The properties of generalized offset linear canonical Hilbert transform and its applications

The Hilbert transform is tightly associated with the Fourier transform. As the offset linear canonical transform (OLCT) has been shown to be useful and powerful in signal processing and optics, the concept of generalized Hilbert transform associated with the OLCT has been proposed in the literature. However, some basic results for the generalized Hilbert transform still remain unknown. Therefore, in this paper, theories and properties of the generalized Hilbert transform have been considered. First, we introduce some basic properties of the generalized Hilbert transform. Then, an important theorem for the generalized analytic signal is presented. Subsequently, the generalized Bedrosian theorem for the generalized Hilbert transform is formulated. In addition, a generalized secure single-sideband (SSB) modulation system is also presented. Finally, the simulations are carried out to verify the validity and correctness of the proposed results.