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.