c stat<span class="_ _1"></span>istics h<span class="_ _1"></span>ave <span class="_ _1"></span>the </div><div class="t m0 x14 h3 y46 ff1 fs1 fc0 sc0 ls2b ws45">advantages<span class="_ _1"></span> of <span class="_ _1"></span>the FL<span class="_ _1"></span>OS an<span class="_ _1"></span>d cy<span class="_ _1"></span>clic statistics<span class="_ _1"></span>. Sim<span class="_ _1"></span>ulation <span class="_ _1"></span>results<span class="_ _1"></span> </div><div class="t m0 x14 h3 y47 ff1 fs1 fc0 sc0 ls3 ws46">demons<span class="_ _1"></span>trate th<span class="_ _1"></span>e ef<span class="_ _1"></span>fectiv<span class="_ _1"></span>eness an<span class="_ _1"></span>d r<span class="_ _1"></span>obustn<span class="_ _1"></span>ess of<span class="_ _1"></span> the<span class="_ _1"></span> new </div><div class="t m0 x14 h3 y48 ff1 fs1 fc0 sc0 ls3a ws2">statistics<span class="_ _1"></span>. </div><div class="t m0 x16 h3 y49 ff1 fs1 fc0 sc0 ls1c ws2">II.<span class="ff4 ls2"> <span class="_ _4"> </span><span class="ff1">I</span></span></div><div class="t m0 x17 h3 y4a ff1 fs5 fc0 sc0 ls1d ws2">MPULSIVE <span class="fs1 ls2">N</span><span class="ls3b ws47">OISE<span class="_ _1"></span> AN<span class="_ _1"></span>D <span class="fs1 ls2 ws2">I<span class="fs5 ls3c">TS </span>E</span><span class="ls3d ws48">FFECT ON </span></span></div><div class="t m0 x18 h3 y4b ff1 fs1 fc0 sc0 ls2 ws2">C<span class="fs5 ls3e">YCLOSTATIONAR<span class="_ _0"></span>ITY</span> </div><div class="t m0 x15 h3 y4c ff1 fs1 fc0 sc0 ls3f ws49">Alph<span class="_ _1"></span>a-sta<span class="_ _1"></span>ble m<span class="_ _1"></span>odel<span class="_ _1"></span> is th<span class="_ _1"></span>e onl<span class="_ _1"></span>y<span class="_ _1"></span> one w<span class="_ _1"></span>hose m<span class="_ _1"></span>embers<span class="_ _1"></span> sati<span class="_ _1"></span>sfy<span class="_ _1"></span> </div><div class="t m0 x14 h3 y4d ff1 fs1 fc0 sc0 ls2 ws4a">the stability<span class="_ _1"></span> an<span class="_ _1"></span>d the Gener<span class="_ _1"></span>alized Cent<span class="_ _1"></span>er Lim<span class="_ _1"></span>it Theorem<span class="_ _1"></span> [6]. </div><div class="t m0 x14 h3 y4e ff1 fs1 fc0 sc0 ls40 ws4b">The fam<span class="_ _1"></span>ily of st<span class="_ _1"></span>able <span class="_ _1"></span>distribut<span class="_ _1"></span>ions<span class="_ _1"></span> define<span class="_ _1"></span>d by it<span class="_ _1"></span>s chara<span class="_ _1"></span>cterist<span class="_ _1"></span>ic </div><div class="t m0 x14 h3 y4f ff1 fs1 fc0 sc0 ls22 ws4c">functio<span class="_ _0"></span>n as follo<span class="_ _0"></span>ws: </div><div class="t m0 x14 h8 y50 ff5 fs1 fc0 sc0 ls2 ws2"> </div><div class="t m0 x19 h9 y51 ff1 fs6 fc0 sc0 ls41 ws4d">exp{<span class="_ _5"> </span>[<span class="_ _3"></span>1<span class="_ _6"> </span>sgn(<span class="_ _7"> </span>)<span class="_ _8"> </span>tan(<span class="_ _9"> </span>)]},<span class="_ _0"></span> 1</div><div class="t m0 x1a h9 y52 ff1 fs6 fc0 sc0 ls2 ws2">2</div><div class="t m0 x1b h9 y53 ff1 fs6 fc0 sc0 ls2 ws2">2</div><div class="t m0 x19 h9 y54 ff1 fs6 fc0 sc0 ls42 ws4e">exp{<span class="_ _5"> </span>[<span class="_ _3"></span>1<span class="_ _6"> </span>sgn(<span class="_ _7"> </span>)<span class="_ _a"> </span>log<span class="_ _b"> </span>]},<span class="_ _c"></span> 1</div><div class="t m0 x1c ha y55 ff1 fs7 fc0 sc0 ls43 ws2">()</div><div class="t m0 x1d hb y51 ff6 fs6 fc0 sc0 ls44 ws2">jat<span class="_ _4"> </span>t<span class="_ _d"> </span>j<span class="_ _e"> </span>t</div><div class="t m0 x1d hb y54 ff6 fs6 fc0 sc0 ls44 ws2">jat<span class="_ _4"> </span>t<span class="_ _d"> </span>j<span class="_ _e"> </span>t<span class="_ _f"> </span>t</div><div class="t m0 x1e hc y55 ff6 fs7 fc0 sc0 ls2 ws2">t</div><div class="t m1 x1f hd y56 ff5 fs8 fc0 sc0 ls2 ws2">&#945;</div><div class="t m1 x1f hd y57 ff5 fs8 fc0 sc0 ls2 ws2">&#945;</div><div class="t m2 x20 he y58 ff5 fs9 fc0 sc0 ls45 ws2">&#945;&#960;</div><div class="t m2 x21 he y59 ff5 fs9 fc0 sc0 ls46 ws2">&#947;&#946;<span class="_ _10"> </span>&#945;</div><div class="t m2 x21 he y5a ff5 fs9 fc0 sc0 ls46 ws2">&#947;&#946;<span class="_ _11"> </span>&#945;</div><div class="t m2 x22 he y5b ff5 fs9 fc0 sc0 ls2 ws2">&#960;</div><div class="t m3 x23 hf y55 ff5 fsa fc0 sc0 ls2 ws2">&#981;</div><div class="t m0 x24 h10 y51 ff5 fs6 fc0 sc0 ls47 ws2">&#8722;+<span class="_ _12"> </span>&#8800;</div><div class="t m0 x24 h10 y54 ff5 fs6 fc0 sc0 ls47 ws2">&#8722;+<span class="_ _13"> </span>=</div><div class="t m0 x25 h11 y5c ff7 fs7 fc0 sc0 ls2 ws2">&#9127;</div><div class="t m0 x25 h11 y5d ff7 fs7 fc0 sc0 ls2 ws2">&#9130;</div><div class="t m0 x26 h12 y5e ff5 fs7 fc0 sc0 ls2 ws2">=</div><div class="t m0 x25 h11 y5f ff7 fs7 fc0 sc0 ls2 ws2">&#9128;</div><div class="t m0 x25 h11 y60 ff7 fs7 fc0 sc0 ls2 ws2">&#9130;</div><div class="t m0 x25 h11 y61 ff7 fs7 fc0 sc0 ls2 ws2">&#9129;</div><div class="t m0 x27 h12 y5e ff5 fs7 fc0 sc0 ls48 ws4f">. (1) </div><div class="t m0 x14 ha y62 ff1 fs7 fc0 sc0 ls49 ws50">Thus a s<span class="_ _1"></span>table <span class="_ _1"></span>distributi<span class="_ _1"></span>on is c<span class="_ _1"></span>ompletely<span class="_ _1"></span> determ<span class="_ _1"></span>ined by<span class="_ _1"></span> four </div><div class="t m0 x14 ha y63 ff1 fs7 fc0 sc0 ls4a ws51">param<span class="_ _1"></span>eters: 1) the loca<span class="_ _1"></span>tion param<span class="_ _1"></span>eter </div><div class="t m0 x1b h12 y64 ff6 fs1 fc0 sc0 ls2 ws2">a<span class="_ _14"> </span><span class="ff1 fs7">(<span class="_ _15"> </span></span>a<span class="_ _16"></span><span class="ff5 fs7 ls48">&#8722;&#8734;<span class="_"> </span>&lt;<span class="_ _17"> </span>&lt;<span class="_"> </span>&#8734;<span class="_"> </span><span class="ff1 ls4b ws52">),<span class="_ _1"></span> 2) th<span class="_ _1"></span>e </span></span></div><div class="t m0 x14 ha y65 ff1 fs7 fc0 sc0 ls4c ws53">scale p<span class="_ _1"></span>aram<span class="_ _1"></span>eter </div><div class="c x19 y66 w2 h13"><div class="t m4 x0 h14 y67 ff5 fsb fc0 sc0 ls2 ws2">&#947;</div></div><div class="t m0 x28 ha y68 ff1 fs7 fc0 sc0 ls2 ws2">(</div><div class="t m0 x29 h15 y69 ff1 fsc fc0 sc0 ls2 ws2">0</div><div class="c x2a y6a w3 h16"><div class="t m3 x0 h17 y67 ff5 fsd fc0 sc0 ls2 ws2">&#947;</div></div><div class="t m0 x2b h18 y69 ff5 fsc fc0 sc0 ls2 ws2">&gt;</div><div class="t m0 x2c ha y68 ff1 fs7 fc0 sc0 ls4d ws54">), 3) the ind<span class="_ _0"></span>ex of skewness </div><div class="c x2d y6b w4 h16"><div class="t m3 x0 h17 y67 ff5 fsd fc0 sc0 ls2 ws2">&#946;</div></div><div class="t m0 x2e ha y6c ff1 fs7 fc0 sc0 ls2 ws2">(</div><div class="t m0 x2f h15 y6d ff1 fsc fc0 sc0 ls4e ws2">11</div><div class="c x30 y6b w3 h16"><div class="t m3 x0 h17 y67 ff5 fsd fc0 sc0 ls2 ws2">&#946;</div></div><div class="t m0 x31 h18 y6d ff5 fsc fc0 sc0 ls4f ws2">&#8722;&#8804;<span class="_ _18"> </span>&#8804;</div><div class="t m0 x32 ha y6c ff1 fs7 fc0 sc0 ls50 ws55">), 4)<span class="_ _1"></span> the<span class="_ _1"></span> characte<span class="_ _1"></span>ristic<span class="_ _1"></span> expon<span class="_ _1"></span>ent </div><div class="t m4 x33 h19 y6c ff5 fse fc0 sc0 ls2 ws2">&#945;</div><div class="t m0 x34 ha y6c ff1 fs7 fc0 sc0 ls2 ws2">(<span class="_ _19"> </span><span class="fsf ls51">02</span></div><div class="t m4 x35 h19 y6c ff5 fse fc0 sc0 ls2 ws2">&#945;</div><div class="t m0 x36 h1a y6c ff5 fsf fc0 sc0 ls52 ws2">&lt;&#8804;<span class="_ _1a"></span><span class="ff1 fs7 ls53">). </span></div><div class="t m0 x14 ha y6e ff1 fs7 fc0 sc0 ls54 ws56">When skewness </div><div class="t m0 x28 h15 y6f ff1 fsc fc0 sc0 ls2 ws2">0</div><div class="c x17 y70 w3 h16"><div class="t m3 x0 h17 y67 ff5 fsd fc0 sc0 ls2 ws2">&#946;</div></div><div class="t m0 x37 h18 y6f ff5 fsc fc0 sc0 ls2 ws2">=</div><div class="t m0 x38 ha y71 ff1 fs7 fc0 sc0 ls55 ws57">, th<span class="_ _1"></span>e di<span class="_ _1"></span>stri<span class="_ _1"></span>buti<span class="_ _1"></span>on<span class="_ _1"></span> is s<span class="_ _1"></span>ymm<span class="_ _1"></span>etric<span class="_ _1"></span> ab<span class="_ _1"></span>out t<span class="_ _1"></span>he<span class="_ _1"></span> </div><div class="t m0 x14 ha y72 ff1 fs7 fc0 sc0 ls56 ws2">center<span class="_ _1"></span> </div><div class="t m0 x39 ha y73 ff6 fs1 fc0 sc0 ls2 ws2">a<span class="_ _1b"> </span><span class="ff1 fs7 ws58">. Symm<span class="_ _1"></span>etric st<span class="_ _1"></span>able di<span class="_ _1"></span>stribu<span class="_ _1"></span>tions<span class="_ _1"></span> with<span class="_ _1"></span> characte<span class="_ _1"></span>risti<span class="_ _1"></span>c </span></div><div class="t m0 x14 ha y74 ff1 fs7 fc0 sc0 ls57 ws2">expone<span class="_ _0"></span>nt</div><div class="t m4 x3a h19 y75 ff5 fse fc0 sc0 ls2 ws2">&#945;</div><div class="t m0 x1c ha y75 ff1 fs7 fc0 sc0 ls58 ws59">ar<span class="_ _0"></span>e called<span class="_ _0"></span> symmetr<span class="_ _0"></span>ic </div><div class="t m4 x3b h19 y75 ff5 fse fc0 sc0 ls2 ws2">&#945;</div><div class="t m0 x3c h1b y75 ff6 fs1 fc0 sc0 ls2 ws2">-<span class="ff1 fsf ls59 ws5a">stable or<span class="_ _0"></span> <span class="_ _14"> </span></span><span class="fsf ls5a">SS</span></div><div class="t m4 x3d h19 y75 ff5 fse fc0 sc0 ls2 ws2">&#945;</div><div class="t m0 x3e h1b y75 ff1 fsf fc0 sc0 ls5b ws2">. </div><div class="t m0 x15 h1b y76 ff1 fsf fc0 sc0 ls5c ws5b">The funda<span class="_ _0"></span>mental of the spec<span class="_ _0"></span>tral corr<span class="_ _0"></span>elation theor<span class="_ _0"></span>y of </div><div class="t m0 x14 h1b y77 ff1 fsf fc0 sc0 ls5d ws5c">cyclosta<span class="_ _1"></span>tionary<span class="_ _1"></span> time-<span class="_ _1"></span>series is com<span class="_ _1"></span>prehens<span class="_ _1"></span>ive given<span class="_ _1"></span> in [1<span class="_ _1"></span>]. This<span class="_ _1"></span> </div><div class="t m0 x14 h1b y78 ff1 fsf fc0 sc0 ls5e ws5d">main<span class="_ _1"></span>ly includes<span class="_ _1"></span> the <span class="_ _1"></span>limit cy<span class="_ _1"></span>clic<span class="_ _1"></span> autoc<span class="_ _1"></span>orrelati<span class="_ _1"></span>on and<span class="_ _1"></span> lim<span class="_ _1"></span>it cyclic<span class="_ _1"></span> </div><div class="t m0 x14 h1b y79 ff1 fsf fc0 sc0 ls5f ws5e">spect<span class="_ _1"></span>rum, w<span class="_ _1"></span>hich are <span class="_ _1"></span>the p<span class="_ _1"></span>roperty<span class="_ _1"></span> of w<span class="_ _1"></span>hat is call<span class="_ _1"></span>ed sec<span class="_ _1"></span>ond-or<span class="_ _1"></span>der </div><div class="t m0 x14 h1b y7a ff1 fsf fc0 sc0 ls60 ws5f">perio<span class="_ _1"></span>dicity o<span class="_ _1"></span>r cy<span class="_ _1"></span>clostationa<span class="_ _1"></span>rity<span class="_ _1"></span>. As [1]<span class="_ _1"></span> reve<span class="_ _1"></span>als that<span class="_ _1"></span> cy<span class="_ _1"></span>clic </div><div class="t m0 x14 h1b y7b ff1 fsf fc0 sc0 ls61 ws60">autocor<span class="_ _1"></span>relation<span class="_ _1"></span> is the F<span class="_ _1"></span>ourie<span class="_ _1"></span>r coeff<span class="_ _1"></span>icient of<span class="_ _1"></span> the F<span class="_ _1"></span>ourie<span class="_ _1"></span>r seri<span class="_ _1"></span>es </div><div class="t m0 x14 h1b y7c ff1 fsf fc0 sc0 ls62 ws61">expansi<span class="_ _1"></span>on of<span class="_ _3"></span> second-o<span class="_ _1"></span>rder<span class="_ _1"></span> autoc<span class="_ _1"></span>orrel<span class="_ _1"></span>ation f<span class="_ _1"></span>uncti<span class="_ _1"></span>on. <span class="_ _1"></span>The </div><div class="t m0 x14 h1b y7d ff1 fsf fc0 sc0 ls5d ws62">definition<span class="_ _1"></span> of cy<span class="_ _1"></span>clic aut<span class="_ _1"></span>ocor<span class="_ _1"></span>relation<span class="_ _1"></span> is, </div><div class="t m0 x12 h1c y7e ff1 fs5 fc0 sc0 ls63 ws63">This w<span class="_ _1"></span>or<span class="_ _1"></span>k was sup<span class="_ _1"></span>porte<span class="_ _1"></span>d by<span class="_ _1"></span> the Nat<span class="_ _1"></span>ional<span class="_ _1"></span> Scie<span class="_ _1"></span>nce F<span class="_ _1"></span>oundat<span class="_ _1"></span>ion o<span class="_ _1"></span>f Chi<span class="_ _1"></span>na </div><div class="t m0 x11 h1c y7f ff1 fs5 fc0 sc0 ls64 ws64">under <span class="_ _0"></span>Grant 6<span class="_ _0"></span>087212<span class="_ _0"></span>2 </div><div class="t m0 x3f h1d y80 ff8 fs4 fc0 sc0 ls2 ws2">978-1-4244-6252-0/11/$26.00 &#169;2011 IEEE</div></div><div class="pi" data-data='{"ctm":[1.611639,0.000000,0.000000,1.611639,0.000000,0.000000]}'></div></div> </body> </html>
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