Structures for multidimensional FIR perfect reconstruction filter banks

Structures for maximally decimated multidimensional filter banks which achieve perfect reconstruction are presented. There are no restrictions on the sampling lattice or dimensions. These are polyphase structures that can be cascaded to give finite impulse response (FIR) analysis and synthesis filters. The authors briefly review some important concepts and results of multidimensional filter banks and establish some notation. Then they present structures based on matrices whose elements are shifts. There are certain constraints that are imposed on these matrices. Next, structures based on elementary matrices that are used to effect elementary row or column operations are presented. Some useful properties of these structures are discussed.