东北大学学报（自然科学版）

东北大学学报:自然科学版 ›› 2015, Vol. 36 ›› Issue (11): 1535-1539.DOI: 10.12068/j.issn.1005-3026.2015.11.004

• 信息与控制 • 上一篇    下一篇

经验模态分解中一种改进的包络线拟合算法

吴贤规， 王安娜， 会国涛   

  1. (东北大学 信息科学与工程学院， 辽宁 沈阳110819)
  • 收稿日期:2014-11-12 修回日期:2014-11-12 出版日期:2015-11-15 发布日期:2015-11-10
  • 通讯作者: 吴贤规
  • 作者简介:吴贤规(1980-)，男，朝鲜平壤人，东北大学博士研究生； 王安娜(1956-)，女，辽宁鞍山人，东北大学教授，博士生导师.
  • 基金资助:
    国家自然科学基金青年基金资助项目(61403073).

An Improved Envelope Fitting Algorithm for the Empirical Mode Decomposition

WU Xian-gui， WANG An-na， HUI Guo-tao   

  1. School of Information Science & Engineering， Northeastern University， Shenyang 110819， China.
  • Received:2014-11-12 Revised:2014-11-12 Online:2015-11-15 Published:2015-11-10
  • Contact: WU Xian-gui
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摘要： 针对经验模态分解(empirical mode decomposition， EMD)过程中存在的包络线拟合问题，提出了一种精确消除欠冲现象的改进算法.该算法首先确定利用三次样条插值(cubic spline interpolation， CSI)进行包络线拟合时所产生的欠冲区间，然后通过单调分段三次多项式插值法对欠冲区间包络线进行补偿.该改进的包络线能紧紧地包住原始信号，而不影响信号本身的特征，尽可能保持前包络线的平滑性.仿真结果表明，提出的方法可以有效地消除由CSI所造成的欠冲现象，拟合出更好的包络线，进一步提高EMD的分解精度.

关键词: 希尔伯特-黄变换, 经验模态分解, 欠冲现象, 包络线拟合, 单调分段三次多项式插值

Abstract: Due to the envelope fitting problem exists in the process of empirical mode decomposition， an improved algorithm was proposed which could eliminate the undershoot phenomenon exactly. Firstly， in this improved algorithm， the cubic spline interpolation was used to determine the regions of undershoot which generated during the execution of envelope fitting. Secondly， the envelope intervals of undershoot regions were compensated by the monotone piecewise cubic polynomial interpolation. The original signal could be wrapped tightly by this modified envelope， which did not affect the characteristics of signal itself， and could keep the smoothness of previous envelope as well as possible. The simulation results showed that the undershoot phenomenon caused by cubic spline interpolation could be effectively eliminated and the envelope could be obtained better by this algorithm. In addition， the accuracy of empirical mode decomposition could be further improved.

Key words: Hilbert-Huang transform, empirical mode decomposition, undershoot phenomenon, envelope fitting, monotone piecewise cubic polynomial interpolation

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