基于EMD算法的滤波系统设计.docVIP

摘 要 快速傅里叶、Wigner-Ville变换、小波变换在分析非线性非平稳信号时都存在着各自的缺陷与不足。为了更好地解决这些问题，本文采用了经验模态分解EMD (Empirical Mode Decomposition)来对信号进行分析和滤波。EMD 分解将复杂信号分解成有限个固有模态函数 IMF（Intrinsic Mode Functions）之和，具有很高的频率分辨率和自适应性。本文对经验模态分解整个理论体系进行了深入的研究，重点研究了EMD 时频分析的应用和基于 EMD 的滤波方法。 本文首先引入了瞬时频率的概念，论述了IMF的基本概念和EMD分解算法原理，并且分析了EMD算法的特点，结合IMF给出了边际谱和Hilbert谱的物理含义，对整个 EMD 时频分析理论进行了详细的论述。分析EMD时频分析方法在模态混叠、停止准则等方面存在的不足。然后通过仿真实验将EMD时频分析方法与传统的时频分析方法进行了比较研究，验证了EMD时频分析方法具有很高的时频分辨率。最后研究了基于EMD的滤波方法，验证了该方法的有效性及优越性。 关键词：经验模态分解；时频分析；HHT谱 ABSTRACT Fast Fourier, Wigner-Ville transform and wavelet transform have their own flaws and shortcomings when anglicizing the nonlinear and non-stationary signals. In order to solve these problems, the empirical mode decomposition EMD (Empirical Mode Decomposition) used to signal analysis and filtering in this article. EMD decomposes a complex signal into a finite number of IMF (Intrinsic Mode Functions), and EMD is a high frequency resolution and adaptive method. In this paper, the entire theoretical systems of empirical mode decomposition have been researched deeply, focused on the filtering methods based on EMD and EMD application of time-frequency analysis. In this article, the concept of instantaneous frequency is introduced firstly. Then, the basic concepts of IMF and principles of EMD decomposition algorithm are discussed, and the characteristics of the EMD algorithm are analyzed. Combined with IMF, it is given that the physical meaning of the Hilbert marginal spectrum and the Hilbert spectrum are formulated, and the theories of the whole time-frequency analysis are discussed in detail. Besides, the problem of EMD time-frequency method is also analyzed, including modes mixing, end effect, sifting stop condition and so on. Secondly, compared to traditional time-frequency analysis methods, show that EMD spectrum has perfect time-frequency concentration. Finally, study the EMD-based filtering method, and verified the validity and the superiority of the method. Keywords: EMD; ti