Running Head: Filter Banks over Commutative Rings Contact Address:

The relation between ladder and lattice implementations of twochannel lter banks is discussed and it is shown that these two concepts di er in general. An elementary proof is given for the fact that over any integral domain which is not a eld there exist causal realizable perfect reconstructing lter banks that can not be implemented with causal lifting lters. A complete parametrization of lter banks with coe cients in local rings and semiperfect rings is given. 2 Q rational numbers Z integers Z=NZ integers modulo N List of Symbols A a commutative ring with identit