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    • U-系统与V-系统的理论及应用综述

    CHEN Wei,CAI Zhan-chuan,LI Jian,LIANG Yan-yan,XIONG Gang-qiang,SONG Rui-xia

    Journal of Graphics（2022）

    江南大学 | 澳门科技大学计算机科学与工程学院 | 澳门理工大学应用科学学院 | 广东医科大学 | 北方工业大学

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    Abstract
    传统的Fourier级数在逼近间断信号时因Gibbs现象的干扰,会产生比较大的误差.针对此问题,国内学者齐东旭教授带领的课题组提出了非连续正交函数系的研究课题,其中U-系统和V-系统是两类典型的非连续完备正交函数系.从数学理论上来说,U-系统和V-系统分别是对著名的Walsh函数和Haar函数由分段常数向分段k次多项式进行推广的结果,其最重要的特点是函数系中既有光滑函数又有各个层次的间断函数.因此,U,V-系统可以处理连续和间断并存的信息,在一定程度上弥补了Fourier分析和连续小波的缺憾.本文从理论与应用2个方面对U,V-系统进行了综述.在理论方面,首先介绍了单变量U-系统与V-系统各自的构造方法,其次介绍三角域上U,V-系统的构造方法,最后介绍U,V-系统的主要性质.在应用方面,介绍了若干具有代表性的应用案例.
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    【要点】：本文综述了U-系统和V-系统理论及其应用，这两类非连续完备正交函数系能处理连续和间断并存的信息，弥补了傅里叶分析和连续小波变换的不足。
    

    【方法】：文章首先阐述了单变量U-系统和V-系统的构造方法，然后介绍了它们在三角域上的构造，最后总结了U-系统和V-系统的主要性质。
    

    【实验】：文中提供了若干应用案例，展示了U-系统和V-系统在处理不同类型信号和信息处理方面的实际效果，但没有具体提及实验使用的数据集名称。