Saving the bandwidth in the fractional domain by generalized Hilbert transform pair relations

In this paper, we develop some methods to save the bandwidth required in the fractional domain. The fractional domain is the transformed domain of the fractional Fourier transform (FRFT). It is the intermediate of the time domain and the frequency domain. We find that, with the aid of the fractional Hilbert transform and other techniques, we can save 1/2 or 3/4 of the bandwidth in the fractional domain if the signal is causal, real, a real signal multiplied by chirp, a fractal, or a finite duration signal. The efficiency of the FRFT can hence be improved.