Low-complexity design of 2-D half-band filters

This paper presents an efficient method for designing two-dimensional (2-D) half-band digital filter using the singular-value-decomposition (SVD). The 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. The most important point is that each 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. One example is given to illustrate the effectiveness of the new cascaded structure.