On the realizability of biorthogonal, m-dimensional two-band filter banks

We show an algebraic approach for the design of ladder structures for causal biorthogonal filter banks. The key ingredient of the approach is known in literature as Euclid´s algorithm. Using this algorithm we derive some strong result on the design freedom for ladder structures. In particular we show that the dimensionality of the problem plays an important role. We end by with some conjectures concerning the extensions to multichannel and noncausal filter banks