信号时频分析与包络的数学模型

项目名称： 信号时频分析与包络的数学模型

项目编号： No.11426087

项目类型： 专项基金项目

立项/批准年度： 2015

项目学科： 数理科学和化学

项目作者： 杨利军

作者单位： 河南大学

项目金额： 3万元

中文摘要： 非平稳非线性信号之时频分析是当前信息科学中的研究热点，其核心的问题是计算信号瞬时振幅和瞬时频率，从而给出其时频分布。对这些问题的研究可归结到信号包络这一基本概念。然而，包络的严格数学定义和理论并没有建立起来。已有的包络模型都是经验的估计算法。本项目拟从对包络的物理内涵的理解和数学表达出发，拟采用算子模型建立包络的数学理论，进而对算子方程的存在性等性质给予研究。在求解上，采用离散化模型通过优化方法计算。本研究力图从源头上建立包络的数学理论，同时从算法上解决经验包络的欠包现象等问题。另外，我们将在包络理论的基础上，研究单分量信号的模型和时频分析，并给出信号自适应稀疏表示方法。本项目属于信息科学与数理科学的交叉研究课题，所得的成果不仅能丰富相关学科的理论知识，而且有广阔的应用前景。

中文关键词： 包络；经验模式分解（EMD）；时频分析；最优化；

英文摘要： The time-frequency analysis for nonstationary and nonlinear signals is one of the hottest research points in current information science, the key problem in which is to compute the instantaneous frequency and instantaneous amplitude of a signal and finally give the time-frequency distribution. These can be turned down to the reaserch on the envelope, which is a fundamental concept in signal analysis. It's known that the rigorous mathematical thoery on envelope has not been established yet and the existing models are empirical. In this project, we plan to establish the mathematical theory of signal envelope by defining an envelope operator based on the understanding on the physical attributes of the envelope of signals. And we will use the optimization algorithm to calculate the discrete envelope. This is an original research for the mathematical theory of signal envelope. It can avoid the undershoot problems which usually appear in the empirical models. We will further study the mathematical model for the mono-component signal and its time-freqency analysis, and design the algorithm for adaptive and sparse representation of the signals. This project is an interdisciplinary research of mathematics science and information science. The expected achievements will not only enrich the theory of time-frequency analysis

英文关键词： Envelope；Empirical mode Decomposition (EMD)；Time-frequency analysis；Optimization；