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EMD算法、信号分解与信号自适应表示
其他题名EMD algorithm, signal decomposition and adaptive signal representation
轩波
学位类型工学博士
导师彭思龙
2007-06-05
学位授予单位中国科学院研究生院
学位授予地点中国科学院自动化研究所
学位专业模式识别与智能系统
关键词时频分析 瞬时频率 Emd Gabor滤波器组 Time-frequency Analysis Instantaneous Frequency Emd Gabor Filter Banks
摘要信号分析的主要目的是研究和表征信号的基本性质,而信号的表示方法直接影响到信号分析的结果和效率,因此人们期望寻找最有效和最能揭示信号本质特征的信号表达方式。 信号通常是一个随时间变化的函数,人们也通常强调随时间变换的信号幅度值。实际上,信号的频率也可能随时间变换,例如日常生活中常接触到的调频广播,变化着的色彩等。因此,信号的时间-频率域联合分析(简称为时频分析)就成了信号处理的重要领域和难点。时频分析的目的是得到信号的各个频率成份在时间上和空间上的变化规律。瞬时频率正是反映频率成份随时间变化规律的量,因此对瞬时频率的研究也称为时频分析的重点。 另一方面,实际信号往往由多个频率成份叠加而成,直接分析这样的多分量信号是困难的。因此,在对信号进行分析之前先将这些成份分离开也是一项重要的工作。 本文借助信号分解的思想对一维信号的时频分析和二维信号的空频分析进行了研究,以求得到信号的自适应表达。 本文从瞬时频率出发,重点对经验模式分解(EMD)这一新兴的时频分析工具进行了深入研究。首先,本文综述了常见的信号分解算法。这些算法有的是简单的对数值进行分解,有的则要借助复杂的数学理论。然后,文章讨论了信号瞬时频率的定义,如何理解瞬时频率,以及关于瞬时频率的一些悖论。接着,本文介绍了Huang为解决这些悖论引入的EMD算法及其改进算法,并分析了这些算法的优缺点。最后,还是从瞬时频率出发,本文提出了基于带宽的EMD算法,并给出了对该算法的物理解释及其收敛性的讨论。 本文在二维数据的空间-频率分析方面也做了一定的探索。首先,介绍了现有的二维EMD算法,并指出它们存在的一些问题。然后,从多分量AM-FM图像表达和二维信号瞬时频率出发,讨论在求取二维瞬时频率时遇到的困难。最后,提出基于带宽的二维EMD算法和基于Gabor滤波器的自适应频域分解,并用二维EMD算法和Gabor滤波器组构成了二维图像的单分量分解框架。 理论分析和实验结果表明,本论文的算法在创新性、精确度、算法复杂度和适用性方面有着各自的优势。本课题在改进EMD算法、信号时频分析和信号自适应表达方面也做了有益尝试。
其他摘要The main aim of signal analysis is to research and represent the basic property of the analyzed signal. The representation form of the signal affect the result of the signal analysis directly. We want to find the representation form which is the most efficient in reflecting the intrinsic characteristics of the analyzed signal. Usually, signal is a function which varies with time. we are accustomed to research the values of the varying signal, but the frequency of a signal can also varies with time. For this reason, the time-frequency analysis is an important and difficult research field. The aim of the time-frequency analysis is to analysis how the frequency components vary in local time or local space and utilize these time-frequency features to accomplish signal processing assignments. The instantaneous frequency is exactly the quantity which can reflect the varying rules of different frequency components, and it is an important research object in time-frequency analysis domain. Complicated signal often consists of many different frequency components. It is difficult to analysis this signal directly. The decomposition of these components is also an important step before we analysis the origin signal. This thesis researches the time-frequency of analysis one-dimension signal and two-dimension image based on the idea of signal decomposition. In the first two chapters, this thesis researches the empirical mode decomposition (EMD) based on the discussion about instantaneous frequency. At first, many signal decomposition algorithms are reviewed. Then, many questions about instantaneous frequency are researched, such as the definition of instantaneous frequency, the interpretation of the instantaneous frequency and some paradoxes about it. And then, the EMD algorithm proposed to deal with these paradoxes is introduced. This thesis also represents many improved EMD algorithms. At last, a new EMD algorithm based on bandwidth is proposed, and the physical interpretation and the convergence of the algorithm are also discussed. This thesis also does some research in domain of two-dimensional signal time-frequency analysis. At first, some two-dimensional EMD algorithm are introduced, and the drawback of them is discussed. Then the two-dimensional instantaneous frequency is researched. At last, the bandwidth based two-dimensional EMD algorithm is proposed. Simultaneously, This thesis bring out a Gabor filter bank based IMF decomposition algorithm. The combination of two-dimensional EMD and Gabor filter bank composes an image decomposition and representation framework. Theory analysis and experiment results indicate that the algorithms proposed in this thesis have respective advantages, such as innovation, accuracy, simplicity, applicability, etc. This thesis explores a reasonable way to improve EMD, to research time-frequency analysis, and to represent signal adaptively.
馆藏号XWLW1096
其他标识符200418014628035
语种中文
文献类型学位论文
条目标识符http://ir.ia.ac.cn/handle/173211/6000
专题毕业生_博士学位论文
推荐引用方式
GB/T 7714
轩波. EMD算法、信号分解与信号自适应表示[D]. 中国科学院自动化研究所. 中国科学院研究生院,2007.
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