Design and application of discrete-time fractional Hilbert transformer

In this paper, the design problems and applications of the fractional Hilbert transformer (FHT) are investigated. First, the conventional Hilbert transformer is generalized to FHT. Its corresponding analytic signal is also defined to construct a single-sideband (SSB) signal for saving communication bandwidth. Then, several methods are presented to design finite and infinite impulse response FHTs including the Hilbert transformer-based method, all-pass filter-based method, optimization methods, etc. Next, we propose a secure SSB communication in which the fractional order of FHT is used as a secret key for demodulation. Finally, the two-dimensional FHT is used to detect edges or corners of digital images.