In this paper, we provide an overview of the definition, digital realizations and applications of the Fractional Fourier transform. Specifically, the paper discusses various approaches for digital realizations of the FrFT and compares their advantages and disadvantages, and then, explains the implementation procedure of DFRFT through sampling of FrFT in detail. Furthermore,the paper introduces the applications of FrFT in digital watermarking signal detection and parameter estimation,physiological signal denoising,and illuminates systematically their algorithm principles and process-ing procedures. Finally, the paper summarizes the advantages of the fractional Fourier transform in non-stationary and time-varying complex signal processing,and looks ahead to the research and development directions in the future.%本文综述了分数阶Fourier变换的定义、数值化实现方法及其应用.重点比较了三种数值化实现方法的优缺点,详细阐释了离散采样型数值化方法的实现过程.此外,本文对分数阶Fourier变换在数字水印、信号检测与参数估计和生理信号去噪等信号处理中的应用做了概述,系统阐释其算法原理与处理过程.最后,总结了分数阶Fourier变换在时变、非平稳等复杂信号处理中表现出的优势,并展望了今后的研究发展方向.
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