【作者】 邵岩；

【导师】 杨广学；

【作者基本信息】 哈尔滨理工大学 ， 电子与通信工程（专业学位）， 2016， 硕士

【摘要】 分数阶傅里叶变换(FRFT)是经过传统傅里叶变换的研究后提出的算法,是傅里叶变换在分数次幂上的运算,具有对信号空间-频率联合作用的信息处理能力。1980年科学家纳米亚提出了分数阶傅里叶变换的完整概念,经过几十年的研究,分数阶傅里叶变换算法的定义种类、公式推导过程和物理意义取得了丰富的成果,分数阶傅里叶变换算法的逐步完善,使得其算法在科技应用领域中提供了保障。随后在90年代初期,Almeida从物理意义角度给分数阶傅里叶变换做出了形象的表示,其算法可以理解为在由时域和频域组成的平面内的旋转,随后Ozaktas等人在1996年提出了分数阶傅里叶变换的离散算法,快速的离散算法给海洋探测、雷达捕获等信号分析技术的应用中提供了新方向。本文全面解释了分数阶傅里叶变换的定义,研究了分数阶傅里叶变换的离散算法,通过对算法的仿真应用,从实际应用角度对分数阶傅里叶变换在信号处理领域进行分析,验证了其算法的可靠性,比较了分数阶傅里叶变换与其他时频分析算法的联系。采用常用的线性调频信号,应用分数阶傅里叶变换对信号进行模拟,通过图形的形式清晰的描述了信号经过分数阶傅里叶变换处理后的效果。分数阶傅里叶变换能够同时获取信息的时频频域的信息,适合分析非平稳信号,分数阶傅里叶变换从信号角度可以认为是线性调频信号(LFM)的基分解,没有交叉项干扰的问题,能够有效检测和估计含有噪声的线性调频信号,用分数阶傅里叶变换的算法对滚动轴承故障进行诊断,分析结果表明用分数阶傅里叶算法可以有效地降低其他分量和噪声的互相干扰,准确提取目标分量,仿真结果进一步证实了这一方法的优越性。更多还原

【Abstract】 The fractional Fourier transform(FRFT) is an extension and further study on the basis of traditional Fourier transform. It is considered as the traditional Fourier transform to the n-th power, where n is an integer. This new transform has an unique characteristic which separates it from other algorithms. It can transform a function to any intermediate domain between time and frequency. The conception of FRFT was originally proposed by V. Namias. After decades of development, FRFT has achieved great success in the aspects of form definitions, algorithm conducting process, and physical meanings. The completion of the system theory of the fractional Fourier transform provided a strong theoretical base for the future development of its applications in the engineering field. In 1993, Almeida proposed a new physical meaning of the fractional Fourier transform, which indicates this transform can be comprehended as a rotation of frequency. Later on, Ozaktas et al. proposed the discrete algorithm in the application of the fractional Fourier transform in 1996, which further made FRFT become an innovative tool in the field of digital signal processing. In recent years, fractional Fourier transform has been widely used in the underwater acoustic, radar, and other fields of study.This dissertation starts with the definition and the properties of fractional Fourier transform, and studies its discrete numerical calculation method and demonstrates its relationships with other time-frequency analysis algorithms. Common frequency modulation(LFM) signals have been simulated by applying the FRFT theory. The process of applying the FRFT theory analyzing signals has been clearly described through the forms of graphs.FRFT can simultaneously obtain the information of the signal properties in time and frequency. It can also be comprehended as the base resolving of the LFM. In this dissertation, FRFT has been used to analyze the single component Chirp signal. The results of this analysis show that the fractional Fourier transform algorithm can effectively reduce the mutual interference of other components and noise. Additionally, this method is capable of extracting the target component accurately. The simulation results in this dissertation also proves the superiority of this method.更多还原