广义希尔伯特变换及其数字实现.pdf

第 34 卷第 2 期电子科技大学学报
2005 年 4 月 Journal of UEST of China Apr. 2005
广义希尔伯特变换及其数字实现
魏永豪,袁晓,滕旭东,赵元英
(四川大学电子信息学院成都 610064)

【摘要】基于广义Hilbert变换将传统的Hilbert变换由整数阶向分数阶的推广,其应用领域也得到了扩展。首
先,在频域定义广义Hilbert变换,利用广义Hilbert变换来构造新的广义解析信号。然后从数字信号处理角度来考察
理想的广义数字Hilbert变换器的基本性质及其数字实现。文中利用窗函数法和频率采样法设计了FIR广义数字
Hilbert变换器,并分析了设计误差。
关键词分数Hilbert变换; 广义解析信号; FIR滤波器; 设计误差
中图分类号 ; 文献标识码 A

Generalized Hilbert Transform and Digital Realization

WEI Yong-hao,YUAN Xiao,TENG Xu-dong,ZHAO Yuan-ying
(School of Electronic and Information, Sichuan Univ Chengdu 610064)

Abstract Fractional Hilbert transform, a generalization of Hilbert transform from integral order to
fractional order, extends the application fields. Firstly, generalized Hilbert transform is defined in the
frequency domain, and it can be used to construct a new kind of analytic signal——generalized analytic
signal. Then basic properties and digital realization of ideal generalized digital Hilbert transformer are
investigated from the viewpoint of digital signal processing. Finally digital FIR filter design using
window method and frequency sampling method are studied, and error analysis is given.
Key words fractional Hilbert transform; generalized analytic signal; FIR filter; error analysis

Hilbert变换在工程上被称为90°移相变换器[1],其实质就是对信号的正频部分移相π− 2/ rad,负频部分
移相π 2/ ra