【作者】 谢啸虎；

【导师】 熊盛武；

【作者基本信息】 武汉理工大学 ， 计算机应用技术， 2009， 硕士

【摘要】 非平稳信号是日常生活和科学研究中经常观察到的现象,这些信号往往持续时间有限,存在产生和消亡。传统的信号频域分析法一傅立叶分析只适用于分析信号组成分量的频率不随时间变化的平稳信号,因此人们针对非平稳信号的分析引入了在时频二维平面上表征信号的新方法一时频分析方法。随后,各种时频分析技术,例如STFT、小波分析等,也都得到了快速地发展。其中,上世纪末,Huang等人首次提出的一种新的信号分析理论—希尔伯特-黄变换(HilbertHuang Transform)被公认为是对时频分析技术的一个突破。分析和改进HHT变换是本论文研究的核心问题。本文在深入分析了HHT变换的基础上,指出了HHT目前存在的一些缺点:在EMD分解的过程中,细小特征尺度可能会丢失;对与存在跳跃性变化的信号的分解存在模态混叠现象;以及HHT变换不能实现信号的即时分析,即不具备边提供数据边进行时频分析的能力。针对以上缺点,本文提出了如下改进1)提出了Cur-EMD算法,在EMD分解中采用曲率极值点代替幅度极值点作为信号的特征时间尺度,克服了原始EMD中细小特征尺度分解不完全的缺点,提高了EMD分解和HHT分析的精度;2)对EMD分解中筛选过程进行了改进,提出了信号的特征时间尺度平稳度的概念和检测信号突变点的方法,当信号的时间尺度存在着跳跃性变化时,较好的解决了原方法中严重的模态混叠现象;3)传统上,因为HHT变换涉及到整个信号的反复样条插值,因此HHT分析必须针对一个完整的信号。本文采用阿克玛插值法替代三次样条插值,并提出了一种“分而治之”的递归模态分解法,探讨了将HHT应用于即时信号分析的可能性,当信号在连续输入的时,经过一个有限的延迟,该算法就可以给出当前的时频分析结果。本文通过编程(Matlab和Java)实现以上各算法,并完成了一系列数值试验,直观的给出了不同时频分析方法得到的结果。数值试验的结果证明改进后的算法具有分析精度更高,有效消除模态混叠等优点,证实了改进的有效性。最后,本文介绍时频分析技术在作者参与的一个实际项目中的应用。在这个项目中,时频分析技术主要被用于信号去噪以及图像纹理分析两个方面。更多还原

【Abstract】 Non-stationary signal can be often observed in our daily life and scientific research.For those signals,they are generated suddenly and wither away in a limited time.However,traditional frequency-analysis like Fourier transform is applicable only when the components of the signal last forever and have frequencies that are constant.So,the time-frequency analysis has been introduced as a new method to analysis the non-stationary signal.The new method represents signals in a two-dimensional plane of time and frequency.Different kind of time-frequency technologies including Sort Time Fourier Transform and Wavelet Analysis has been well developed since then.Among them,the new proposed Hilbert-Huang Transform (HHT) is commonly considered as a breakthrough to time-frequency analysis.This thesis will focus on discussions and improvements base on it.Base on the summary and a relatively thorough analysis of HHT,The thesis point out its deficiencies:There is possibility of losing tiny components in the process of Empirical Mode Decomposition;Aliasing phenomenon arises if the characteristic scales of signal suddenly changed;And,HHT cannot analyze the real-time signal. That means it is unable to analyze the signal the same time it being provided. Against those deficiencies,several improvements have been proposed here:1) the thesis proposes the Cur-EMD algorithm which adopts curvature extremes instead of amplitude extremes as the characteristic scales in the decomposition.Comparing to the traditional EMD algorithm,Cur-EMD boasts a higher precision.2) The thesis defines the conception of Mutation Point and the way to detect it.Thanks to this conception,an improved decomposition method of HHT has been proposed in this thesis.The new method can effectively avoid the aliasing phenomenon caused by the sudden change of the characteristic scales.3) Traditionally,because of HHT involves the repeated spline interpolate of an entire signal,the signal that HHT analyzes must be integrated.This thesis gives a discussion of a new improved decomposition base on the notion of "divide and rule".In additional,the new method adopts Akima interpolate instead of spline interpolate.All those together make it possible for using HHT to analyze real-time signal.That is the algorithm can give the current time-frequency analysis result of a consecutive input signal after a limited delay.In this thesis we implement the algorithms mentioned above by programming(Matlab and Java),and make a series of numerical experimentation.Based on the clearly presented results comes after different Time-Frequency analysis methods,this thesis gives an analysis and proves the efficiency of the improved algorithm.Finally,this thesis introduces an application of the proposed Time-Frequency analysis technology methods in a project that the author participated in.In this project,the Time-Frequency analysis technology was mainly used in aspects of signal de-noising and texture analysis for images.更多还原