单分量信号模型与自适应信号分解算法的研究

单分量信号是时频分析中一个十分重要的概念，其含义是在任意时刻信号只有一个频率分量。然而，但目前为止，仍未见有单分量信号的统一认可的数学定义，人们并不知道如何准确地判断一个信号的单分量性。因此，为单分量信号建立合理的数学模型，进而设计有效的自适应信号分解算法，仍然是非平稳信号处理领域内的很有挑战性的基础性难题。在本项目中，我们将深入研究时频分析与非平稳信号处理领域内的若干重要问题，开展如下工作：（1）建立单分量信号一种新的数学模型，并通过细致的讨论说明该模型的物理合理性；（2）将压缩感知技术与匹配追踪算法引入非平稳信号处理领域，提出有效的自适应信号分解算法，并从理论上给出算法的性能分析。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。

The notion of the mono-component signal plays a fundamental role in time-frequency analysis, where ‘mono-component'' means the signal involves only one oscillatory mode at any time instance. However, up until now, there is no clear and accepted definition of the mono-component signal, it is still hard to judge whether or not a signal is a mono-component one. Therefore, establishing a reasonable mathematical model for mono-component signals and designing efficient algorithms for adaptive signal decomposition are still challenging fundamental issues in non-stationary signal processing. In this project, we shall make an intensive study of several important issues in time-frequency analysis and non-stationary signal processing, and do the following tasks: (1) A new mathematical model for mono-component signals will be proposed, and its physical rationality will be thoroughly discussed; (2) Compressive sensing technique and matching pursuit algorithm will be applied to the processing of non-stationary siganls, and efficient algorithms for adaptive signal decomposition will be proposed, algorithms’ performances will also be analyzed. This is a cross subject of information science and mathematical sciences, its achievements will not only enrich the theoretical knowledge of related disciplines but also have broad prospects for application.