Efficient design of two-dimensional diamond-shaped filters

In this paper, we propose an efficient approach for designing two-dimensional (2-D) diamond-shaped digital filter with narrow transition band using the singular-value-decomposition (SVD). The SVD of zero-phase diamond-shaped frequency response generates a set of one-dimensional (1-D) frequency responses which can be approximated using the cascade of a zero-phase lowpass filter (or a lowpass half-advance digital filter) and a set of 1-D filters. Each 1-D filter only requires a single multiplication to get an output sample, so the resulting whole 2-D diamond-shaped filter has considerably reduced computational complexity as compared with the existing direct design approach. One diamond-shaped example is given to illustrate the effectiveness of the new cascaded structure.