广义希尔伯特变换及其数字实现

Generalized Hilbert Transform and Digital Realization

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。

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.