Imposing structure on the Smith form of an (integer) periodicity matrix N = U V leads to e cient m-D DFT implementations. For resampling matrices, i.e. non-singular rational matrices, we introduce Smith form decomposition algorithms to generate matrices whose diagonal elements exhibit minimum variance and U matrices with minimum norm. Such structure simpli es non-uniform m-D lter bank design.

The constructive second-order proofs that we study are associated with inductive definitions on classes of finite structures, where each structure represents a database state. To an inductive definition of a predicate P on a class K corresponds a uniform proof of P i.e a function which for each structure U defines a proof of P in U In the second section, we review the definition of an inductive...