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ThreeColumnLayout_leftColumn__Tf0iY"> <div> <div> <div id="article-table-of-contents" data-ismobile="false"> <div class="TableOfContents_tableOfContents__tmWzJ"> <div class="TableOfContents_tableOfContents__title__sU5vH"> 在这一页上</gydF4y2Badiv> <a class="TableOfContents_tableOfContents__item__zC0yd" href="#abstract">文摘</一个><一个class="TableOfContents_tableOfContents__item__zC0yd" href="#introduction">介绍</一个><一个class="TableOfContents_tableOfContents__item__zC0yd" href="#discussion-and-future-development">讨论</一个><一个class="TableOfContents_tableOfContents__item__zC0yd" href="#references">引用</一个><一个class="TableOfContents_tableOfContents__item__zC0yd" href="#copyright">版权</一个><一个class="TableOfContents_tableOfContents__item__zC0yd" href="#related-articles">相关文章</一个></div> </div> </div> </div> </div> <div class="ant-col ThreeColumnLayout_middleColumn__Pn_ys"> <div class="ArticleMiddleSection_articleMiddleSection__DtVY3"> <div class="articleHeader"> <div class="articleHeader__specialIssue"> <span class="articleHeader__specialIssue_tag">特殊的问题</年代p一个n><h2class="articleHeader__specialIssue_title">学术软件应用电磁大脑映射使用梅格和脑电图</h2><一个href="//www.newsama.com/journals/cin/si/138743/" class="articleHeader__specialIssue_url" target="_blank" rel="noreferrer">把这个特殊的问题</一个></div> <strong>研究文章|<gydF4y2Ba!-- -->开放获取</年代trong><div class="articleHeader__meta"> <span>体积<gydF4y2Ba!-- -->2011年<gydF4y2Ba!-- -->|</年代p一个n><年代p一个n>文章的ID<gydF4y2Ba!-- -->406391年<gydF4y2Ba!-- -->|</年代p一个n><年代p一个nclass="articleHeader__meta_doiLink"><a href="https://doi.org/10.1155/2011/406391" aria-label="Doi-link" target="_blank" rel="noreferrer">https://doi.org/10.1155/2011/406391</一个></年代p一个n></div> <div class="simpleShowMore"> <button class="simpleShowMore__button">显示引用</gydF4y2Babutton> </div> <h1 class="articleHeader__title">PyEEG:一个开放源码的Python模块为脑电图/梅格特征提取</h1><gydF4y2Badiv class="articleHeader__authors"> <span class="articleHeader__authors_author"><strong>福勒斯特保盛</年代trong><一个href="//www.newsama.com/cdn-cgi/l/email-protection" aria-label="Mail Option"><span role="img" class="anticon"> <svg version="1.0" xmlns="http://www.w3.org/2000/svg" width="1em" height="1em" viewbox="0 0 1401 1101"> <path fill="#6ba439" d="M132.5 2.1C101.4 6 71.1 20.5 48.3 42.4c-22.7 21.7-37.5 48.3-44.6 80l-2.2 10.1v837l2.2 10.1c6.7 30 19.3 53.9 39.8 75.3 23.3 24.3 56.4 40.9 90 45 12.8 1.6 1122.2 1.6 1135 0 38.9-4.8 75.9-25.6 100-56.4 15-19.3 24.2-39 29.8-63.9l2.2-10.1v-837l-2.2-10.1c-7.1-31.8-21.9-58.3-44.6-80.1-20.2-19.2-43.9-31.7-73.6-38.5l-9.6-2.3L705 1.4c-321.9-.1-568.5.2-572.5.7zm1123.4 99.5c1.7.4 3.1 1 3.1 1.4 0 .5-125.6 87.7-279 194L700.9 490.2 422 297C268.5 190.7 143 103.4 143 103c0-.5 1-1.1 2.3-1.3 3.5-.7 1107.1-.8 1110.6-.1zM401 404c164.4 113.8 299.4 207 300 207 .6 0 135.6-93.2 300.1-207 164.5-113.9 299.3-207 299.5-207 .2 0 .4 170.9.4 379.7 0 417.9.5 386-6.1 398.3-6.2 11.6-19 21.4-31.9 24.4-5.8 1.4-67.4 1.6-562 1.6s-556.2-.2-562-1.6c-12.9-3-25.7-12.8-31.9-24.4-6.6-12.3-6.1 19.6-6.1-398.3 0-208.8.2-379.7.5-379.7S236.6 290.1 401 404z"></path> </svg></span></a>,<年代up>1</gydF4y2Ba年代up></年代p一个n><年代pan class="articleHeader__authors_author">鑫刘<gydF4y2Ba!-- -->,<年代up>2</gydF4y2Ba年代up></年代p一个n><年代pan class="articleHeader__authors_author">和<gydF4y2Ba!-- -->克里斯蒂娜张<年代up>3</gydF4y2Ba年代up></年代p一个n></div> <div class="simpleShowMore"> <button class="simpleShowMore__button">显示更多</gydF4y2Babutton> </div> <div class="articleHeader__academicEditor"> <strong>学术编辑器:</年代trong><年代p一个n>Sylvain Baillet</年代p一个n></div> <div class="articleHeader__timeline"> <div class="articleHeader__timeline_item "> <strong>收到了</年代trong><年代p一个n>2010年8月31日</年代p一个n></div> <div class="articleHeader__timeline_item "> <strong>修改后的</年代trong><年代p一个n>2010年10月26日</年代p一个n></div> <div class="articleHeader__timeline_item "> <strong>接受</年代trong><年代p一个n>2010年12月31日</年代p一个n></div> <div class="articleHeader__timeline_item articleHeader__timeline_item_sticky"> <strong>发表</年代trong><年代p一个n>2011年3月29日</年代p一个n></div> </div> </div> <div class="articleBody"> <div class="xml-content"> <h4 class="header" id="abstract">文摘</h4><p>gydF4y2Ba从脑电图信号计算机辅助诊断的神经疾病(或其他生理信号,可视为时间序列,例如,MEG)是一个新兴领域,得到了太多的关注。特征提取是一个关键的组件在EEG信号的分析。在我们之前的作品中,我们实现了许多脑电图特征提取功能在Python编程语言。Python是越来越多的在科学计算,一个开源的Python模块中提取脑电图的特点计算神经科学家有可能节省很多时间。在本文中,我们介绍PyEEG,脑电图特征提取的一个开源的Python模块。</p><年代p一个nclass="end-abs"></span> <h4 id="introduction">1。介绍</h4><p>gydF4y2Ba计算机辅助诊断基于脑电图可能在过去十年已成为一些神经系统疾病如阿尔茨海默病(<一个href="#B1">1</一个>,<gydF4y2Ba一个href="#B2">2</一个>和癫痫<一个href="#B3">3</一个>,<gydF4y2Ba一个href="#B4">4</一个>]。实现系统可以在这些疾病的早期诊断非常有用。例如,传统的癫痫的诊断可能需要训练有素的医生视觉屏幕而冗长的脑电图记录计算机辅助系统可以缩短这个耗时的过程通过检测和挑选感兴趣的脑电图段医生<一个href="#B5">5</一个>,<gydF4y2Ba一个href="#B6">6</一个>]。最重要的是,计算机可以扩展我们分析信号的能力。最近,研究人员已经开发出系统(<一个href="#B3">3</一个>,<gydF4y2Ba一个href="#B4">4</一个>,<gydF4y2Ba一个href="#B7">7</一个>,<gydF4y2Ba一个href="#B8">8</一个>),希望可以使用(任何)随机发作(即。,non- - - - - -年代e我zure)EEG records for epilepsy diagnosis in instances that are difficult for physicians to make diagnostic decisions with their naked eyes. In addition to analyzing existing signals, this computer-based approach can help us model the brain and predict future signals, for example, seizure prediction [<一个href="#B9">9</一个>,<gydF4y2Ba一个href="#B10">10</一个>]。</p><p>gydF4y2Ba上述系统依赖于描述EEG信号某些特性,一个步骤被称为特征提取。脑电图特征可以来自不同的领域,研究时间序列:从信号处理功率谱密度,从计算几何分形维度,从信息熵理论,等等。一个开源工具,可以提取脑电特征有利于计算神经科学社区由于特征提取是反复调用EEG信号分析。由于Python的科学计算中越来越受欢迎,特别是在计算神经科学,脑电图特征提取的Python模块将非常有用。作为回应,我们开发了PyEEG,脑电图特征提取的Python模块,并测试它在我们以前的癫痫脑电图研究[<一个href="#B3">3</一个>,<gydF4y2Ba一个href="#B8">8</一个>,<gydF4y2Ba一个href="#B11">11</一个>]。</p><p>gydF4y2Ba在科学计算和其他流行的编程语言相比如c++或MATLAB, Python是一种开放源码脚本语言简单的语法和各种高级库(详细的优点Python,阅读<一个href="http://www.python.org/about/" target="_blank">http://www.python.org/about/</一个>),比如Scipy (<一个href="http://www.scipy.org/" target="_blank">http://www.scipy.org/</一个>),允许用户运行MATLAB代码后轻微的修改。有几个流行的开源Python项目已经在神经影像社区,如NIPY (<一个href="http://nipy.sourceforge.net/" target="_blank">http://nipy.sourceforge.net/</一个>)。然而,在神经生理学社区,Python还不很受欢迎。因为我们不知道有任何开放源码工具在Python中(或其他编程语言)可以提取脑电特征如前所述,本文介绍并释放PyEEG。</p><p>gydF4y2Ba虽然最初设计为脑电图,PyEEG也可以用来分析其他生理信号,可视为时间序列,特别是梅格信号代表电流的磁场诱导的神经电活动。</p><p>gydF4y2Ba剩下的纸是组织如下。节<一个href="#sec2">2</一个>,我们介绍PyEEG的框架。部分<一个href="#sec3">3</一个>给出了定义计算脑电图特征。教程应用PyEEG到公共的脑电图数据集节中给出<一个href="#sec4">4</一个>。部分<一个href="#sec5">5</一个>总结了纸。</p><h4gydF4y2Baid="main-framework">2。主要框架</h4><p>PgydF4y2BayEEG的目标用户是程序员(谁写程序)在计算神经科学。图<一个href="//www.newsama.com/journals/cin/2011/406391/fig1/" target="_blank">1</一个>显示了它的框架。PyEEG Python模块,只关注从脑电图/梅格片段中提取特征。因此,它不包含函数导入数据的各种格式或导出功能分类器。这是由于构建开源软件的模块化和组成原则表明,小程序,可以通过简单的接口工作在一起比大整体项目。因为开源工具如脑电图/梅格数据进口商(如EEGLab, Biosig,等等)和分类器前端已经可用,不需要我们去重新发明轮子。用户可以很容易地钩PyEEG了各种现有的开源软件来构建他们的脑电图/梅格研究工具链。</p><gydF4y2Badiv class="partial-carousel-wrapper"> <div class="floats-partial-section"> <div class="floats-partial-content"> <div class="partial-carousel--full-image partial-carousel-cd7d53529fdd2b9e353f834210071757"> <div 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class="caption-text">图1</年代p一个n><一个一个r我一个- - - - - -label="View full page" class="caption-partial-url" href="//www.newsama.com/journals/cin/2011/406391/fig1/" title="" target="_blank"></a> </div> <div class="floats-partial-caption-text"> <table> <tbody> <tr> <td>PyEEG框架。</tgydF4y2Bad> </tr> </tbody> </table> </div> </div> </div> </div> <p>PyEEG由两组功能。<年代p一个nclass="list"><span class="list-item"><span class="list-label">(1)</年代p一个n><年代p一个nclass="list-content"><i>预处理功能</我>,不返回任何特性值。到目前为止只有两个功能已经实现。<年代p一个n年代tyle="font-family:monospace">embed_seq ()</年代p一个n>构建嵌入序列(从给定的延迟和嵌入维数)<年代p一个n年代tyle="font-family:monospace">first_order_diff ()</年代p一个n>计算一阶微分序列。一个可以构建高订单通过不断运用微分序列一阶微分计算。</年代p一个n></年代p一个n><span class="list-item"><span class="list-label">(2)</年代p一个n><年代p一个nclass="list-content"><i>特征提取功能</我>,返回特性值。这些都是列在表中<一个href="//www.newsama.com/journals/cin/2011/406391/tab1/" target="_blank">1</一个>。</年代p一个n></年代p一个n></span></p> <div class="floats-partial-section partial-other-wrapper" data-section="tab1"> <div class="floats-partial-footer"> <div class="floats-partial-caption"> <span class="caption-text">表1</年代p一个n><一个一个r我一个- - - - - -label="View full page" class="caption-partial-url" href="//www.newsama.com/journals/cin/2011/406391/tab1/" title="" target="_blank"></a> </div> <div class="floats-partial-caption-text"> PyEEG-supported特性和提取函数的返回类型。</gydF4y2Badiv> <a class="table-thumb-overlay" href="//www.newsama.com/journals/cin/2011/406391/tab1" target="_blank" aria-label="View full page"></a> </div> </div> <p>PyEEG标准Python库和SciPy,只使用功能<我>事实上的</我>科学计算的Python模块。PyEEG没有定义任何新的数据结构,而是只使用标准的Python和NumPy数据结构。原因是我们想要简化PyEEG的使用,尤其是对用户没有编程背景。所有函数的输入是一个时间序列作为一个浮点数的列表和一组可选的特征提取参数。参数有默认值。特征提取的输出函数是一个浮点数,如果特性是一个标量或浮点数的列表(向量)。在PyEEG细节功能是可用的参考指南<一个href="http://PyEEG.SourceForge.net/" target="_blank">http://PyEEG.SourceForge.net/</一个>。</p><h4gydF4y2Baid="supported-feature-extraction">3所示。支持特征提取</h4><p>gydF4y2Ba在本节中,我们详细的定义和计算程序提取脑电图的特性(如表所示<一个href="//www.newsama.com/journals/cin/2011/406391/tab1/" target="_blank">1</一个>在PyEEG)。因为有很多参数和各种算法的一个特性,提取一个特性的数值PyEEG可能不同于其他工具箱中提取。用户可能需要调整我们的代码或使用非默认值的参数,以满足他们的需求。请注意,该指数的一个数组或一个向量从本节1比0。</p><h5我d="sec3.1">3.1。功率谱强度和相对强度比</h5><p>gydF4y2Ba一个时间序列<年代vg height="14.375" id="M2" style="vertical-align:-3.13504pt;width:97.1875px;" version="1.1" viewbox="0 0 97.1875 14.375" width="97.1875" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.375)"> <g transform="translate(72,-60.5)"> <text transform="matrix(1,0,0,-1,-71.95,63.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-60.91,60.55)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-56.04,63.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="5.2137508" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-43.95,60.55)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-39.08,63.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="5.2137508" y="0"> …</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="19.79225" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="25.006001" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-7.19,60.55)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,1.54,63.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ]</t年代p一个n></text> </g> </g> </svg>,表示其快速傅里叶变换(FFT)的结果<年代vg height="14.375" id="M3" style="vertical-align:-3.13504pt;width:108.45px;" version="1.1" viewbox="0 0 108.45 14.375" width="108.45" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.375)"> <g transform="translate(72,-60.5)"> <text transform="matrix(1,0,0,-1,-71.95,63.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-57.91,60.55)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-53.03,63.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="5.2012482" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-37.95,60.55)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-33.07,63.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="5.2012482" y="0"> …</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="19.79225" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="24.993498" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,1.81,60.55)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,10.54,63.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ]</t年代p一个n></text> </g> </g> </svg>。一个连续频带<年代vg height="14.625" id="M4" style="vertical-align:-3.25792pt;width:25.5875px;" version="1.1" viewbox="0 0 25.5875 14.625" width="25.5875" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.625)"> <g transform="translate(72,-60.3)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-65.01,60.47)"> <tspan style="font-size: 8.75px; " x="0" y="0"> l</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="2.4330561" y="0"> o</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="6.6165118" y="0"> w</t年代p一个n></text> </g> </g> </svg>来<年代vg height="16.85" id="M5" style="vertical-align:-5.03984pt;width:20.362499px;" version="1.1" viewbox="0 0 20.362499 16.85" width="20.362499" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,16.85)"> <g transform="translate(72,-58.52)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-65.01,60.47)"> <tspan style="font-size: 8.75px; " x="0" y="0"> u</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="4.3759999" y="0"> p</t年代p一个n></text> </g> </g> </svg>切成<年代vg height="10.325" id="M6" style="vertical-align:-0.0pt;width:13.2875px;" version="1.1" viewbox="0 0 13.2875 10.325" width="13.2875" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.325)"> <g transform="translate(72,-63.74)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>垃圾箱,可以平等的宽度。边界向量指定的垃圾箱<年代vg height="14.475" id="M7" style="vertical-align:-3.13504pt;width:147.0125px;" version="1.1" viewbox="0 0 147.0125 14.475" width="147.0125" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.475)"> <g transform="translate(72,-60.42)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="5.87641" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="12.152916" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="18.366907" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="28.481834" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="40.522224" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="44.685722" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-20.32,60.47)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-15.44,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="5.2012482" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-3.29,60.47)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代p一个n></text> <text transform="matrix(1,0,0,-1,1.58,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="5.2012482" y="0"> …</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="19.79225" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="24.993498" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,33.52,60.47)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,41.39,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ]</t年代p一个n></text> </g> </g> </svg>,这样的频率上下<年代vg height="9.9250002" id="M8" style="vertical-align:-0.13794pt;width:4.9875002px;" version="1.1" viewbox="0 0 4.9875002 9.9250002" width="4.9875002" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,9.925)"> <g transform="translate(72,-64.06)"> <text transform="matrix(1,0,0,-1,-71.95,64.25)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>th本是<年代vg height="14.5875" id="M9" style="vertical-align:-3.2316pt;width:12.825px;" version="1.1" viewbox="0 0 12.825 14.5875" width="12.825" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.5875)"> <g transform="translate(72,-60.33)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-65.01,60.47)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>和<年代vg height="14.925" id="M10" style="vertical-align:-3.49493pt;width:25.7875px;" version="1.1" viewbox="0 0 25.7875 14.925" width="25.7875" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.925)"> <g transform="translate(72,-60.06)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-65.01,60.47)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="2.7218721" y="0"> +</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="8.7169924" y="0"> 1</t年代p一个n></text> </g> </g> </svg>,分别。常用的不平等的垃圾箱脑电图/梅格节奏,,<年代vg height="13.6375" id="M11" style="vertical-align:-2.21957pt;width:69.175003px;" version="1.1" viewbox="0 0 69.175003 13.6375" width="69.175003" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.6375)"> <g transform="translate(72,-61.09)"> <text transform="matrix(1,0,0,-1,-71.95,63.35)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="8.3645067" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="12.528006" y="0"> 0</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="18.779507" y="0"> 。</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="21.905256" y="0"> 5</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="26.081259" y="0"> - - - - - -</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="28.169258" y="0"> 4</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="36.483753" y="0"> H</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="45.510921" y="0"> z</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="51.062252" y="0"> )</t年代p一个n></text> </g> </g> </svg>,<年代vg height="13.45" id="M12" style="vertical-align:-2.21957pt;width:57.775002px;" version="1.1" viewbox="0 0 57.775002 13.45" width="57.775002" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.45)"> <g transform="translate(72,-61.24)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="8.6270704" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="12.790569" y="0"> 4</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="16.966572" y="0"> - - - - - -</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="19.054571" y="0"> 7</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="27.369066" y="0"> H</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="36.396233" y="0"> z</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="41.947563" y="0"> )</t年代p一个n></text> </g> </g> </svg>,<年代vg height="13.45" id="M13" style="vertical-align:-2.21957pt;width:66.212502px;" version="1.1" viewbox="0 0 66.212502 13.45" width="66.212502" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.45)"> <g transform="translate(72,-61.24)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="9.1271896" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="13.290689" y="0"> 8</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="17.46669" y="0"> - - - - - -</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="19.554691" y="0"> 1</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="25.806192" y="0"> 2</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="34.120686" y="0"> H</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="43.147854" y="0"> z</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="48.699184" y="0"> )</t年代p一个n></text> </g> </g> </svg>,<年代vg height="13.55" id="M14" style="vertical-align:-2.29482pt;width:73.9375px;" version="1.1" viewbox="0 0 73.9375 13.55" width="73.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.55)"> <g transform="translate(72,-61.16)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="9.0521717" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="13.215671" y="0"> 1</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="19.467171" y="0"> 2</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="23.643173" y="0"> - - - - - -</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="25.731174" y="0"> 3</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="31.982674" y="0"> 0</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="40.297169" y="0"> H</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="49.324333" y="0"> z</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="54.875668" y="0"> )</t年代p一个n></text> </g> </g> </svg>,<年代vg height="13.6125" id="M15" style="vertical-align:-2.34499pt;width:80.974998px;" version="1.1" viewbox="0 0 80.974998 13.6125" width="80.974998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.6125)"> <g transform="translate(72,-61.11)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="8.427022" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="12.590521" y="0"> 3</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="18.842022" y="0"> 0</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="23.018023" y="0"> - - - - - -</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="25.106024" y="0"> 1</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="31.357525" y="0"> 0</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="37.609024" y="0"> 0</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="45.923519" y="0"> H</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="54.950684" y="0"> z</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="60.502018" y="0"> )</t年代p一个n></text> </g> </g> </svg>。对于这些箱子,我们有<年代vg height="13.3125" id="M16" style="vertical-align:-1.95624pt;width:183.625px;" version="1.1" viewbox="0 0 183.625 13.3125" width="183.625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.3125)"> <g transform="translate(72,-61.35)"> <text transform="matrix(1,0,0,-1,-71.95,63.35)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="5.87641" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="12.152916" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="18.366907" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="28.481834" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="40.522224" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="44.685722" y="0"> 0</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="50.937222" y="0"> 。</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="54.062973" y="0"> 5</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="60.314472" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="65.528221" y="0"> 4</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="71.779724" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="76.980972" y="0"> 7</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="83.232468" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="88.44622" y="0"> 1</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="94.697723" y="0"> 2</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="100.94922" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="106.16297" y="0"> 3</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="112.41447" y="0"> 0</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="118.66597" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="123.86722" y="0"> 1</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="130.11871" y="0"> 0</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="136.37022" y="0"> 0</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="142.62172" y="0"> ]</t年代p一个n></text> </g> </g> </svg>。</p><p>gydF4y2Ba功率谱密度(PSI) [<一个href="#B12">12</一个>)的<年代vg height="10.7375" id="M17" style="vertical-align:-0.13794pt;width:8.6000004px;" version="1.1" viewbox="0 0 8.6000004 10.7375" width="8.6000004" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.7375)"> <g transform="translate(72,-63.41)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>本评估<年代p一个nclass="equation" id="EEq1"> <svg height="57.737499" id="M18" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 57.737499" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,57.7375)"> <g transform="translate(72,-25.81)"> <text transform="matrix(1,0,0,-1,96.64,44.64)"> <tspan style="font-size: 12.50px; " x="0" y="0"> P</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="6.9641709" y="0"> 年代</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="13.915839" y="0"> 我</t年代p一个n></text> <text transform="matrix(1,0,0,-1,114.72,41.52)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,123.43,44.64)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</t年代p一个n></text> <text transform="matrix(1,0,0,-1,136.27,60.14)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="3.96" y="-1.76"> </t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="11.407952" y="-1.76"> (</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="14.322368" y="-1.76"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,155.45,59.72)"> <tspan style="font-size: 6.25px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 6.25px; " x="3.3885839" y="0"> +</t年代p一个n><t年代p一个n style="font-size: 6.25px; " x="7.6712041" y="0"> 1</t年代p一个n></text> <text transform="matrix(1,0,0,-1,166.75,61.9)"> <tspan style="font-size: 8.75px; " x="0" y="0"> /</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="2.4330561" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,174.04,59.72)"> <tspan style="font-size: 6.25px; " x="0" y="0"> 年代</t年代p一个n></text> <text transform="matrix(1,0,0,-1,176.97,61.9)"> <tspan style="font-size: 8.75px; " x="0" y="0"> )</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="2.9100001" y="1.76"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,151.98,38.09)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,135.47,30.59)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="2.7218721" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="8.7169924" y="0"> ⌊</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="12.82168" y="0"> </t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="20.269632" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="23.184048" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,163.51,28.4)"> <tspan style="font-size: 6.25px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,167.4,30.59)"> <tspan style="font-size: 8.75px; " x="0" y="0"> /</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="2.4330561" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,174.69,28.4)"> <tspan style="font-size: 6.25px; " x="0" y="0"> 年代</t年代p一个n></text> <text transform="matrix(1,0,0,-1,177.62,30.59)"> <tspan style="font-size: 8.75px; " x="0" y="0"> )</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="2.9144161" y="0"> ⌋</t年代p一个n></text> <text transform="matrix(1,0,0,-1,186.72,46.23)"> <tspan style="font-size: 12.50px; " x="0" y="0"> |</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="0" y="3.1600001"> |</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="2.5" y="1.59"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,199.1,41.52)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,202.32,46.23)"> <tspan style="font-size: 12.50px; " x="0" y="0"> |</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="0" y="3.1600001"> |</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="4.5900002" y="1.59"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="19.75614" y="1.59"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="29.996096" y="1.59"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="42.036484" y="1.59"> 1</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="48.287987" y="1.59"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="53.501736" y="1.59"> 2</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="59.753235" y="1.59"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="64.966988" y="1.59"> …</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="79.545486" y="1.59"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="84.759239" y="1.59"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="97.062187" y="1.59"> −</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="108.40241" y="1.59"> 1</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="114.65391" y="1.59"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="271.79999" y="1.59"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="275.9635" y="1.59"> 1</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="282.215" y="1.59"> )</t年代p一个n></text> </g> </g> </svg></span>在哪里<年代vg height="14.5875" id="M19" style="vertical-align:-3.22281pt;width:13.675px;" version="1.1" viewbox="0 0 13.675 14.5875" width="13.675" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.5875)"> <g transform="translate(72,-60.33)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-65.01,60.47)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 年代</t年代p一个n></text> </g> </g> </svg>是采样率,<年代vg height="10.325" id="M20" style="vertical-align:-0.0pt;width:14.8375px;" version="1.1" viewbox="0 0 14.8375 10.325" width="14.8375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.325)"> <g transform="translate(72,-63.74)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>该系列长度。</p><p>gydF4y2Ba相对强度比(RIR) [<一个href="#B12">12</一个>)定义PSI<年代p一个nclass="equation" id="EEq2"> <svg height="43.799999" id="M21" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 43.799999" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,43.8)"> <g transform="translate(72,-36.96)"> <text transform="matrix(1,0,0,-1,105,52.72)"> <tspan style="font-size: 12.50px; " x="0" y="0"> R</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="8.3395014" y="0"> 我</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="12.503" y="0"> R</t年代p一个n></text> <text transform="matrix(1,0,0,-1,125.84,49.6)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,133.74,52.72)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="28.129999" y="-10.78"> P</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="35.09417" y="-10.78"> 年代</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="42.045837" y="-10.78"> 我</t年代p一个n></text> <text transform="matrix(1,0,0,-1,179.95,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <g> <path d="m 146.98,55.85 52.28,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,146.98,40.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ∑</t年代p一个n></text> <text transform="matrix(1,0,0,-1,158.4,47.04)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="6.669024" y="0"> −</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="12.664144" y="0"> 1</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="0" y="9.9300003"> </t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="4.7435842" y="9.9300003"> =</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="10.738704" y="9.9300003"> 1</t年代p一个n></text> <text transform="matrix(1,0,0,-1,175.94,40.81)"> <tspan style="font-size: 12.50px; " x="0" y="0"> P</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="6.9641709" y="0"> 年代</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="13.915839" y="0"> 我</t年代p一个n></text> <text transform="matrix(1,0,0,-1,194.02,37.68)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,200.46,52.72)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="15.166139" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="23.50564" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="35.546028" y="0"> 1</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="41.797527" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="46.998775" y="0"> 2</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="53.250278" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="58.464027" y="0"> …</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="73.055031" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="78.256279" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="90.559227" y="0"> −</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="101.91196" y="0"> 1</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="108.16345" y="0"> 。</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="273.66" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="277.82349" y="0"> 2</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="284.07501" y="0"> )</t年代p一个n></text> </g> </g> </svg></span>PSI和RIR都是矢量特性。</p><h5gydF4y2Baid="sec3.2">3.2。彼得罗森分形维数(PFD)</h5><p>PFDgydF4y2Ba的定义是一个时间序列<年代p一个nclass="equation" id="eq1"> <svg height="41.349998" id="M22" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 41.349998" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,41.35)"> <g transform="translate(72,-38.92)"> <text transform="matrix(1,0,0,-1,97.89,54.11)"> <tspan style="font-size: 12.50px; " x="0" y="0"> P</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="6.9641709" y="0"> F</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="13.915839" y="0"> D</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="26.406336" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="108.61" y="-9.3000002"> l</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="112.08583" y="-9.3000002"> o</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="118.33733" y="-9.3000002"> g</t年代p一个n></text> <text transform="matrix(1,0,0,-1,224.56,60.25)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="4.3759999" y="0"> 0</t年代p一个n></text> <text transform="matrix(1,0,0,-1,233.81,63.41)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <g> <path d="m 137.54,57.24 177,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,137.54,43.53)"> <tspan style="font-size: 12.50px; " x="0" y="0"> l</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="3.4758339" y="0"> o</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="9.727334" y="0"> g</t年代p一个n></text> <text transform="matrix(1,0,0,-1,155.6,40.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="4.3759999" y="0"> 0</t年代p一个n></text> <text transform="matrix(1,0,0,-1,164.85,43.53)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="13.415719" y="0"> +</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="24.755939" y="0"> l</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="28.231773" y="0"> o</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="34.483273" y="0"> g</t年代p一个n></text> <text transform="matrix(1,0,0,-1,207.67,40.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="4.3759999" y="0"> 0</t年代p一个n></text> <text transform="matrix(1,0,0,-1,219.01,41.02)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="22.049999" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="5.8499999" y="-2.51"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="16.490053" y="-2.51"> /</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="27.9" y="-2.51"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="41.31572" y="-2.51"> +</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="52.655941" y="-2.51"> 0</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="58.90744" y="-2.51"> 。</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="62.033192" y="-2.51"> 4</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="68.284691" y="-2.51"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,297.94,40.41)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,302.84,41.02)"> <tspan style="font-size: 12.50px; " x="12.9" y="-13.09"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="5.8514042" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="171.28" y="-11.31"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="175.4435" y="-11.31"> 3</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="181.69499" y="-11.31"> )</t年代p一个n></text> </g> </g> </svg></span>在哪里<年代vg height="10.325" id="M23" style="vertical-align:-0.0pt;width:14.8375px;" version="1.1" viewbox="0 0 14.8375 10.325" width="14.8375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.325)"> <g transform="translate(72,-63.74)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>是系列长度,<年代vg height="14.3625" id="M24" style="vertical-align:-3.2316pt;width:19.549999px;" version="1.1" viewbox="0 0 19.549999 14.3625" width="19.549999" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.3625)"> <g transform="translate(72,-60.51)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-61.31,60.66)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>是标志的数量变化信号的导数(<一个href="#B13">13</一个>]。pdf是一个标量的特性。</p><h5gydF4y2Baid="sec3.3">3.3。Higuchi分形维数(HFD)</h5><p>H我guchi的算法(<一个href="#B14">14</一个>)结构<年代vg height="10.7375" id="M25" style="vertical-align:-0.13794pt;width:8.6000004px;" version="1.1" viewbox="0 0 8.6000004 10.7375" width="8.6000004" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.7375)"> <g transform="translate(72,-63.41)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>新系列从原始系列<年代vg height="14.375" id="M26" style="vertical-align:-3.13504pt;width:97.1875px;" version="1.1" viewbox="0 0 97.1875 14.375" width="97.1875" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.375)"> <g transform="translate(72,-60.5)"> <text transform="matrix(1,0,0,-1,-71.95,63.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-60.91,60.55)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-56.04,63.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="5.2137508" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-43.95,60.55)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-39.08,63.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="5.2137508" y="0"> …</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="19.79225" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="25.006001" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-7.19,60.55)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,1.54,63.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ]</t年代p一个n></text> </g> </g> </svg>通过<年代p一个nclass="equation" id="EEq3"> <svg height="17.3125" id="M27" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 17.3125" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,17.3125)"> <g transform="translate(72,-58.15)"> <text transform="matrix(1,0,0,-1,123.19,63.2)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,130.07,60.07)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,136.78,63.2)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="5.2012482" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,148.86,60.07)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="6.2139201" y="0"> +</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="12.20904" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,166.32,63.2)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="5.2012482" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,178.4,60.07)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="6.2139201" y="0"> +</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="12.20904" y="0"> 2</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="16.585039" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,200.23,63.2)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="5.2012482" y="0"> …</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="19.79225" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="24.993498" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,232.11,60.07)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="6.2139201" y="0"> +</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="12.20904" y="0"> ⌊</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="16.313728" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="19.228144" y="0"> </t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="26.676096" y="0"> −</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="32.671215" y="0"> </t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="38.885136" y="0"> )</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="41.799553" y="0"> /</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="44.232609" y="0"> </t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="48.976192" y="0"> ⌋</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="53.080879" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,290.44,63.2)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="183.67999" y="1.25"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="187.84351" y="1.25"> 4</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="194.095" y="1.25"> )</t年代p一个n></text> </g> </g> </svg></span>在哪里<年代vg height="12.8875" id="M28" style="vertical-align:-1.76814pt;width:92.474998px;" version="1.1" viewbox="0 0 92.474998 12.8875" width="92.474998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,12.8875)"> <g transform="translate(72,-61.69)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="12.340461" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="24.38085" y="0"> 1</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="30.632351" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="35.8461" y="0"> 2</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="42.097603" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="47.298847" y="0"> …</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="61.889851" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="67.1036" y="0"> </t年代p一个n></text> </g> </g> </svg>。</p><p>gydF4y2Ba对于每个时间序列由(<一个href="#EEq3">4</一个>),长度<年代vg height="13.45" id="M29" style="vertical-align:-2.21957pt;width:47.674999px;" version="1.1" viewbox="0 0 47.674999 13.45" width="47.674999" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.45)"> <g transform="translate(72,-61.24)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="8.8521242" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="13.015623" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="21.892754" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="27.094002" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="33.870628" y="0"> )</t年代p一个n></text> </g> </g> </svg>是计算<年代p一个nclass="equation" id="eq2"> <svg height="43.6875" id="M30" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 43.6875" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,43.6875)"> <g transform="translate(72,-37.05)"> <text transform="matrix(1,0,0,-1,84.93,48.52)"> <tspan style="font-size: 12.50px; " x="56.84" y="-10.8"> ∑</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="10.927622" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="15.103624" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="23.980755" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="29.182001" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="35.95863" y="0"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="43.597961" y="0"> =</t年代p一个n></text> <text transform="matrix(1,0,0,-1,153.19,65.71)"> <tspan style="font-size: 8.75px; " x="0" y="0"> ⌊</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="4.1046882" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="7.019104" y="0"> </t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="14.467056" y="0"> −</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="20.462175" y="0"> </t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="26.676096" y="0"> )</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="29.590511" y="0"> /</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="32.023567" y="0"> </t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="36.767151" y="0"> ⌋</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="0" y="11.08"> </t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="2.7218721" y="11.08"> =</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="8.7169924" y="11.08"> 2</t年代p一个n></text> <text transform="matrix(1,0,0,-1,196.65,61.04)"> <tspan style="font-size: 12.50px; " x="0" y="0"> |</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="0" y="3.3800001"> |</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="2.5" y="1.7"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,206.03,56.22)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="6.2139201" y="0"> +</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="12.20904" y="0"> </t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="14.930912" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,228.98,59.34)"> <tspan style="font-size: 12.50px; " x="0" y="0"> −</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="11.340221" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,247.2,56.22)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="6.2139201" y="0"> +</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="12.20904" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="15.123456" y="0"> </t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="17.845327" y="0"> −</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="23.840448" y="0"> 1</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="28.216448" y="0"> )</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="31.130863" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,283.57,61.04)"> <tspan style="font-size: 12.50px; " x="0" y="0"> |</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="0" y="3.3800001"> |</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="4.5900002" y="1.6900001"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="8.753499" y="1.6900001"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="22.156715" y="1.6900001"> −</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="33.509438" y="1.6900001"> 1</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="39.760941" y="1.6900001"> )</t年代p一个n></text> <g> <path d="m 141.77,51.64 185.73,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,196.14,39.77)"> <tspan style="font-size: 12.50px; " x="132.55" y="-8.75"> 。</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="0" y="0"> ⌊</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="7.939405" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="12.115407" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="25.531126" y="0"> −</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="36.871346" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="45.748478" y="0"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="51.999977" y="0"> /</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="55.475811" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="62.252438" y="0"> ⌋</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="70.191841" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="277.98001" y="-11.63"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="282.14349" y="-11.63"> 5</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="288.39499" y="-11.63"> )</t年代p一个n></text> </g> </g> </svg></span></p> <p>计算的平均长度<年代vg height="19.975" id="M31" style="vertical-align:-3.80836pt;width:145.27499px;" version="1.1" viewbox="0 0 145.27499 19.975" width="145.27499" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,19.975)"> <g transform="translate(72,-56.02)"> <text transform="matrix(1,0,0,-1,-71.95,59.87)"> <tspan style="font-size: 12.50px; " x="43.630001" y="0.02"> ∑</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="8.8521242" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="13.015623" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="19.79225" y="0"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="27.419079" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="39.459469" y="0"> (</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-16.89,66.1)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="0" y="9.9300003"> </t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="2.7218721" y="9.9300003"> =</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="8.7169924" y="9.9300003"> 1</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-3.3,59.87)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="8.8521242" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="13.015623" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="16.904057" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="22.105305" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="28.881929" y="0"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="33.045429" y="0"> ]</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="37.208927" y="0"> /</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="40.684761" y="0"> </t年代p一个n></text> </g> </g> </svg>。</p><p>gydF4y2Ba这个过程重复<年代vg height="14.5875" id="M32" style="vertical-align:-3.22282pt;width:31.700001px;" version="1.1" viewbox="0 0 31.700001 14.5875" width="31.700001" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.5875)"> <g transform="translate(72,-60.33)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-65.17,60.47)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 米</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="6.8090558" y="0"> 一个</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="10.694944" y="0"> x</t年代p一个n></text> </g> </g> </svg>次为每个<年代vg height="10.7375" id="M33" style="vertical-align:-0.13794pt;width:8.6000004px;" version="1.1" viewbox="0 0 8.6000004 10.7375" width="8.6000004" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.7375)"> <g transform="translate(72,-63.41)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>从1到<年代vg height="14.5875" id="M34" style="vertical-align:-3.22282pt;width:31.700001px;" version="1.1" viewbox="0 0 31.700001 14.5875" width="31.700001" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.5875)"> <g transform="translate(72,-60.33)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-65.17,60.47)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 米</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="6.8090558" y="0"> 一个</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="10.694944" y="0"> x</t年代p一个n></text> </g> </g> </svg>,然后使用最小二乘法来确定直线的斜率的曲线最适合<年代vg height="13.5625" id="M35" style="vertical-align:-2.21957pt;width:57.849998px;" version="1.1" viewbox="0 0 57.849998 13.5625" width="57.849998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.5625)"> <g transform="translate(72,-61.15)"> <text transform="matrix(1,0,0,-1,-71.95,63.41)"> <tspan style="font-size: 12.50px; " x="0" y="0"> l</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="3.4758339" y="0"> n</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="13.890833" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="18.054333" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="26.906456" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="31.069956" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="37.846581" y="0"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="42.010078" y="0"> )</t年代p一个n></text> </g> </g> </svg>与<年代vg height="13.5625" id="M36" style="vertical-align:-2.21957pt;width:48.537498px;" version="1.1" viewbox="0 0 48.537498 13.5625" width="48.537498" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.5625)"> <g transform="translate(72,-61.15)"> <text transform="matrix(1,0,0,-1,-71.95,63.41)"> <tspan style="font-size: 12.50px; " x="0" y="0"> l</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="3.4758339" y="0"> n</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="13.890833" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="18.054333" y="0"> 1</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="24.305832" y="0"> /</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="27.781666" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="34.558292" y="0"> )</t年代p一个n></text> </g> </g> </svg>。斜率是Higuchi分形维数。HFD是一个标量的特性。</p><h5我d="sec3.4">3.4。Hjorth参数</h5><p>gydF4y2Ba一个时间序列<年代vg height="14.375" id="M37" style="vertical-align:-3.13504pt;width:97.1875px;" version="1.1" viewbox="0 0 97.1875 14.375" width="97.1875" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.375)"> <g transform="translate(72,-60.5)"> <text transform="matrix(1,0,0,-1,-71.95,63.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-60.91,60.55)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-56.04,63.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="5.2137508" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-43.95,60.55)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-39.08,63.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="5.2137508" y="0"> …</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="19.79225" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="25.006001" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-7.19,60.55)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,1.54,63.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ]</t年代p一个n></text> </g> </g> </svg>,Hjorth流动性和复杂性<一个href="#B15">15</一个>),分别定义为<年代vg height="20.4125" id="M38" style="vertical-align:-2.64594pt;width:60.75px;" version="1.1" viewbox="0 0 60.75 20.4125" width="60.75" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,20.4125)"> <g transform="translate(72,-55.67)"> <text transform="matrix(1,0,0,-1,-71.95,58.96)"> <tspan style="font-size: 12.50px; " x="0" y="0"> √</t年代p一个n></text> <g> <path d="m -60.35,70.71 36.9,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,-60.35,58.36)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="12.565515" y="0"> 2</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="18.817015" y="0"> /</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="22.292849" y="0"> T</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="29.932182" y="0"> P</t年代p一个n></text> </g> </g> </svg>和<年代vg height="20.4125" id="M39" style="vertical-align:-3.66795pt;width:151.4375px;" version="1.1" viewbox="0 0 151.4375 20.4125" width="151.4375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,20.4125)"> <g transform="translate(72,-55.67)"> <text transform="matrix(1,0,0,-1,-71.95,58.96)"> <tspan style="font-size: 12.50px; " x="0" y="0"> √</t年代p一个n></text> <g> <path d="m -60.35,70.71 109.45,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,-60.35,59.38)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="16.729013" y="0"> 4</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="25.75618" y="0"> ⋅</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="32.107704" y="0"> T</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="39.747036" y="0"> P</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="46.711208" y="0"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="50.874706" y="0"> /</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="54.35054" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="58.514042" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="71.079552" y="0"> 2</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="80.10672" y="0"> ⋅</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="86.470749" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="99.036263" y="0"> 2</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="105.28777" y="0"> )</t年代p一个n></text> </g> </g> </svg>,在那里<年代vg height="16.1" id="M40" style="vertical-align:-3.2729pt;width:86.324997px;" version="1.1" viewbox="0 0 86.324997 16.1" width="86.324997" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,16.1)"> <g transform="translate(72,-59.12)"> <text transform="matrix(1,0,0,-1,-71.95,62.44)"> <tspan style="font-size: 12.50px; " x="30.110001" y="0.029999999"> ∑</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="43.630001" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="0" y="0"> T</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="7.6393328" y="0"> P</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="18.066835" y="0"> =</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-21.45,59.31)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-18.23,62.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> /</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="3.4758339" y="0"> </t年代p一个n></text> </g> </g> </svg>,<年代vg height="16.1" id="M41" style="vertical-align:-3.2729pt;width:91.3125px;" version="1.1" viewbox="0 0 91.3125 16.1" width="91.3125" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,16.1)"> <g transform="translate(72,-59.12)"> <text transform="matrix(1,0,0,-1,-71.95,62.44)"> <tspan style="font-size: 12.50px; " x="34.330002" y="0.029999999"> ∑</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="47.84" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="12.565515" y="0"> 2</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="22.280346" y="0"> =</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-17.46,59.31)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-14.24,62.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> /</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="3.4758339" y="0"> </t年代p一个n></text> </g> </g> </svg>,<年代vg height="18.0625" id="M42" style="vertical-align:-3.2729pt;width:150.77499px;" version="1.1" viewbox="0 0 150.77499 18.0625" width="150.77499" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,18.0625)"> <g transform="translate(72,-57.55)"> <text transform="matrix(1,0,0,-1,-71.95,60.86)"> <tspan style="font-size: 12.50px; " x="34.330002" y="0.02"> ∑</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="12.565515" y="0"> 4</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="22.280346" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="47.84" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="52.003498" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-13.3,57.74)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-7.3,60.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> −</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="11.340221" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,10.7,57.74)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="2.7218721" y="0"> −</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="8.7169924" y="0"> 1</t年代p一个n></text> <text transform="matrix(1,0,0,-1,24.29,60.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> )</t年代p一个n></text> <text transform="matrix(1,0,0,-1,28.45,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代p一个n></text> <text transform="matrix(1,0,0,-1,33.33,60.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> /</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="3.4758339" y="0"> </t年代p一个n></text> </g> </g> </svg>,<年代vg height="14.5875" id="M43" style="vertical-align:-3.2316pt;width:87.712502px;" version="1.1" viewbox="0 0 87.712502 14.5875" width="87.712502" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.5875)"> <g transform="translate(72,-60.33)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-65.3,60.47)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-58.61,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="12.040389" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-39.69,60.47)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-33.69,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> −</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="11.340221" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-15.47,60.47)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="2.7218721" y="0"> −</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="8.7169924" y="0"> 1</t年代p一个n></text> </g> </g> </svg>。Hjorth灵活性和复杂性都是标量特征。</p><h5gydF4y2Baid="sec3.5">3.5。谱熵</h5><p>gydF4y2Ba谱熵(<一个href="#B16">16</一个>)定义如下<年代p一个nclass="equation" id="eq3"> <svg height="50.662498" id="M44" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 50.662498" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,50.6625)"> <g transform="translate(72,-31.47)"> <text transform="matrix(1,0,0,-1,126.41,47.82)"> <tspan style="font-size: 12.50px; " x="52.560001" y="-7.25"> 1</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="14.37845" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="26.418839" y="0"> −</t年代p一个n></text> <g> <path d="m 162.59,50.94 39.01,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,162.59,39.07)"> <tspan style="font-size: 12.50px; " x="0" y="0"> l</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="3.4758339" y="0"> o</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="9.727334" y="0"> g</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="20.142332" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="24.305832" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="34.833359" y="0"> )</t年代p一个n></text> <text transform="matrix(1,0,0,-1,207.18,63.76)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,202.79,41.27)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,204.32,34.09)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="2.7218721" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="8.7169924" y="0"> 1</t年代p一个n></text> <text transform="matrix(1,0,0,-1,218.95,47.82)"> <tspan style="font-size: 12.50px; " x="0" y="0"> R</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="8.3395014" y="0"> 我</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="12.503" y="0"> R</t年代p一个n></text> <text transform="matrix(1,0,0,-1,239.79,44.69)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,245.09,47.82)"> <tspan style="font-size: 12.50px; " x="0" y="0"> l</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="3.4758339" y="0"> o</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="9.727334" y="0"> g</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="18.054333" y="0"> R</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="26.393833" y="0"> 我</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="30.557331" y="0"> R</t年代p一个n></text> <text transform="matrix(1,0,0,-1,284,44.69)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,287.22,47.82)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="186.89999" y="-0.79000002"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="191.06349" y="-0.79000002"> 6</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="197.315" y="-0.79000002"> )</t年代p一个n></text> </g> </g> </svg></span>在哪里<年代vg height="14.5" id="M45" style="vertical-align:-3.2316pt;width:30.200001px;" version="1.1" viewbox="0 0 30.200001 14.5" width="30.200001" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.5)"> <g transform="translate(72,-60.4)"> <text transform="matrix(1,0,0,-1,-71.95,63.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> R</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="8.3395014" y="0"> 我</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="12.503" y="0"> R</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-51.11,60.55)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>和<年代vg height="10.325" id="M46" style="vertical-align:-0.0pt;width:13.2875px;" version="1.1" viewbox="0 0 13.2875 10.325" width="13.2875" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.325)"> <g transform="translate(72,-63.74)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>定义在(<一个href="#EEq2">2</一个>)。谱熵是一个标量的特性。</p><h5gydF4y2Baid="sec3.6">3.6。计算熵</h5><p>gydF4y2Ba文献[<一个href="#B17">17</一个>)定义了一个熵测量使用奇异值分解(计算)。让输入信号<年代vg height="14.375" id="M47" style="vertical-align:-3.13504pt;width:97.1875px;" version="1.1" viewbox="0 0 97.1875 14.375" width="97.1875" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.375)"> <g transform="translate(72,-60.5)"> <text transform="matrix(1,0,0,-1,-71.95,63.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-60.91,60.55)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-56.04,63.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="5.2137508" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-43.95,60.55)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-39.08,63.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="5.2137508" y="0"> …</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="19.79225" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="25.006001" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-7.19,60.55)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,1.54,63.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ]</t年代p一个n></text> </g> </g> </svg>。我们构建延迟向量为<年代p一个nclass="equation" id="eq4"> <svg height="20.2875" id="M48" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 20.2875" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,20.2875)"> <g transform="translate(72,-55.77)"> <text transform="matrix(1,0,0,-1,129,61.13)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="36.310001" y="2.51"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="41.099998" y="7.1054274e-015"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="8.5900002" y="-0.0099999998"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="12.753499" y="-0.0099999998"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="16.641932" y="-0.0099999998"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="24.268763" y="-0.0099999998"> =</t年代p一个n></text> <text transform="matrix(1,0,0,-1,176.98,58.01)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,180.2,61.13)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="5.2012482" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,192.28,58.01)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="2.7218721" y="0"> +</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="8.7169924" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,205.98,61.13)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="5.2012482" y="0"> …</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="19.79225" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="25.006001" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,237.86,58.01)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="2.7218721" y="0"> +</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="8.7169924" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="11.631408" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,254.15,55.82)"> <tspan style="font-size: 6.25px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,259.49,58.01)"> <tspan style="font-size: 8.75px; " x="0" y="0"> −</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="5.99512" y="0"> 1</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="10.37112" y="0"> )</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="13.285536" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,277.75,58.62)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="6.8800001" y="-2.51"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="196.37" y="-2.1400001"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="200.53349" y="-2.1400001"> 7</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="206.785" y="-2.1400001"> )</t年代p一个n></text> </g> </g> </svg></span>在哪里<年代vg height="6.8874998" id="M49" style="vertical-align:-0.0627pt;width:8.125px;" version="1.1" viewbox="0 0 8.125 6.8874998" width="8.125" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,6.8875)"> <g transform="translate(72,-66.49)"> <text transform="matrix(1,0,0,-1,-71.95,66.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>是延迟,<年代vg height="14.475" id="M50" style="vertical-align:-3.13504pt;width:17.525px;" version="1.1" viewbox="0 0 17.525 14.475" width="17.525" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.475)"> <g transform="translate(72,-60.42)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-65.3,60.47)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>嵌入维数。在这篇文章中,<年代vg height="14.6" id="M51" style="vertical-align:-3.13504pt;width:52.549999px;" version="1.1" viewbox="0 0 52.549999 14.6" width="52.549999" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.6)"> <g transform="translate(72,-60.32)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-65.3,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-54.55,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="12.027886" y="0"> 2</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="18.279387" y="0"> 0</t年代p一个n></text> </g> </g> </svg>和<年代vg height="10.7625" id="M52" style="vertical-align:-0.0627pt;width:35.325001px;" version="1.1" viewbox="0 0 35.325001 10.7625" width="35.325001" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.7625)"> <g transform="translate(72,-63.39)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="9.8648672" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="21.905256" y="0"> 2</t年代p一个n></text> </g> </g> </svg>。然后由嵌入空间<年代p一个nclass="equation" id="eq5"> <svg height="22.387501" id="M53" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 22.387501" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,22.3875)"> <g transform="translate(72,-54.09)"> <text transform="matrix(1,0,0,-1,97.44,58.7)"> <tspan style="font-size: 12.50px; " x="22.200001" y="2.51"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="116.29" y="2.51"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="146.89999" y="2.51"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="152.75" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="10.164939" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="26.99" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="35.567059" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="39.730556" y="0"> 1</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="45.982056" y="0"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="52.233559" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="57.447308" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="66.024368" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="70.187866" y="0"> 2</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="76.439362" y="0"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="82.690865" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="87.904617" y="0"> …</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="102.48312" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="107.69686" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="122.14" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="135.55573" y="0"> −</t年代p一个n></text> <text transform="matrix(1,0,0,-1,256.85,55.58)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,266.9,58.7)"> <tspan style="font-size: 12.50px; " x="17.59" y="2.51"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="25.530001" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="0" y="0"> −</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="11.340221" y="0"> 1</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="31.93" y="2.51"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="37.781403" y="2.51"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,309.47,66.24)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,316.18,58.7)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 。</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="157.94" y="-1.22"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="162.1035" y="-1.22"> 8</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="168.355" y="-1.22"> )</t年代p一个n></text> </g> </g> </svg></span></p> <p>然后对矩阵进行奇异值分解<年代vg height="10.325" id="M54" style="vertical-align:-0.0pt;width:11.6125px;" version="1.1" viewbox="0 0 11.6125 10.325" width="11.6125" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.325)"> <g transform="translate(72,-63.74)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>生产<年代vg height="10.325" id="M55" style="vertical-align:-0.0pt;width:17.237499px;" version="1.1" viewbox="0 0 17.237499 10.325" width="17.237499" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.325)"> <g transform="translate(72,-63.74)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>奇异值,<年代vg height="10.725" id="M56" style="vertical-align:-3.13504pt;width:68.425003px;" version="1.1" viewbox="0 0 68.425003 10.725" width="68.425003" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.725)"> <g transform="translate(72,-63.42)"> <text transform="matrix(1,0,0,-1,-71.95,66.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-64.61,63.47)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-59.74,66.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="5.2012482" y="0"> …</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="19.79225" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="25.006001" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-27.39,63.47)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>,称为奇异谱。</p><p>gydF4y2Ba然后定义为计算熵<年代p一个nclass="equation" id="EEq4"> <svg height="50.662498" id="M57" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 50.662498" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,50.6625)"> <g transform="translate(72,-31.47)"> <text transform="matrix(1,0,0,-1,150.3,47.82)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,161.21,44.69)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 年代</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="4.6998239" y="0"> V</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="11.018768" y="0"> D</t年代p一个n></text> <text transform="matrix(1,0,0,-1,182.51,47.82)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="12.040389" y="0"> −</t年代p一个n></text> <text transform="matrix(1,0,0,-1,206.4,63.76)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,203.12,41.27)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,204.65,34.09)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="2.7218721" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="8.7169924" y="0"> 1</t年代p一个n></text> <g> <path d="m 219.27,56.06 7.34,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,219.27,47.82)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,226.61,44.69)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,229.83,47.82)"> <tspan style="font-size: 12.50px; " x="0" y="0"> l</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="3.4758339" y="0"> o</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="9.727334" y="0"> g</t年代p一个n></text> <text transform="matrix(1,0,0,-1,247.89,44.65)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代p一个n></text> <g> <path d="m 252.77,56.06 7.34,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,252.77,47.82)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,260.11,44.69)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,263.33,47.82)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="210.78999" y="-0.79000002"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="214.95351" y="-0.79000002"> 9</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="221.205" y="-0.79000002"> )</t年代p一个n></text> </g> </g> </svg></span>在哪里<年代vg height="10.325" id="M58" style="vertical-align:-0.0pt;width:17.237499px;" version="1.1" viewbox="0 0 17.237499 10.325" width="17.237499" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.325)"> <g transform="translate(72,-63.74)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>奇异值的数量和吗<年代vg height="15.875" id="M59" style="vertical-align:-3.13504pt;width:68.425003px;" version="1.1" viewbox="0 0 68.425003 15.875" width="68.425003" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,15.875)"> <g transform="translate(72,-59.3)"> <g> <path d="m -71.95,70.71 7.34,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,-71.95,62.47)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-64.61,59.35)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-59.74,62.47)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="5.2012482" y="0"> …</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="19.79225" y="0"> ,</t年代p一个n></text> <g> <path d="m -34.73,70.71 7.34,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,-34.73,62.47)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-27.39,59.35)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>归一化奇异值,这样吗<年代vg height="21.737499" id="M60" style="vertical-align:-5.35329pt;width:97.087502px;" version="1.1" viewbox="0 0 97.087502 21.737499" width="97.087502" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,21.7375)"> <g transform="translate(72,-54.61)"> <g> <path d="m -71.95,68.24 7.34,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,-71.95,60)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-64.61,56.88)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-57.92,60)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="12.027886" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-38.54,56.88)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-35.32,60)"> <tspan style="font-size: 12.50px; " x="0" y="0"> /</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="3.48" y="0.02"> ∑</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-20.42,66.24)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="0" y="9.9399996"> </t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="3.4045279" y="9.9399996"> =</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="9.3996477" y="9.9399996"> 1</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-6.14,60)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,1.2,56.88)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>。计算熵是一个标量的特性。</p><h5gydF4y2Baid="sec3.7">3.7。费舍尔的信息</h5><p>gydF4y2Ba费舍尔的信息(<一个href="#B18">18</一个>)可以定义规范化奇异谱用于(<一个href="#EEq4">9</一个>)<gydF4y2Ba年代p一个nclass="equation" id="eq6"> <svg height="50.924999" id="M61" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 50.924999" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,50.925)"> <g transform="translate(72,-31.26)"> <text transform="matrix(1,0,0,-1,154.18,47.62)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="9.4772739" y="0"> =</t年代p一个n></text> <text transform="matrix(1,0,0,-1,175.7,63.56)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="8.7957602" y="0"> −</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="14.79088" y="0"> 1</t年代p一个n></text> <text transform="matrix(1,0,0,-1,177.2,41.07)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,178.73,33.89)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="2.7218721" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="8.7169924" y="0"> 1</t年代p一个n></text> <text transform="matrix(1,0,0,-1,196.06,55.68)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <g> <path d="m 201.91,66.43 7.34,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,201.91,58.19)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,209.25,55.07)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="2.7218721" y="0"> +</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="8.7169924" y="0"> 1</t年代p一个n></text> <text transform="matrix(1,0,0,-1,225.62,58.19)"> <tspan style="font-size: 12.50px; " x="0" y="0"> −</t年代p一个n></text> <g> <path d="m 236.96,66.43 7.34,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,236.96,58.19)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,244.3,55.07)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,247.52,55.68)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,253.37,65.73)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代p一个n></text> <g> <path d="m 196.06,50.74 62.19,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <g> <path d="m 221.87,46.62 7.34,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,221.87,38.38)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,229.21,35.25)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,259.44,47.62)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 。</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="208.42999" y="-0.88999999"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="212.59351" y="-0.88999999"> 1</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="218.845" y="-0.88999999"> 0</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="225.0965" y="-0.88999999"> )</t年代p一个n></text> </g> </g> </svg></span>费舍尔是一个标量特征信息。</p><h5gydF4y2Baid="sec3.8">3.8。近似熵</h5><p>gydF4y2Ba近似熵(<年代vg height="14.05" id="M62" style="vertical-align:-2.72116pt;width:36.587502px;" version="1.1" viewbox="0 0 36.587502 14.05" width="36.587502" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.05)"> <g transform="translate(72,-60.76)"> <text transform="matrix(1,0,0,-1,-71.95,63.52)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 一个</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="9.0271664" y="0"> p</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="15.278666" y="0"> E</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="22.917999" y="0"> n</t年代p一个n></text> </g> </g> </svg>)是一个统计参数量化一个时间序列的规律<一个href="#B19">19</一个>]。</p><p><年代vg height="14.05" id="M63" style="vertical-align:-2.72116pt;width:36.587502px;" version="1.1" viewbox="0 0 36.587502 14.05" width="36.587502" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.05)"> <g transform="translate(72,-60.76)"> <text transform="matrix(1,0,0,-1,-71.95,63.52)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 一个</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="9.0271664" y="0"> p</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="15.278666" y="0"> E</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="22.917999" y="0"> n</t年代p一个n></text> </g> </g> </svg>由以下步骤计算。<年代p一个nclass="list"><span class="list-item"><span class="list-label">(1)</年代p一个n><年代p一个nclass="list-content">让输入信号<年代vg height="14.375" id="M64" style="vertical-align:-3.13504pt;width:97.1875px;" version="1.1" viewbox="0 0 97.1875 14.375" width="97.1875" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.375)"> <g transform="translate(72,-60.5)"> <text transform="matrix(1,0,0,-1,-71.95,63.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-60.91,60.55)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-56.04,63.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="5.2137508" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-43.95,60.55)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-39.08,63.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="5.2137508" y="0"> …</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="19.79225" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="25.006001" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-7.19,60.55)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,1.54,63.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ]</t年代p一个n></text> </g> </g> </svg>。</年代p一个n></年代p一个n><span class="list-item"><span class="list-label">(2)</年代p一个n><年代p一个nclass="list-content">建立子序列<年代vg height="15.05" id="M65" style="vertical-align:-3.49493pt;width:188.21249px;" version="1.1" viewbox="0 0 188.21249 15.05" width="188.21249" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,15.05)"> <g transform="translate(72,-59.96)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="6.8766499" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="11.040149" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="14.928582" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="20.129829" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="29.00696" y="0"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="36.646294" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="48.686684" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="52.850182" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-12.22,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-9,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="5.2012482" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,3.09,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="2.7218721" y="0"> +</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="8.7169924" y="0"> 1</t年代p一个n></text> <text transform="matrix(1,0,0,-1,16.68,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="5.2012482" y="0"> …</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="19.79225" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="24.993498" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,48.56,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="2.7218721" y="0"> +</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="8.7169924" y="0"> </t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="14.930912" y="0"> −</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="20.926031" y="0"> 1</t年代p一个n></text> <text transform="matrix(1,0,0,-1,74.36,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ]</t年代p一个n></text> </g> </g> </svg>为<年代vg height="12.3" id="M66" style="vertical-align:-1.29163pt;width:93.625px;" version="1.1" viewbox="0 0 93.625 12.3" width="93.625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,12.3)"> <g transform="translate(72,-62.16)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 1</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="9.7148314" y="0"> ≤</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="21.75522" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="29.119488" y="0"> ≤</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="41.159878" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="54.575596" y="0"> −</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="65.915817" y="0"> </t年代p一个n></text> </g> </g> </svg>,在那里<年代vg height="7.1374998" id="M67" style="vertical-align:-0.10033pt;width:11.225px;" version="1.1" viewbox="0 0 11.225 7.1374998" width="11.225" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,7.1375)"> <g transform="translate(72,-66.29)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>子序列的长度。在[<一个href="#B7">7</一个>),<gydF4y2Ba年代vg height="12.8875" id="M68" style="vertical-align:-1.76814pt;width:52.75px;" version="1.1" viewbox="0 0 52.75 12.8875" width="52.75" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,12.8875)"> <g transform="translate(72,-61.69)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="12.340461" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="24.38085" y="0"> 1</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="30.632351" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="35.8461" y="0"> 2</t年代p一个n></text> </g> </g> </svg>或3。</年代p一个n></年代p一个n><span class="list-item"><span class="list-label">(3)</年代p一个n><年代p一个nclass="list-content">让<年代vg height="7.0124998" id="M69" style="vertical-align:-0.0pt;width:6.5px;" version="1.1" viewbox="0 0 6.5 7.0124998" width="6.5" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,7.0125)"> <g transform="translate(72,-66.39)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>代表噪声过滤级别,定义为<年代vg height="11.075" id="M70" style="vertical-align:-0.3135pt;width:71.287498px;" version="1.1" viewbox="0 0 71.287498 11.075" width="71.287498" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.075)"> <g transform="translate(72,-63.14)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="8.5645552" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="20.604944" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="30.157236" y="0"> ×</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="40.934822" y="0"> 年代</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="47.88649" y="0"> D</t年代p一个n></text> </g> </g> </svg>为<年代vg height="12.8875" id="M71" style="vertical-align:-1.76814pt;width:138.6875px;" version="1.1" viewbox="0 0 138.6875 12.8875" width="138.6875" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,12.8875)"> <g transform="translate(72,-61.69)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="10.239957" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="22.280346" y="0"> 0</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="28.531845" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="33.745598" y="0"> 0</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="39.997097" y="0"> 。</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="43.122849" y="0"> 1</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="49.374348" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="54.575596" y="0"> 0</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="60.827095" y="0"> 。</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="63.952847" y="0"> 2</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="70.204346" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="75.418098" y="0"> …</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="90.009094" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="95.210342" y="0"> 0</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="101.46185" y="0"> 。</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="104.58759" y="0"> 9</t年代p一个n></text> </g> </g> </svg>。</年代p一个n></年代p一个n><span class="list-item"><span class="list-label">(4)</年代p一个n><年代p一个nclass="list-content">建立一组子序列<年代vg height="13.8625" id="M72" style="vertical-align:-2.37006pt;width:241.3px;" version="1.1" viewbox="0 0 241.3 13.8625" width="241.3" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.8625)"> <g transform="translate(72,-60.91)"> <text transform="matrix(1,0,0,-1,-71.95,63.32)"> <tspan style="font-size: 12.50px; " x="0" y="0"> {</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="6.00144" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="12.87809" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="17.04159" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="21.905256" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="27.106504" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="35.983635" y="0"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="40.147133" y="0"> }</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="49.624409" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="61.664795" y="0"> {</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="67.666237" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="74.542885" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="78.706383" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="83.570053" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="88.771301" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="97.64843" y="0"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="105.28777" y="0"> ∣</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="112.08939" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="120.42889" y="0"> ∈</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="132.46928" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="136.63278" y="0"> 1</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="142.88428" y="0"> 。</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="146.01004" y="0"> 。</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="149.13579" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="162.5515" y="0"> −</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="173.89172" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="182.76886" y="0"> ]</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="186.93236" y="0"> }</t年代p一个n></text> </g> </g> </svg>,在那里<年代vg height="13.6125" id="M73" style="vertical-align:-2.34499pt;width:42.8125px;" version="1.1" viewbox="0 0 42.8125 13.6125" width="42.8125" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.6125)"> <g transform="translate(72,-61.11)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="6.8766499" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="11.040149" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="15.903816" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="21.105064" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="29.982195" y="0"> )</t年代p一个n></text> </g> </g> </svg>在步骤2中定义。</年代p一个n></年代p一个n><span class="list-item"><span class="list-label">(5)</年代p一个n><年代p一个nclass="list-content">为每一个<年代vg height="13.675" id="M74" style="vertical-align:-2.34499pt;width:118.6875px;" version="1.1" viewbox="0 0 118.6875 13.675" width="118.6875" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.675)"> <g transform="translate(72,-61.06)"> <text transform="matrix(1,0,0,-1,-71.95,63.45)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="6.8766499" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="11.040149" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="14.928582" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="20.129829" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="29.00696" y="0"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="36.646294" y="0"> ∈</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="48.686684" y="0"> {</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="54.688122" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="61.564774" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="65.728271" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="70.591934" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="75.793182" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="84.670319" y="0"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="88.833817" y="0"> }</t年代p一个n></text> </g> </g> </svg>,计算<年代p一个nclass="equation" id="eq7"> <svg height="40.3125" id="M75" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 40.3125" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,40.3125)"> <g transform="translate(72,-39.75)"> <text transform="matrix(1,0,0,-1,157.58,48.65)"> <tspan style="font-size: 12.50px; " x="54.48" y="-11.33"> ∑</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="11.465251" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="15.62875" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="19.517183" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="24.730934" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="33.608063" y="0"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="41.247398" y="0"> =</t年代p一个n></text> <text transform="matrix(1,0,0,-1,223.49,66.24)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="7.4479518" y="0"> −</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="13.443072" y="0"> </t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="0" y="9.9399996"> </t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="3.4045279" y="9.9399996"> =</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="9.3996477" y="9.9399996"> 1</t年代p一个n></text> <text transform="matrix(1,0,0,-1,243.65,60)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,250.42,56.88)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <g> <path d="m 212.06,51.78 42.79,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,216.64,39.9)"> <tspan style="font-size: 12.50px; " x="39.41" y="-8.75"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="13.403216" y="0"> −</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="24.755939" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="251.23" y="-12.85"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="255.39349" y="-12.85"> 1</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="261.64499" y="-12.85"> 1</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="267.89648" y="-12.85"> )</t年代p一个n></text> </g> </g> </svg></span>在哪里<年代p一个nclass="equation" id="eq8"> <svg height="48.1875" id="M76" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 48.1875" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,48.1875)"> <g transform="translate(72,-33.45)"> <text transform="matrix(1,0,0,-1,114.19,49.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,120.97,46.47)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,128.87,49.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="12.04" y="9.7299995"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="58.130001" y="-11.71"> |</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="58.130001" y="-8.54"> |</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="146.25999" y="-11.71"> |</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="146.25999" y="-8.54"> |</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="25.49" y="-10.12"> 1</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="44.231998" y="-10.12"> 我</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="47.707832" y="-10.12"> f</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="60.630001" y="-10.12"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="69.59465" y="-10.12"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="73.758148" y="-10.12"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="77.646584" y="-10.12"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="82.847832" y="-10.12"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="91.72496" y="-10.12"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="98.664124" y="-10.12"> −</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="110.01685" y="-10.12"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="118.969" y="-10.12"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="123.1325" y="-10.12"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="127.99616" y="-10.12"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="133.20992" y="-10.12"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="142.08705" y="-10.12"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="152.23" y="-10.12"> <</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="164.25789" y="-10.12"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="169.35912" y="-10.12"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="25.49" y="9.8699999"> 0</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="44.231998" y="9.8699999"> o</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="50.395977" y="9.8699999"> t</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="53.959332" y="9.8699999"> h</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="60.210831" y="9.8699999"> e</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="65.762161" y="9.8699999"> r</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="70.163216" y="9.8699999"> w</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="79.190384" y="9.8699999"> 我</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="82.666222" y="9.8699999"> 年代</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="87.529884" y="9.8699999"> e</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="93.081215" y="9.8699999"> 。</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="339" y="-7.1054274e-015"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="343.16351" y="-7.1054274e-015"> 1</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="349.41501" y="-7.1054274e-015"> 2</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="355.6665" y="-7.1054274e-015"> )</t年代p一个n></text> </g> </g> </svg></span></span></span><span class="list-item"><span class="list-label">(6)</年代p一个n><年代p一个nclass="list-content"><span class="equation" id="eq9"> <svg height="50.662498" id="M77" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 50.662498" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,50.6625)"> <g transform="translate(72,-31.47)"> <text transform="matrix(1,0,0,-1,83.37,47.82)"> <tspan style="font-size: 12.50px; " x="108.55" y="-7.25"> 1</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="0" y="0"> 一个</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="9.0271664" y="0"> p</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="15.278666" y="0"> E</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="22.917999" y="0"> n</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="31.244997" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="35.408497" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="44.285625" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="49.499378" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="54.600601" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="59.801849" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="71.567169" y="0"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="79.206505" y="0"> =</t年代p一个n></text> <g> <path d="m 175.82,50.94 38.45,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,175.82,39.07)"> <tspan style="font-size: 12.50px; " x="41.73" y="0.99000001"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="13.415719" y="0"> −</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="24.755939" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,225.82,63.76)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="7.4479518" y="0"> −</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="13.443072" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,227.57,41.27)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,229.1,34.09)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="2.7218721" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="8.7169924" y="0"> 1</t年代p一个n></text> <text transform="matrix(1,0,0,-1,247.56,47.82)"> <tspan style="font-size: 12.50px; " x="0" y="0"> l</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="3.4758339" y="0"> n</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="23.190001" y="-8.2200003"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="34.655251" y="-8.2200003"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="38.818748" y="-8.2200003"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="42.707184" y="-8.2200003"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="47.920933" y="-8.2200003"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="56.798065" y="-8.2200003"> )</t年代p一个n></text> <g> <path d="m 260.56,50.94 58.15,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,260.56,39.07)"> <tspan style="font-size: 12.50px; " x="59.349998" y="0.99000001"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="11.465251" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="15.62875" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="19.517183" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="24.730934" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="36.383732" y="0"> +</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="47.736454" y="0"> 1</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="53.987953" y="0"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="69.699997" y="-8.75"> 。</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="207.31" y="-8.75"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="211.4735" y="-8.75"> 1</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="217.72501" y="-8.75"> 3</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="223.9765" y="-8.75"> )</t年代p一个n></text> </g> </g> </svg></span></span></span></span></p> <p> <svg height="14.05" id="M78" style="vertical-align:-2.72116pt;width:36.587502px;" version="1.1" viewbox="0 0 36.587502 14.05" width="36.587502" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.05)"> <g transform="translate(72,-60.76)"> <text transform="matrix(1,0,0,-1,-71.95,63.52)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 一个</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="9.0271664" y="0"> p</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="15.278666" y="0"> E</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="22.917999" y="0"> n</t年代p一个n></text> </g> </g> </svg>是一个标量的特性。</p><h5gydF4y2Baid="sec3.9">3.9。去趋势波动分析</h5><p>gydF4y2Ba去趋势波动分析(DFA)提出了<一个href="#B20">20.</一个>]。</p><p>gydF4y2Ba时间序列的程序计算DFA<年代vg height="14.375" id="M79" style="vertical-align:-3.13504pt;width:97.1875px;" version="1.1" viewbox="0 0 97.1875 14.375" width="97.1875" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.375)"> <g transform="translate(72,-60.5)"> <text transform="matrix(1,0,0,-1,-71.95,63.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-60.91,60.55)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-56.04,63.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="5.2137508" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-43.95,60.55)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-39.08,63.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="5.2137508" y="0"> …</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="19.79225" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="25.006001" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-7.19,60.55)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,1.54,63.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ]</t年代p一个n></text> </g> </g> </svg>如下。<年代p一个nclass="list"><span class="list-item"><span class="list-label">(1)</年代p一个n><年代p一个nclass="list-content">第一次整合<年代vg height="7.1624999" id="M80" style="vertical-align:-0.11285pt;width:8.7250004px;" version="1.1" viewbox="0 0 8.7250004 7.1624999" width="8.7250004" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,7.1625)"> <g transform="translate(72,-66.27)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>到一个新的系列<年代vg height="13.55" id="M81" style="vertical-align:-2.29482pt;width:126.3625px;" version="1.1" viewbox="0 0 126.3625 13.55" width="126.3625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.55)"> <g transform="translate(72,-61.16)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="9.6648188" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="21.705208" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="25.868708" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="32.070194" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="36.233692" y="0"> 1</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="42.485195" y="0"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="46.648693" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="51.862446" y="0"> …</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="66.440941" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="71.654694" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="77.856178" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="82.019676" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="92.659737" y="0"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="96.823235" y="0"> ]</t年代p一个n></text> </g> </g> </svg>,在那里<年代vg height="19.975" id="M82" style="vertical-align:-3.80836pt;width:126.7px;" version="1.1" viewbox="0 0 126.7 19.975" width="126.7" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,19.975)"> <g transform="translate(72,-56.02)"> <text transform="matrix(1,0,0,-1,-71.95,59.87)"> <tspan style="font-size: 12.50px; " x="36.82" y="0.02"> ∑</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="6.201488" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="10.364987" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="17.141613" y="0"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="24.768442" y="0"> =</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-23.71,66.1)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="0" y="9.9300003"> </t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="2.7218721" y="9.9300003"> =</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="8.7169924" y="9.9300003"> 1</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-10.11,59.87)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,0.93,56.75)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,6.92,59.87)"> <tspan style="font-size: 12.50px; " x="0" y="0"> −</t年代p一个n></text> <g> <path d="m 18.27,68.27 6.87,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,18.27,59.87)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="6.8766499" y="0"> )</t年代p一个n></text> </g> </g> </svg>和<年代vg height="12.3125" id="M83" style="vertical-align:-0.11285pt;width:8.7250004px;" version="1.1" viewbox="0 0 8.7250004 12.3125" width="8.7250004" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,12.3125)"> <g transform="translate(72,-62.15)"> <g> <path d="m -71.95,70.71 6.88,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,-71.95,62.31)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>是平均的<年代vg height="10.925" id="M84" style="vertical-align:-3.13504pt;width:86.787498px;" version="1.1" viewbox="0 0 86.787498 10.925" width="86.787498" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.925)"> <g transform="translate(72,-63.26)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-65.07,63.31)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-60.2,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="5.2012482" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-48.11,63.31)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-43.24,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="5.2012482" y="0"> …</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="19.79225" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="25.006001" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-11.36,63.31)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>。</年代p一个n></年代p一个n><span class="list-item"><span class="list-label">(2)</年代p一个n><年代p一个nclass="list-content">综合系列然后切成盒的长度相等<年代vg height="7.1374998" id="M85" style="vertical-align:-0.10033pt;width:7.8874998px;" version="1.1" viewbox="0 0 7.8874998 7.1374998" width="7.8874998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,7.1375)"> <g transform="translate(72,-66.29)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>。在每个箱子的长度<年代vg height="7.1374998" id="M86" style="vertical-align:-0.10033pt;width:7.8874998px;" version="1.1" viewbox="0 0 7.8874998 7.1374998" width="7.8874998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,7.1375)"> <g transform="translate(72,-66.29)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>,最小二乘行适合数据,代表<我>趋势</我>在那个盒子。的<年代vg height="9.8625002" id="M87" style="vertical-align:-2.29482pt;width:7.875px;" version="1.1" viewbox="0 0 7.875 9.8625002" width="7.875" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,9.8625)"> <g transform="translate(72,-64.11)"> <text transform="matrix(1,0,0,-1,-71.95,66.45)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>用直线段的协调<年代vg height="14.6875" id="M88" style="vertical-align:-3.20526pt;width:32.8125px;" version="1.1" viewbox="0 0 32.8125 14.6875" width="32.8125" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.6875)"> <g transform="translate(72,-60.25)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-65.75,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-60.9,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="10.940125" y="0"> )</t年代p一个n></text> </g> </g> </svg>。</年代p一个n></年代p一个n><span class="list-item"><span class="list-label">(3)</年代p一个n><年代p一个nclass="list-content">计算综合系列的均方根波动<年代vg height="30.025" id="M89" style="vertical-align:-6.5653pt;width:227.0125px;" version="1.1" viewbox="0 0 227.0125 30.025" width="227.0125" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,30.025)"> <g transform="translate(72,-47.98)"> <text transform="matrix(1,0,0,-1,-71.95,54.58)"> <tspan style="font-size: 12.50px; " x="37.779999" y="2.8599999"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="7.7268538" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="11.890353" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="18.104343" y="0"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="25.731174" y="0"> =</t年代p一个n></text> <g> <path d="m -20.96,70.71 130.52,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,-20.96,54.58)"> <tspan style="font-size: 12.50px; " x="28.700001" y="0.029999999"> ∑</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="0" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="4.1634989" y="0"> 1</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="10.414999" y="0"> /</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="13.890833" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="24.530886" y="0"> )</t年代p一个n></text> <text transform="matrix(1,0,0,-1,19.17,60.81)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="0" y="9.9300003"> </t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="4.7435842" y="9.9300003"> =</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="10.738704" y="9.9300003"> 1</t年代p一个n></text> <text transform="matrix(1,0,0,-1,34.78,54.58)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="10.364987" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="14.528486" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="21.305113" y="0"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="28.244276" y="0"> −</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="39.584499" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,80.57,51.45)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,85.42,54.58)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="10.940125" y="0"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="15.103624" y="0"> ]</t年代p一个n></text> <text transform="matrix(1,0,0,-1,104.69,59.75)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代p一个n></text> </g> </g> </svg>,其中一部分<年代vg height="14.6875" id="M90" style="vertical-align:-3.20526pt;width:77.099998px;" version="1.1" viewbox="0 0 77.099998 14.6875" width="77.099998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.6875)"> <g transform="translate(72,-60.25)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="6.201488" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="10.364987" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="17.141613" y="0"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="24.080778" y="0"> −</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="35.420998" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-30.32,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-25.47,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="10.940125" y="0"> )</t年代p一个n></text> </g> </g> </svg>被称为消除趋势。</年代p一个n></年代p一个n><span class="list-item"><span class="list-label">(4)</年代p一个n><年代p一个nclass="list-content">波动可以被定义为直线的斜率有关<年代vg height="14.2" id="M91" style="vertical-align:-2.73372pt;width:55.75px;" version="1.1" viewbox="0 0 55.75 14.2" width="55.75" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.2)"> <g transform="translate(72,-60.64)"> <text transform="matrix(1,0,0,-1,-71.95,63.41)"> <tspan style="font-size: 12.50px; " x="0" y="0"> l</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="3.4758339" y="0"> o</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="9.727334" y="0"> g</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="22.217831" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="29.944685" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="34.108185" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="40.322174" y="0"> )</t年代p一个n></text> </g> </g> </svg>来<年代vg height="14.2" id="M92" style="vertical-align:-2.73372pt;width:35.674999px;" version="1.1" viewbox="0 0 35.674999 14.2" width="35.674999" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.2)"> <g transform="translate(72,-60.64)"> <text transform="matrix(1,0,0,-1,-71.95,63.41)"> <tspan style="font-size: 12.50px; " x="0" y="0"> l</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="3.4758339" y="0"> o</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="9.727334" y="0"> g</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="22.217831" y="0"> </t年代p一个n></text> </g> </g> </svg>。</年代p一个n></年代p一个n></span></p> <p>DFA是一个标量的特性。</p><h5gydF4y2Baid="sec3.10">3.10。赫斯特指数</h5><p>gydF4y2Ba赫斯特指数(赫斯特)(<一个href="#B21">21</一个>)也被称为新范围统计(R / S)。计算时间序列的赫斯特指数<年代vg height="14.375" id="M93" style="vertical-align:-3.13504pt;width:128.925px;" version="1.1" viewbox="0 0 128.925 14.375" width="128.925" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.375)"> <g transform="translate(72,-60.5)"> <text transform="matrix(1,0,0,-1,-71.95,63.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="13.340701" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="25.38109" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="29.544588" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-35.52,60.55)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-30.65,63.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="5.2012482" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-18.56,60.55)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-13.69,63.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="5.2012482" y="0"> …</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="19.79225" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="25.006001" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,18.2,60.55)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,26.93,63.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ]</t年代p一个n></text> </g> </g> </svg>第一步是计算时间的累积平均偏差范围内<年代vg height="10.325" id="M94" style="vertical-align:-0.0pt;width:11.225px;" version="1.1" viewbox="0 0 11.225 10.325" width="11.225" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.325)"> <g transform="translate(72,-63.74)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg><span class="equation" id="eq10"> <svg height="50.662498" id="M95" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 50.662498" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,50.6625)"> <g transform="translate(72,-31.47)"> <text transform="matrix(1,0,0,-1,60.31,47.82)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="12.703048" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="16.866547" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="20.779985" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="25.993736" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="34.870869" y="0"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="42.510201" y="0"> =</t年代p一个n></text> <text transform="matrix(1,0,0,-1,121.57,63.76)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,114.86,41.27)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,116.39,34.09)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="2.7218721" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="8.7169924" y="0"> 1</t年代p一个n></text> <text transform="matrix(1,0,0,-1,133.1,45.3)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="5.8499999" y="-2.52"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,145.83,44.69)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,151.83,47.82)"> <tspan style="font-size: 12.50px; " x="0" y="0"> −</t年代p一个n></text> <g> <path d="m 163.17,56.22 6.88,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,163.17,47.82)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="6.8800001" y="2.52"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="14.81" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="29.976139" y="0"> w</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="39.003304" y="0"> h</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="45.254807" y="0"> e</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="50.806137" y="0"> r</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="54.957134" y="0"> e</t年代p一个n></text> <g> <path d="m 227.84,56.22 6.88,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,227.84,47.82)"> <tspan style="font-size: 12.50px; " x="24.9" y="-7.25"> 1</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="10.339981" y="0"> =</t年代p一个n></text> <g> <path d="m 251.42,50.94 8.88,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,251.42,39.07)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,266.47,63.76)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,261.5,41.27)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,263.03,34.09)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="2.7218721" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="8.7169924" y="0"> 1</t年代p一个n></text> <text transform="matrix(1,0,0,-1,277.65,47.82)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,284.53,44.69)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,287.75,47.82)"> <tspan style="font-size: 12.50px; " x="30.879999" y="0.039999999"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="59.32" y="0.039999999"> ]</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="65.559998" y="0"> 。</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="0" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="9.364747" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="16.754021" y="0"> ∈</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="35.049999" y="0"> 1</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="41.301498" y="0"> 。</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="44.42725" y="0"> 。</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="47.553001" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="180.12" y="-0.79000002"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="184.28349" y="-0.79000002"> 1</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="190.535" y="-0.79000002"> 4</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="196.7865" y="-0.79000002"> )</t年代p一个n></text> </g> </g> </svg></span>然后,<年代vg height="13.45" id="M96" style="vertical-align:-2.21957pt;width:61.587502px;" version="1.1" viewbox="0 0 61.587502 13.45" width="61.587502" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.45)"> <g transform="translate(72,-61.24)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> R</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="8.3395014" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="12.503" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="19.37965" y="0"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="23.54315" y="0"> /</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="27.018984" y="0"> 年代</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="33.97065" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="38.134151" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="45.010799" y="0"> )</t年代p一个n></text> </g> </g> </svg>是计算<年代p一个nclass="equation" id="eq11"> <svg height="50.674999" id="M97" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 50.674999" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,50.675)"> <g transform="translate(72,-31.46)"> <text transform="matrix(1,0,0,-1,104.96,63.41)"> <tspan style="font-size: 12.50px; " x="0" y="0"> R</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="10.414999" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="14.578498" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="23.455627" y="0"> )</t年代p一个n></text> <g> <path d="m 104.96,58.32 27.63,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,105.65,46.44)"> <tspan style="font-size: 12.50px; " x="31.610001" y="-8.75"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="0" y="0"> 年代</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="9.039669" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="13.203168" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="22.080297" y="0"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="44.84" y="-16.969999"> 米</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="54.567333" y="-16.969999"> 一个</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="60.118668" y="-16.969999"> x</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="70.533669" y="-16.969999"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="74.697166" y="-16.969999"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="87.412712" y="-16.969999"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="91.576218" y="-16.969999"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="95.489655" y="-16.969999"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="100.6909" y="-16.969999"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="109.56803" y="-16.969999"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="113.73153" y="-16.969999"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="120.67069" y="-16.969999"> −</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="132.02342" y="-16.969999"> 米</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="141.75075" y="-16.969999"> 我</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="145.22659" y="-16.969999"> n</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="155.64159" y="-16.969999"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="159.80508" y="-16.969999"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="172.52063" y="-16.969999"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="176.68413" y="-16.969999"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="180.59758" y="-16.969999"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="185.79883" y="-16.969999"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="194.67595" y="-16.969999"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="198.83945" y="-16.969999"> )</t年代p一个n></text> <g> <path d="m 150.49,58.32 158.17,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,167.62,35.2)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <g> <path d="m 180.83,54.19 110.71,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,180.83,37.69)"> <tspan style="font-size: 12.50px; " x="29.02" y="0.029999999"> ∑</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="0" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="4.1634989" y="0"> 1</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="10.414999" y="0"> /</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="13.890833" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="22.767963" y="0"> )</t年代p一个n></text> <text transform="matrix(1,0,0,-1,221.28,43.92)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="0" y="9.9300003"> </t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="2.7393761" y="9.9300003"> =</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="8.7344961" y="9.9300003"> 1</t年代p一个n></text> <text transform="matrix(1,0,0,-1,234.89,35.17)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="4.7800002" y="-2.52"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="13.744651" y="-2.52"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="17.90815" y="-2.52"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="21.821589" y="-2.52"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="28.760754" y="-2.52"> −</t年代p一个n></text> <g> <path d="m 275,46.09 6.87,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,275,37.69)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="6.8699999" y="2.52"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,286.66,45.22)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代p一个n></text> <text transform="matrix(1,0,0,-1,309.86,55.19)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 。</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="158.00999" y="6.5900002"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="162.17349" y="6.5900002"> 1</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="168.425" y="6.5900002"> 5</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="174.6765" y="6.5900002"> )</t年代p一个n></text> </g> </g> </svg></span>赫斯特指数是通过计算产生的直线的斜率<年代vg height="13.5625" id="M98" style="vertical-align:-2.21957pt;width:90.324997px;" version="1.1" viewbox="0 0 90.324997 13.5625" width="90.324997" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.5625)"> <g transform="translate(72,-61.15)"> <text transform="matrix(1,0,0,-1,-71.95,63.41)"> <tspan style="font-size: 12.50px; " x="0" y="0"> l</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="3.4758339" y="0"> n</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="15.966331" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="20.129829" y="0"> R</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="28.469332" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="32.632832" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="38.846821" y="0"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="43.010319" y="0"> /</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="46.486153" y="0"> 年代</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="53.43782" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="57.601322" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="63.815311" y="0"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="67.978813" y="0"> )</t年代p一个n></text> </g> </g> </svg>与<年代vg height="13.5625" id="M99" style="vertical-align:-2.21957pt;width:38.275002px;" version="1.1" viewbox="0 0 38.275002 13.5625" width="38.275002" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.5625)"> <g transform="translate(72,-61.15)"> <text transform="matrix(1,0,0,-1,-71.95,63.41)"> <tspan style="font-size: 12.50px; " x="0" y="0"> l</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="3.4758339" y="0"> n</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="15.966331" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="20.129829" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="26.343821" y="0"> )</t年代p一个n></text> </g> </g> </svg>为<年代vg height="13.125" id="M100" style="vertical-align:-1.95624pt;width:66.612503px;" version="1.1" viewbox="0 0 66.612503 13.125" width="66.612503" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.125)"> <g transform="translate(72,-61.5)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="9.6773224" y="0"> ∈</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="21.71771" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="25.88121" y="0"> 2</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="32.13271" y="0"> 。</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="35.258461" y="0"> 。</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="38.384209" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="49.024261" y="0"> ]</t年代p一个n></text> </g> </g> </svg>。赫斯特指数是一个标量的特性。</p><h4gydF4y2Baid="using-pyeeg-on-real-data">4所示。使用PyEEG真实数据</h4><p>gydF4y2Ba在本节中,我们使用PyEEG真正的脑电图数据集来演示它的使用在日常研究。</p><p>gydF4y2Ba数据集(<一个href="http://epileptologie-bonn.de/cms/front_content.php?idcat=193&lang=3" target="_blank">http://epileptologie-bonn.de/cms/front_content.php?idcat=193&lang=3</一个>),从Klinik皮毛Epileptologie,德国波恩大学(<一个href="#B22">22</一个>之前,已广泛应用于癫痫的研究。总共有五个组,每个包含100单通道脑电图段。每个部分都有4096个样本。数据集A和B是颅外的脑电图从5健康志愿者睁大眼睛和闭上眼睛,分别。集C和D是在发作期颅内数据而设置E发作的时间。段D从病灶内,而在海马结构的C是相反的半球的大脑。集C, D, E是由5个病人的脑电图。数据的光谱带宽0.5 -85 Hz。请参阅[<一个href="#B22">22</一个>为更多的细节。</p><p>gydF4y2Ba使用PyEEG就像使用任何其他Python模块。用户只需要导入PyEEG然后根据需要调用它的函数。PyEEG是作为一个Python文件提供。因此,它只需要下载并放置在Python模块搜索路径上的一个目录,比如工作目录。另外,<年代p一个n年代tyle="font-family:monospace">PYTHONPATH环境</年代p一个n>环境变量可以设置为指向PyEEG的位置。</p><p>gydF4y2Ba在Python解释器,我们第一次进口PyEEG和加载数据<年代p一个nclass="list"><span class="list-item"><span class="list-label"></span><span class="list-content"> <svg height="8.8500004" id="M101" style="vertical-align:-0.30096pt;width:32.237499px;" version="1.1" viewbox="0 0 32.237499 8.8500004" width="32.237499" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,8.85)"> <g transform="translate(72,-64.92)"> <text transform="matrix(1,0,0,-1,-71.95,65.27)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ></t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="8.5645552" y="0"> ></t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="17.12911" y="0"> ></t年代p一个n></text> </g> </g> </svg><span style="font-family:monospace">进口pyeeg</年代p一个n></年代p一个n></span><span class="list-item"><span class="list-label"></span><span class="list-content"> <svg height="8.8500004" id="M102" style="vertical-align:-0.30096pt;width:32.237499px;" version="1.1" viewbox="0 0 32.237499 8.8500004" width="32.237499" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,8.85)"> <g transform="translate(72,-64.92)"> <text transform="matrix(1,0,0,-1,-71.95,65.27)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ></t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="8.5645552" y="0"> ></t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="17.12911" y="0"> ></t年代p一个n></text> </g> </g> </svg><span style="font-family:monospace">fid = (“Z001开放。txt”、“r”)</年代p一个n></年代p一个n></span><span class="list-item"><span class="list-label"></span><span class="list-content"> <svg height="8.8500004" id="M103" style="vertical-align:-0.30096pt;width:32.237499px;" version="1.1" viewbox="0 0 32.237499 8.8500004" width="32.237499" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,8.85)"> <g transform="translate(72,-64.92)"> <text transform="matrix(1,0,0,-1,-71.95,65.27)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ></t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="8.5645552" y="0"> ></t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="17.12911" y="0"> ></t年代p一个n></text> </g> </g> </svg><span style="font-family:monospace">tmp = fid.readlines ()</年代p一个n></年代p一个n></span><span class="list-item"><span class="list-label"></span><span class="list-content"> <svg height="8.8500004" id="M104" style="vertical-align:-0.30096pt;width:32.237499px;" version="1.1" viewbox="0 0 32.237499 8.8500004" width="32.237499" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,8.85)"> <g transform="translate(72,-64.92)"> <text transform="matrix(1,0,0,-1,-71.95,65.27)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ></t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="8.5645552" y="0"> ></t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="17.12911" y="0"> ></t年代p一个n></text> </g> </g> </svg><span style="font-family:monospace">data =(浮动的k (k) tmp)</年代p一个n></年代p一个n></span></span></p> <p>在哪里<年代p一个n年代tyle="font-family:monospace">Z001.txt</年代p一个n>第一段设置的数据类型<年代p一个n年代tyle="font-family:monospace">数据</年代p一个n>是<年代p一个n年代tyle="font-family:monospace">列表</年代p一个n>。加载脑电图数据后,我们可以使用PyEEG提取功能如下(使用所有缺省参数):<年代p一个nclass="list"><span class="list-item"><span class="list-label"></span><span class="list-content"> <svg height="8.8500004" id="M105" style="vertical-align:-0.30096pt;width:32.237499px;" version="1.1" viewbox="0 0 32.237499 8.8500004" width="32.237499" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,8.85)"> <g transform="translate(72,-64.92)"> <text transform="matrix(1,0,0,-1,-71.95,65.27)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ></t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="8.5645552" y="0"> ></t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="17.12911" y="0"> ></t年代p一个n></text> </g> </g> </svg><span style="font-family:monospace">DFA = pyeeg.dfa(数据)</年代p一个n></年代p一个n></span><span class="list-item"><span class="list-label"></span><span class="list-content"> <svg height="8.8500004" id="M106" style="vertical-align:-0.30096pt;width:32.237499px;" version="1.1" viewbox="0 0 32.237499 8.8500004" width="32.237499" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,8.85)"> <g transform="translate(72,-64.92)"> <text transform="matrix(1,0,0,-1,-71.95,65.27)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ></t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="8.5645552" y="0"> ></t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="17.12911" y="0"> ></t年代p一个n></text> </g> </g> </svg><span style="font-family:monospace">DFA</年代p一个n></年代p一个n></span><span class="list-item"><span class="list-label"></span><span class="list-content"><span style="font-family:monospace">0.81450526948129354</年代p一个n></年代p一个n></span><span class="list-item"><span class="list-label"></span><span class="list-content"> <svg height="8.8500004" id="M107" style="vertical-align:-0.30096pt;width:32.237499px;" version="1.1" viewbox="0 0 32.237499 8.8500004" width="32.237499" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,8.85)"> <g transform="translate(72,-64.92)"> <text transform="matrix(1,0,0,-1,-71.95,65.27)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ></t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="8.5645552" y="0"> ></t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="17.12911" y="0"> ></t年代p一个n></text> </g> </g> </svg><span style="font-family:monospace">Hurst_Exponent = pyeeg.hurst(数据)</年代p一个n></年代p一个n></span><span class="list-item"><span class="list-label"></span><span class="list-content"> <svg height="8.8500004" id="M108" style="vertical-align:-0.30096pt;width:32.237499px;" version="1.1" viewbox="0 0 32.237499 8.8500004" width="32.237499" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,8.85)"> <g transform="translate(72,-64.92)"> <text transform="matrix(1,0,0,-1,-71.95,65.27)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ></t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="8.5645552" y="0"> ></t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="17.12911" y="0"> ></t年代p一个n></text> </g> </g> </svg><span style="font-family:monospace">Hurst_Exponent</年代p一个n></年代p一个n></span><span class="list-item"><span class="list-label"></span><span class="list-content"><span style="font-family:monospace">0.68053321812240675</年代p一个n></年代p一个n></span><span class="list-item"><span class="list-label"></span><span class="list-content"> <svg height="8.8500004" id="M109" style="vertical-align:-0.30096pt;width:32.237499px;" version="1.1" viewbox="0 0 32.237499 8.8500004" width="32.237499" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,8.85)"> <g transform="translate(72,-64.92)"> <text transform="matrix(1,0,0,-1,-71.95,65.27)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ></t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="8.5645552" y="0"> ></t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="17.12911" y="0"> ></t年代p一个n></text> </g> </g> </svg><span style="font-family:monospace">PFD = pyeeg.pfd(数据)</年代p一个n></年代p一个n></span><span class="list-item"><span class="list-label"></span><span class="list-content"> <svg height="8.8500004" id="M110" style="vertical-align:-0.30096pt;width:32.237499px;" version="1.1" viewbox="0 0 32.237499 8.8500004" width="32.237499" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,8.85)"> <g transform="translate(72,-64.92)"> <text transform="matrix(1,0,0,-1,-71.95,65.27)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ></t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="8.5645552" y="0"> ></t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="17.12911" y="0"> ></t年代p一个n></text> </g> </g> </svg><span style="font-family:monospace">PFD</年代p一个n></年代p一个n></span><span class="list-item"><span class="list-label"></span><span class="list-content"><span style="font-family:monospace">0.58651018327048932</年代p一个n></年代p一个n></span></span></p> <p>由于空间限制,我们不能打印所有特征值的脑电图段。相反,我们想象的平均特性(除了RIR和PSI)在每个五套的图<一个href="//www.newsama.com/journals/cin/2011/406391/fig2/" target="_blank">2</一个>。误差线代表在每组的方差特性。棘”五集绘制在图<一个href="//www.newsama.com/journals/cin/2011/406391/fig3/" target="_blank">3</一个>。用户可以改建这些照片并得到平均在Python解释器的功能测试脚本(<一个href="http://code.google.com/p/pyeeg/wiki/TestScript" target="_blank">http://code.google.com/p/pyeeg/wiki/TestScript</一个>从我们的项目网站。</p><gydF4y2Badiv class="partial-carousel-wrapper"> <div class="floats-partial-section"> <div class="floats-partial-content"> <div class="partial-carousel--full-image partial-carousel-e0c6d1f08554e0450df94b86bb6d2b49"> <div class="partial-carousel--single-image"> <img loading="lazy" alt="(一)gydF4y2Ba" src="https://static.hindawi.com/articles/cin/volume-2011/406391/figures/406391.fig.002a.jpg"> <br> <strong>(一)</年代trong></div> <div class="partial-carousel--single-image"> <img loading="lazy" alt="(b)gydF4y2Ba" src="https://static.hindawi.com/articles/cin/volume-2011/406391/figures/406391.fig.002b.jpg"> <br> <strong>(b)</年代trong></div> <div class="partial-carousel--single-image"> <img loading="lazy" alt="(c)gydF4y2Ba" src="https://static.hindawi.com/articles/cin/volume-2011/406391/figures/406391.fig.002c.jpg"> <br> <strong>(c)</年代trong></div> <div class="partial-carousel--single-image"> <img loading="lazy" alt="(d)gydF4y2Ba" src="https://static.hindawi.com/articles/cin/volume-2011/406391/figures/406391.fig.002d.jpg"> <br> <strong>(d)</年代trong></div> <div class="partial-carousel--single-image"> <img loading="lazy" alt="(e)gydF4y2Ba" src="https://static.hindawi.com/articles/cin/volume-2011/406391/figures/406391.fig.002e.jpg"> <br> <strong>(e)</年代trong></div> <div class="partial-carousel--single-image"> <img loading="lazy" alt="(f)gydF4y2Ba" src="https://static.hindawi.com/articles/cin/volume-2011/406391/figures/406391.fig.002f.jpg"> <br> <strong>(f)</年代trong></div> <div class="partial-carousel--single-image"> <img loading="lazy" alt="(g)gydF4y2Ba" src="https://static.hindawi.com/articles/cin/volume-2011/406391/figures/406391.fig.002g.jpg"> <br> <strong>(g)</年代trong></div> <div class="partial-carousel--single-image"> <img loading="lazy" alt="(h)gydF4y2Ba" src="https://static.hindawi.com/articles/cin/volume-2011/406391/figures/406391.fig.002h.jpg"> <br> <strong>(h)</年代trong></div> <div class="partial-carousel--single-image"> <img loading="lazy" alt="(我)gydF4y2Ba" src="https://static.hindawi.com/articles/cin/volume-2011/406391/figures/406391.fig.002i.jpg"> <br> <strong>(我)</年代trong></div> <div class="partial-carousel--single-image"> <img loading="lazy" alt="(j)gydF4y2Ba" src="https://static.hindawi.com/articles/cin/volume-2011/406391/figures/406391.fig.002j.jpg"> <br> <strong>(j)</年代trong></div> </div> </div> <div class="floats-partial-middle"> <div class="floats-partial-middle--thumbs"> <div class="partial-carousel-dots-e0c6d1f08554e0450df94b86bb6d2b49 partial-carousel-thumbnail"> <button aria-label="Slide to (a) " class="partial-carousel-dot"><img loading="lazy" alt="(一)gydF4y2Ba" src="https://static.hindawi.com/articles/cin/volume-2011/406391/thumbnails/406391.fig.002a_th.jpg"><br><strong>(一)</年代trong></button> <button aria-label="Slide to (b) " class="partial-carousel-dot"><img loading="lazy" alt="(b)gydF4y2Ba" src="https://static.hindawi.com/articles/cin/volume-2011/406391/thumbnails/406391.fig.002b_th.jpg"><br><strong>(b)</年代trong></button> <button aria-label="Slide to (c) " class="partial-carousel-dot"><img loading="lazy" alt="(c)gydF4y2Ba" src="https://static.hindawi.com/articles/cin/volume-2011/406391/thumbnails/406391.fig.002c_th.jpg"><br><strong>(c)</年代trong></button> <button aria-label="Slide to (d) " class="partial-carousel-dot"><img loading="lazy" alt="(d)gydF4y2Ba" src="https://static.hindawi.com/articles/cin/volume-2011/406391/thumbnails/406391.fig.002d_th.jpg"><br><strong>(d)</年代trong></button> <button aria-label="Slide to (e) " class="partial-carousel-dot"><img loading="lazy" alt="(e)gydF4y2Ba" src="https://static.hindawi.com/articles/cin/volume-2011/406391/thumbnails/406391.fig.002e_th.jpg"><br><strong>(e)</年代trong></button> <button aria-label="Slide to (f) " class="partial-carousel-dot"><img loading="lazy" alt="(f)gydF4y2Ba" src="https://static.hindawi.com/articles/cin/volume-2011/406391/thumbnails/406391.fig.002f_th.jpg"><br><strong>(f)</年代trong></button> <button aria-label="Slide to (g) " class="partial-carousel-dot"><img loading="lazy" alt="(g)gydF4y2Ba" src="https://static.hindawi.com/articles/cin/volume-2011/406391/thumbnails/406391.fig.002g_th.jpg"><br><strong>(g)</年代trong></button> <button aria-label="Slide to (h) " class="partial-carousel-dot"><img loading="lazy" alt="(h)gydF4y2Ba" src="https://static.hindawi.com/articles/cin/volume-2011/406391/thumbnails/406391.fig.002h_th.jpg"><br><strong>(h)</年代trong></button> <button aria-label="Slide to (i) " class="partial-carousel-dot"><img loading="lazy" alt="(我)gydF4y2Ba" src="https://static.hindawi.com/articles/cin/volume-2011/406391/thumbnails/406391.fig.002i_th.jpg"><br><strong>(我)</年代trong></button> <button aria-label="Slide to (j) " class="partial-carousel-dot"><img loading="lazy" alt="(j)gydF4y2Ba" src="https://static.hindawi.com/articles/cin/volume-2011/406391/thumbnails/406391.fig.002j_th.jpg"><br><strong>(j)</年代trong></button> </div> </div> <div class="floats-partial-middle--nav"> <div class="partial-carousel-next-prev-e0c6d1f08554e0450df94b86bb6d2b49 partial-carousel-next-prev"> <button aria-label="Previous" class="carousel-prev"></button> <button aria-label="Next" class="carousel-next"></button> </div> </div> </div> <div class="floats-partial-footer"> <div class="floats-partial-caption"> <span class="caption-text">图2</年代p一个n><一个一个r我一个- - - - - -label="View full page" class="caption-partial-url" href="//www.newsama.com/journals/cin/2011/406391/fig2/" title="" target="_blank"></a> </div> <div class="floats-partial-caption-text"> <table> <tbody> <tr> <td>分布的十个特征提取PyEEG每组。</tgydF4y2Bad> </tr> </tbody> </table> </div> </div> </div> </div> <div class="partial-carousel-wrapper"> <div class="floats-partial-section"> <div class="floats-partial-content"> <div class="partial-carousel--full-image partial-carousel-e50b1ed122baec47494fc7bf5e66dfa9"> <div class="partial-carousel--single-image"> <img loading="lazy" alt="(一)gydF4y2Ba" src="https://static.hindawi.com/articles/cin/volume-2011/406391/figures/406391.fig.003a.jpg"> <br> <strong>(一)</年代trong></div> <div class="partial-carousel--single-image"> <img loading="lazy" alt="(b)gydF4y2Ba" src="https://static.hindawi.com/articles/cin/volume-2011/406391/figures/406391.fig.003b.jpg"> <br> <strong>(b)</年代trong></div> <div class="partial-carousel--single-image"> <img loading="lazy" alt="(c)gydF4y2Ba" src="https://static.hindawi.com/articles/cin/volume-2011/406391/figures/406391.fig.003c.jpg"> <br> <strong>(c)</年代trong></div> <div class="partial-carousel--single-image"> <img loading="lazy" alt="(d)gydF4y2Ba" src="https://static.hindawi.com/articles/cin/volume-2011/406391/figures/406391.fig.003d.jpg"> <br> <strong>(d)</年代trong></div> <div class="partial-carousel--single-image"> <img loading="lazy" alt="(e)gydF4y2Ba" src="https://static.hindawi.com/articles/cin/volume-2011/406391/figures/406391.fig.003e.jpg"> <br> <strong>(e)</年代trong></div> </div> </div> <div class="floats-partial-middle"> <div class="floats-partial-middle--thumbs"> <div class="partial-carousel-dots-e50b1ed122baec47494fc7bf5e66dfa9 partial-carousel-thumbnail"> <button aria-label="Slide to (a) " class="partial-carousel-dot"><img loading="lazy" alt="(一)gydF4y2Ba" src="https://static.hindawi.com/articles/cin/volume-2011/406391/thumbnails/406391.fig.003a_th.jpg"><br><strong>(一)</年代trong></button> <button aria-label="Slide to (b) " class="partial-carousel-dot"><img loading="lazy" alt="(b)gydF4y2Ba" src="https://static.hindawi.com/articles/cin/volume-2011/406391/thumbnails/406391.fig.003b_th.jpg"><br><strong>(b)</年代trong></button> <button aria-label="Slide to (c) " class="partial-carousel-dot"><img loading="lazy" alt="(c)gydF4y2Ba" src="https://static.hindawi.com/articles/cin/volume-2011/406391/thumbnails/406391.fig.003c_th.jpg"><br><strong>(c)</年代trong></button> <button aria-label="Slide to (d) " class="partial-carousel-dot"><img loading="lazy" alt="(d)gydF4y2Ba" src="https://static.hindawi.com/articles/cin/volume-2011/406391/thumbnails/406391.fig.003d_th.jpg"><br><strong>(d)</年代trong></button> <button aria-label="Slide to (e) " class="partial-carousel-dot"><img loading="lazy" alt="(e)gydF4y2Ba" src="https://static.hindawi.com/articles/cin/volume-2011/406391/thumbnails/406391.fig.003e_th.jpg"><br><strong>(e)</年代trong></button> </div> </div> <div class="floats-partial-middle--nav"> <div class="partial-carousel-next-prev-e50b1ed122baec47494fc7bf5e66dfa9 partial-carousel-next-prev"> <button aria-label="Previous" class="carousel-prev"></button> <button aria-label="Next" class="carousel-next"></button> </div> </div> </div> <div class="floats-partial-footer"> <div class="floats-partial-caption"> <span class="caption-text">图3</年代p一个n><一个一个r我一个- - - - - -label="View full page" class="caption-partial-url" href="//www.newsama.com/journals/cin/2011/406391/fig3/" title="" target="_blank"></a> </div> <div class="floats-partial-caption-text"> <table> <tbody> <tr> <td>每一组的平均PSI。注意,规模<年代vg height="9.8625002" id="M111" style="vertical-align:-2.29482pt" version="1.1" viewbox="0 0 7.875 9.8625002" width="7.875" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,9.8625)"> <g transform="translate(72,-64.11)"> <text transform="matrix(1,0,0,-1,-71.95,66.45)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>设在集合<年代vg height="10.475" id="M112" style="vertical-align:-0.0pt" version="1.1" viewbox="0 0 9.6750002 10.475" width="9.6750002" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.475)"> <g transform="translate(72,-63.62)"> <text transform="matrix(1,0,0,-1,-71.95,63.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> E</t年代p一个n></text> </g> </g> </svg>远远大于其他集。</tgydF4y2Bad> </tr> </tbody> </table> </div> </div> </div> </div> <p>从数据<一个href="//www.newsama.com/journals/cin/2011/406391/fig2/" target="_blank">2</一个>和<一个href="//www.newsama.com/journals/cin/2011/406391/fig3/" target="_blank">3</一个>,我们可以看到,健康,发作,发作的脑电图信号有不同的分布对于大多数功能。表<一个href="//www.newsama.com/journals/cin/2011/406391/tab2/" target="_blank">2</一个>在这个实验中使用的参数列表。</p><gydF4y2Badiv class="floats-partial-section partial-other-wrapper" data-section="tab2"> <div class="floats-partial-footer"> <div class="floats-partial-caption"> <span class="caption-text">表2</年代p一个n><一个一个r我一个- - - - - -label="View full page" class="caption-partial-url" href="//www.newsama.com/journals/cin/2011/406391/tab2/" title="" target="_blank"></a> </div> <div class="floats-partial-caption-text"> 在我们的示例中使用的参数值。</gydF4y2Badiv> <a class="table-thumb-overlay" href="//www.newsama.com/journals/cin/2011/406391/tab2" target="_blank" aria-label="View full page"></a> </div> </div> <h4 id="discussion-and-future-development">5。讨论和未来发展</h4><p>gydF4y2Ba到目前为止,我们已经列出的特性,可以提取PyEEG及其定义。实现棒的精确定义虽然更快的算法可能存在。还有许多其他的脑电图特点,比如李雅普诺夫指数,在PyEEG还没有被实现。更脑电图的功能将被添加到PyEEG将来当我们完成单元测试和文档为每一个函数。在个人电子邮件,一些开源项目,如ConnectomeViewer (<一个href="http://www.connectomeviewer.org/viewer" target="_blank">http://www.connectomeviewer.org/viewer</一个>)和NIPY / PBrain (<一个href="http://nipy.sourceforge.net/pbrain/" target="_blank">http://nipy.sourceforge.net/pbrain/</一个>),表示有兴趣包括PyEEG进他们的代码。因此,我们将继续保持PyEEG只要它能使整个计算神经科学社区受益。</p><h4gydF4y2Baid="availability">可用性</h4><p>gydF4y2Ba该软件是v下发布的GNU GPL。3在Google代码:<一个href="http://code.google.com/p/pyeeg/" target="_blank">http://code.google.com/p/pyeeg/</一个>。不需要商业软件PyEEG运行。因为Python是跨平台,PyEEG可以运行在Linux、Mac OS和Windows。</p></gydF4y2Badiv> </div> <div class="ArticleReferences_xmlContent__TZqgx"> <h4 class="ArticleReferences_references__dHBcT" id="references">引用</h4><olgydF4y2Baclass="ArticleReferences_orderedReferences__K1TM4"> <li class="ArticleReferences_articleReference__7aCxy" id="B1"> <div class="referenceContent"> <p class="referenceText">j . 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Litt”看到下面成了新奇检测癫痫颅内脑电图的分析,“<我>机器学习研究杂志》上</我>7卷,第1044 - 1025页,2006年。</p>gydF4y2Ba视图:<gydF4y2Ba!-- --> <a href="https://scholar.google.com/scholar_lookup?title=One-class%20novelty%20detection%20for%20seizure%20analysis%20from%20intracranial%20EEG&author=A.%20B.%20Gardner&author=A.%20M.%20Krieger&author=G.%20Vachtsevanos&author=B.%20Litt&publication_year=2006" target="_blank" rel="noreferrer">谷歌学术搜索</一个></div></li> <li class="ArticleReferences_articleReference__7aCxy" id="B6"> <div class="referenceContent"> <p class="referenceText">c . w . Ko和h·w·钟”,通过人工神经网络自动峰值检测使用原始脑电图数据:数据准备和在线识别的局限性影响,”<我>临床神经生理学</我>,卷111,不。3、477 - 481年,2000页。</p>gydF4y2Ba视图:<gydF4y2Ba!-- --> <a href="https://doi.org/10.1016/S1388-2457(99)00284-9" target="_blank" rel="noreferrer">出版商的网站</一个><年代p一个nclass="sep">|</年代p一个n><一个href="https://scholar.google.com/scholar_lookup?title=Automatic%20spike%20detection%20via%20an%20artificial%20neural%20network%20using%20raw%20EEG%20data%3A%20effects%20of%20data%20preparation%20and%20implications%20in%20the%20limitations%20of%20online%20recognition&author=C.%20W.%20Ko&author=H.%20W.%20Chung&publication_year=2000" target="_blank" rel="noreferrer">谷歌学术搜索</一个></div></li> <li class="ArticleReferences_articleReference__7aCxy" id="B7"> <div class="referenceContent"> <p class="referenceText">诉Srinivasan、c . Eswaran和n . Sriraam”近似entropy-based癫痫脑电图检测使用人工神经网络,”<我>我EEE在生物医学信息技术</我>,11卷,不。3、288 - 295年,2007页。</p>gydF4y2Ba视图:<gydF4y2Ba!-- --> <a href="https://doi.org/10.1109/TITB.2006.884369" target="_blank" rel="noreferrer">出版商的网站</一个><年代p一个nclass="sep">|</年代p一个n><一个href="https://scholar.google.com/scholar_lookup?title=Approximate%20entropy-based%20epileptic%20EEG%20detection%20using%20artificial%20neural%20networks&author=V.%20Srinivasan&author=C.%20Eswaran&author=N.%20Sriraam&publication_year=2007" target="_blank" rel="noreferrer">谷歌学术搜索</一个></div></li> <li class="ArticleReferences_articleReference__7aCxy" id="B8"> <div class="referenceContent"> <p class="referenceText">f·s·鲍,j·m·高,j . 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