Design of multidimensional filter banks for non-separable sampling

Results from the design of multidimensional filter banks with arbitrary sampling patterns are presented, with emphasis on the particular cases of quincunx and hexagonal sampling. Conditions for what is and what is not achievable given specific design constraints (such as perfectly diamond-shaped filters, linear phase, and paraunitariness) are stated. Useful cascade structures are given, and the issue of completeness is addressed. The hexagonal case is analyzed, and a structure allowing perfect reconstruction while yielding linear phase and paraunitary filters is proposed. Two applications are considered: obtaining directional subband decomposition with hexagonal filters, and decomposition of interlaced and progressively scanned television with quincunx ones.