基于B样条基函数的经验模态分解理论与方法研究

The empirical mode decomposition (EMD) method has attracted much attention for its ability of processing non-stationary signals adaptively. However, EMD is a method based on experience, and it lacks the rigorous theoretical foundation, which seriously restricting its development and application. This project investigates the basic theoretical of EMD by combining B-spline interpolation technique with the EMD algorithm. An analytical study of the EMD method based on B-spline basis functions is conducted from the signal processing perspective. The iterative B-spline filter is designed, and a mathematical expression of intrinsic mode function (IMF) based on the iterative B-spline filter is derived to resolve the problem of EMD lacking theoretical foundation. The resolution properties of EMD based on B-spline basis functions are analyzed. The EMD is equivalent to a multi-rate signal processing systems. The sampling theory is used to analyze EMD resolution to reveal the root causes of EMD generating new components and its adaptability. The Doppler signal detection technology based on EMD for radio fuze is researched. The Doppler signal detection algorithm based on EMD is proposed to improve the Doppler signal perception capability and target detection sensitivity for radio fuze, and to verify the correctness of the theoretical analysis on EMD. In this project, we can derive an analytical expression of EMD which lays a solid foundation for the establishment of the theoretical framework of EMD, and provides a useful theoretical and technical support for application of the EMD method.

经验模态分解(EMD)能够自适应地处理非平稳信号而受到广泛关注，但它是基于经验的方法，没有解析表达式致使其缺乏严格理论基础，严重制约了其发展和应用。本项目将B样条插值技术与EMD算法相结合进行EMD基础理论研究。从数字信号处理角度对基于B样条基函数的EMD进行解析分析，构造迭代B样条滤波器，推导基于迭代B样条滤波器的IMF数学表达式，给出EMD解析表达式，解决EMD理论基础缺乏问题；研究基于B样条基函数的EMD分辨特性，将EMD等效为一个多采样率信号处理系统，运用采样理论来分析其分辨率，揭示EMD产生新成分及其自适应性的根源；研究无线电引信多普勒信号的EMD检测技术，提出多普勒信号的EMD检测算法，提高引信对多普勒信号的感知能力和探测灵敏度，验证对EMD理论分析的正确性。项目成果可实现对EMD的解析表示，为完善EMD理论体系及建立其理论框架奠定基础，并为EMD应用提供理论支撑和技术支持。

经验模态分解(EMD)是处理非平稳信号的有力工具，但它是基于经验的方法，缺乏严格的理论基础。针对这一问题，该项目对基于B样条基函数的EMD进行了解析分析，研究了基于B样条基函数的EMD分辨特性，在对EMD进行数学描述的基础上，研究了无线电引信多普勒信号的检测方法。.从数字信号处理的角度对EMD筛分过程进行了分析。研究了极值采样，证明了极值采样是亚奈奎斯特采样，用时不变模型对非均匀极值采样进行了描述。分析了非均匀B样条插值，将非均匀B样条插值等效为一个插值器跟随一个时变滤波器。研究了信号的包络，将信号的上、下包络定义为由极值序列重建后的信号，基于B样条推导了信号包络的数学表达式。对EMD的筛分过程进行了数学描述，给出了EMD筛分过程抽取本征模态函数(IMF)的矩阵表达式。.基于B样条基函数，推导了迭代B样条滤波器的数学表达式，证明了迭代B样条滤波器的幅频特性随迭代次数增多而改善。基于迭代B样条滤波器，分析了EMD的分辨特性，发现EMD的抗噪能力随筛分次数增多而降低，进而指出了EMD分辨特性只能在一定程度上随筛分次数增多而提高。.分析了无线电引信多普勒信号的特点，建立了近场区多普勒引信回波信号的模型。提出了极值滤波算法，用于多频信号的自适应分解。提出了基于STFT和EMD的多普勒信号检测算法，实现了对多普勒信号瞬时频率的估计，进而提升对多普勒信号的感知能力。.该项目将B样条插值技术与EMD算法相结合进行了EMD基础理论研究，给出了EMD抽取IMF的数学表达式，实现了对EMD筛分过程的数学描述。该项目的研究为完善EMD理论体系及建立EMD理论框架奠定了一定的基础，进而为EMD算法的进一步研究和实际应用提供有益的理论支撑和技术支持。