Design of 1-D and 2-D Linear-phased Half-band Filters

1차원 및 2차원 선형 반대역 필터의 설계에 관한 연구

In this paper we consider efficient 1-D and 2-D linear-phased half-band filter designs. We first introduce a new derivation of the existing Vaidynathan-Nguyen 's half-band filter design method, which verifies that the design provides optimal half-band filters. We then propose an approximately-linear-phased IIR half-band filter design method, which is based on the all-pass equalizer design with the linear phase -$\omega$/2. Finally, we propose an efficient method to design optimal 2-D half-band filters, for which we utilize a 2-D all pass prototype filter of half the order of the desired 2-D half-band filters.