Issues in nonuniform filter banks

This paper concerns biorthogonal filter banks. It is shown that a tree structured filter bank is biorthogonal if it is equivalent to a tree structured filter bank whose matching constituent levels on the analysis and synthesis sides are themselves biorthogonal pairs. We then show that a stronger statement can be made about dyadic Filter Banks in general: That a dyadic filter bank is biorthogonal if both the analysis and synthesis banks can be decomposed into dyadic trees. We further show that these decompositions are stability preserving. These results thus generalize earlier comparable results for orthogonal filter banks.