Considerations in multidimensional filter bank design

Onedimensional (1D) and multidimensional (MD) analysis/synthesis filter banks have attracted much attention recently. While 1D filer banks have been well studied and various design approaches have been successfully developed, many problems in the MD case remain unsolved. In this paper, we exploit a number of issues in MD filter bank design, including: the choice of permissible passband supports, the cyclic property of decimation matrices that is required for filter bank design using transformations, etc. We also propose a class of useful tree-structure filter banks, which apply to the commonly-used hexagonal decimation.