Structurally regular unimodular filter banks

In this paper, we present the structural conditions for imposing regularity onto first-order unimodular filter banks (a.k.a. lapped unimodular transforms, LUT). For this purpose, we propose to parameterize non-singular matrices using a special lattice structure by which rational-coefficient unimodular filter banks can readily be designed. We consider two types of LUT factorizations and derive the corresponding structural conditions for regularity. Consequently, regular first-order unimodular filter banks can be designed using unconstrained optimizations, as the proposed structures always guarantee regularity. Design examples of regular first-order unimodular filter banks are presented to illustrate the proposed theory.