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近年来,分数阶Fourier变换在光学、信号处理等领域得到越来越广泛的应用,离散化成为其得以应用的关键.由于分数阶Fourier变换的离散算法不像离散Fourier变换那样可以简单地通过在时域和分数阶Fourier域直接离散化采样得到,因此分数阶Fourier变换的离散算法成为近年来的研究重点.根据分数阶Fourier变换离散化的发展历史,对其重要研究进展和现状进行了系统归纳和简要评述,包括:分数阶Fourier域采样和重构;离散时间分数阶Fourier变换和分数阶Fourier级数;离散分数阶Fourier变换(包括目前3种主要类型:线性加权型、采样型和特征分解型);以及和分数阶Fourier变换紧密相关的其他离散分数阶酉变换;并指出了应用背景和发展方向.有助于读者全面了解分数阶Fourier变换离散计算,进一步促进其工程应用.
In recent years, fractional Fourier transform has been more and more widely used in optics, signal processing and other fields, and discretization has become the key to its application.As the discrete Fourier transform of fractional Fourier transform is not as discrete Fourier transform, Time domain and fractional Fourier domain are directly discretized sampling, so the discrete Fourier transform fractional algorithm has become the focus of recent years.According to the development history of fractional Fourier transform discretization, its important research progress and status quo are systematically summarized And brief comments, including: fractional Fourier domain sampling and reconstruction; discrete time fractional Fourier transform and fractional Fourier series; discrete fractional Fourier transform (including the current three main types: linear weighting, sampling and eigendecomposition And other discrete Fractional Unitary Transform closely related to Fractional Fourier Transform. It also points out the application background and development direction, which helps readers fully understand the discrete Fourier Transform calculation and further promote its engineering application.