Generalization of the Fractional Hilbert Transform

In this letter, we generalize the fractional Hilbert transform of a real signal to get an analytic version which contains no negative spectrum while maintaining the essential information of the real signal. We also present a secure single-sideband (SSB) modulation system in which the angle of the fractional Fourier transform and the phase of the fractional Hilbert transform are used as double keys for demodulation.