Special Structure for Designing Low-Complexity 2-D Half-Band Filters

This paper presents a special structure for designing low-complexity two-dimensional (2-D) half-band digital filter with very sharp transition band. Performing the singular-valuedecomposition (SVD) of zero-phase half-band frequency response generates a set of one-dimensional (1-D) frequency responses which can be approximated using the cascade of a half-advance digital filter and a set of 1-D filters. Each such a 1-D filter only requires a single multiplication to get an output sample, so the resulting whole 2-D half-band filter has considerably reduced computational complexity as compared with the existing direct design approach. To minimize the peak errors of the magnitude response of the resulting 2-D half-band filter, we parallelize one extra section to the structure and then minimize the peak errors using a nonlinear optimization method, which reduces the design problem to a minimax design. Since the whole structure only consists of a set of simple 1-D filters, the complexity is extremely low. One minimax design example is given to illustrate the effectiveness of the proposed special structure. Index Terms — Digital filter, 2-D filter, singular-valuedecomposition, minimax design.