Optimum masking levels and coefficient sparseness for Hilbert transformers and half-band filters designed using the frequency-response masking technique

• Main Authors: Lim, Yong Ching, Yu, Ya Jun, Saramäki, Tapio
• Other Authors: School of Electrical and Electronic Engineering
• Format: Article
• Language: English
• Published: 2009
• Subjects: DRNTU::Engineering::Electrical and electronic engineering
• Online Access: https://hdl.handle.net/10356/91521; http://hdl.handle.net/10220/6006
• Institution: Nanyang Technological University

Hilbert transformers and half-band filters are two very important special classes of finite-impulse response filters often used in signal processing applications. Furthermore, there exists a very close relationship between these two special classes of filters in such a way that a half-band filter can be derived from a Hilbert transformer in a straightforward manner and vice versa. It has been shown that these two classes of filters may be synthesized using the frequency-response masking (FRM) technique resulting in very efficient implementation when the filters are very sharp. While filters synthesized using the FRM technique has been characterized for the general low-pass case, Hilbert transformers and half-band filters synthesized using the FRM technique have not been characterized. The characterization of the two classes of filter is a focus of this paper. In this paper, we re-develop the FRM structure for the synthesis of Hilbert transformer from a new perspective. This new approach uses a frequency response correction term produced by masking the frequency response of a sparse coefficient filter, whose frequency response is periodic, to sharpen the bandedge of a low-order Hilbert transformer. Optimum masking levels and coefficient sparseness for the Hilbert transformers are derived; corresponding quantities for the half-band filters are obtained via the close relationship between these two classes of filters.