New results and open problems on nonuniform filter-banks

Nonuniform filter-banks (FB's) have traditionally been built either by cascading uniform ones in a tree structure or by direct design methods that lead to near-perfect reconstruction. However many theoretical issues remain unresolved. This paper begins by pointing out a number of these issues, and summarizes the known conditions for existence of nonuniform perfect reconstruction (PR) FB's. As a new contribution, we simplify some of these conditions and make them more explicit. We provide examples that illustrate some hitherto unobserved connections between these conditions.