Analytical design of fractional Hilbert transformer using fractional differencing

Conventionally, fractional differencing (FD) has been successfully used to generate a fractal process called fractional Brownian motion, and the fractional Hilbert transformer (FHT) has been also applied to the edge detection of images and the construction of secure single-side band (SSB) communication systems. In this paper, the relation between FD and FHT is investigated so that FD can be applied to design the FHT directly. The proposed design method not only provides a closed-form transfer function but also ensures that the designed fractional Hilbert transformer is stable. One design example is demonstrated to illustrate the effectiveness of the new design method.