Title :
Analytical design of fractional Hilbert transformer using fractional differencing
Author :
Tseng, Chien-Cheng
Author_Institution :
Dept. of Comput. & Commun. Eng., Nat. Kaohsiung First Univ. of Sci. & Technol., Taiwan
Abstract :
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.
Keywords :
Hilbert transforms; all-pass filters; circuit stability; digital filters; frequency response; transfer functions; 1-D filter; analytical design; closed-form transfer function; design method; edge detection; fractal process; fractional Brownian motion; fractional Hilbert transformer; fractional differencing; frequency response; secure single-side band communication system construction; stable allpass filter; Amplitude modulation; Bandwidth; Delay; Design methodology; Discrete transforms; Fourier transforms; Fractals; Image edge detection; Signal analysis; Transfer functions;
Conference_Titel :
Circuits and Systems, 2003. ISCAS '03. Proceedings of the 2003 International Symposium on
Print_ISBN :
0-7803-7761-3
DOI :
10.1109/ISCAS.2003.1205801