基于廣義Hilbert變換將傳統(tǒng)的Hilbert變換由整數(shù)階向分數(shù)階的推廣，其應用領(lǐng)域也得到了擴展。首先，在頻域定義廣義Hilbert變換，利用廣義Hilbert變換來構(gòu)造新的廣義解析信號。然后從數(shù)字信號處理角度來考察理想的廣義數(shù)字Hilbert變換器的基本性質(zhì)及其數(shù)字實現(xiàn)。文中利用窗函數(shù)法和頻率采樣法設(shè)計了FIR廣義數(shù)字Hilbert變換器，并分析了設(shè)計誤差.

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.