对称离散傅里叶变换的推广  

Promotion for symmetric discrete Fourier transform

作　　者：李锐 付建伟 唐律 张青[2] LI Rui;FU Jianwei;TANG Lü;ZHANG Qing(School of Electrical Engineering and Automation,Hubei Normal University,Huangshi 435002,China;School of Mechanical Science and Engineering,Huazhong University of Science and Technology,Wuhan 430074,China)

机构地区：[1]湖北师范大学电气工程与自动化学院,湖北黄石435002 [2]华中科技大学机械科学与工程学院,湖北武汉730074

出　　处：《华中科技大学学报（自然科学版）》2024年第9期85-93,共9页Journal of Huazhong University of Science and Technology(Natural Science Edition)

基　　金：国家自然科学基金资助项目(52275056,42274229,52175094)。

摘　　要：详细介绍了对称离散傅里叶变换(SDFT),推导可见SDFT比常规离散傅里叶变换(ODFT)更适合作为傅里叶变换(FT)的离散形式.聚焦到对称的物理意义和重要性,论述了SDFT的改进、窗函数、采样函数、正交性和吉布斯现象,以及SDFT具备而ODFT所不具备的对称性、插值性质和时频域积分性质.此外,还综述了偶数采样函数、采样函数的循环性和离散频率傅里叶变换等.结论表明:该研究可填补我国在数字信号分析基础理论研究的空白,补齐我国在数字信号分析领域基础薄弱的短板.The article provides a detailed introduction to the symmetric discrete Fourier transform(SDFT),and deduces that SDFT is more suitable as a discrete form of Fourier transform(FT) than the conventional discrete Fourier transform(ODFT).The physical significance and importance of symmetry was focused on.The improvements,window functions,sampling functions,orthogonality,and Gibbs phenomenon of SDFT were discussed in detail,as well as the symmetry,interpolation,and time-frequency domain integration properties that SDFT possesses but ODFT does not.In addition,even sampling functions,the cyclicity of sampling functions,and the discrete frequency Fourier transform were also introduced.The conclusion shows that this study can fill the gap in the basic theoretical research of digital signal analysis in China and fill the gaps in China's weak foundation in the field of digital signal analysis.

关 键 词：离散傅里叶变换 对称离散傅里叶变换 对称性 奇偶性 采样函数 离散频率傅里叶变换 吉布斯现象 

分 类 号：TN911.72[电子电信—通信与信息系统]