Two-dimensional IFlR structures using generalized factorizable filters

In this paper we extend the idea of interpolated FIR (IFIR) filters to the two-dimensional (2-D) case. IFIR filters make for the reduction of the computational weight, in the one-dimensional (1-D) case as well as in the 2-D case. In the 1-D case, the justification to such a performance advantage rests upon the relationship between filter order, transition bandwidth and minimax errors for equiripple linear-phase filters. Even though no similar relation is known for minimax, optimal multidimensional filters, a qualitatively parallel behaviour is shared by a class of suboptimal filters ("Generalized Factorizable") recently introduced by Chen and Vaidyanathan, for which an efficient implementation exists. In our scheme, we use Generalized Factorizable filters for both the stages of the IFIR structure. An interesting problem peculiar to the multidimensional case is the choice of the sublattice which represents the definition support of the first-stage (shaping) filter. We present a strategy to choose (given the spectral support of the desired frequency response) the optimal sublattice, and to design the second-stage (interpolator) filter in order to achieve low overall computational weight.