随机多重分形信号的广义分数阶奇异性谱分析理论及应用

项目名称： 随机多重分形信号的广义分数阶奇异性谱分析理论及应用

项目编号： No.61301216

项目类型： 青年科学基金项目

立项/批准年度： 2014

项目学科： 无线电电子学、电信技术

项目作者： 张淑宁

作者单位： 南京理工大学

项目金额： 28万元

中文摘要： 以非平稳随机多重分形信号为对象，借鉴分数阶傅里叶变换（FRFT）思想，将时间维和奇异性维度耦合到分数域，提出分数阶奇异性谱分析（FSSA）理论，解决奇异性谱分析中时域局部性缺失及时间-奇异性多重分形谱（TSMFS）中奇异谱交叉项问题，建立广义FSSA理论。包括：①提出FSSA分析的概念，基于线性奇异调制信号构建时间-奇异的分数域分形空间，探索信号在分数奇异域展开的概念、基本原理和特性；②基于FSSA与奇异性谱分析、短时奇异性谱及TSMFS间的旋转变换关系，提出广义FSSA理论及基于FSSA的分形重构技术；③提出联合FSSA、FRFT和分数阶微积分的信号处理技术，研究信号的FSSA与其分数阶微分的FSSA关系，研究基于分数阶微分和FSSA的信号处理技术，并应用于自然分形噪声背景下噪声抑制、目标检测和参数估计。该研究对丰富奇异性谱分析理论、发展分形信号处理理论和技术有重要的理论、应用价值。

中文关键词： 随机多重分形信号；分数阶奇异性谱；分数阶微积分；多重分形重构；信号检测与识别

英文摘要： The theory of fractional singularity spectrum analysis (FSSA )of stochastic multifractal signal is put forward and generalized fractional singularity spectrum distribution is set up .The dimension and singular dimension is coupled to fractional domain in this theory from the thought of fractional fourier transform. The problem of time domain part deficiency for singularity spectrum analysis and singular spectrum cross terms of time - singularity multifractal spectrum（TSMFS） theory are solved in the above theory.The research is as followings. ①The concept of FSSA analysis is put forward. The expanding properties in FSSA scores and time - domain singularity plane for multi-component linear Chirp singularity of modulation signal are studied.② The transform connection between FSSA and traditional SSA,short-time singularity spectrum distribution and TSMFS is studied. The generalized fractional singular spectrum analysis theory and signal reconstruction technology is established. ③The signal processing technique of mixing FSSA,FRFT and fractional calculus is proposed.The relation between FSSA and fractional calculus is studied based on fractional calculus theory.Signal processing based on fractional calculus and FSSA is studied.Noise eliminating, signal detection and parameters estimation under fractal noise is stud

英文关键词： random multi-fractal signals；fractional singularity spectrum；fractional calculus；multi-fractional signal reconstruction；singal detection and recognition