基于分数阶微积分和分数低阶统计量的信号处理新方法及应用研究

项目名称： 基于分数阶微积分和分数低阶统计量的信号处理新方法及应用研究

项目编号： No.61201419

项目类型： 青年科学基金项目

立项/批准年度： 2013

项目学科： 电子学与信息系统

项目作者： 盛虎

作者单位： 大连交通大学

项目金额： 20万元

中文摘要： 针对现存具有重尾分布和长相关/局部相关性质的分数阶随机信号分析方法的局限性，本项目以分数阶微积分和分数低阶统计量理论为基础，系统研究具有重尾分布、长相关/局部相关分数阶随机信号特性，探究如何融合分数阶微积分和分数低阶统计量的信号处理技术，构建基于可变阶次、分布阶次分数阶系统模型，探讨分数阶信号合成方法，建立可靠的分数阶模型，准确估计分数阶模型参数；设计可变阶次、分布阶次分数阶滤波器，分析此类分数阶滤波器的性质；探讨可变阶次、分布阶次分数阶模型、分数阶滤波器的离散化方法。此外，本研究还将研究如何将这些分数阶信号处理技术应用到复杂的生物医学信号分析、处理中。本项目的研究成果有望克服现存具有重尾分布或长相关/局部相关性质的随机信号处理方法的缺点和局限性，为得到性能更为优良且适用范围更广泛的分数阶信号处理方法提供了一个新的思路和新途径。

中文关键词： 信号处理；随机信号；分数阶微积分；alpha稳定分布；分数阶滤波器

英文摘要： In this project, the novel fractional signal processing techniques will be studied to improve the existing signal processing techniques, which are used to analyze heavy-tailed distribution, long-range dependent(LRD) or local dependent random signals. These novel signal processing techniques are based on the fractional calculus and fractional low order statistic. Firstly, the characteristics of heavy-tailed distribution, long range dependent/local dependent random signals will be studied in this project; Secendly, the distributed-order fractiona model or variable-order fractional model will be analyzed, and the parameters of the model will be estimated; Thirdly, the design of distributed-order and variable-order fractional filters will be studied, the characteristics of this kind of fractional filters will be explored; Fourthly, the discretization method of the distributed-order/variable-order fractional model and filters will be provided. Furthermore, the above novel fractional signal processing techniques will be applied in biomedical signals to estimate the reliability of the fractional signal processing techniques studied in this project.The research results in this project will overcome the shortcomings and limits of existing techniques which were used to analyze heavy-tailed distribution, long-range depende

英文关键词： Signal processing；Random signal；Fractional calculus；Alpha stable distribution；Fractional-order filter