Generation of dual N-channel filterbanks with hilbert-transformed motherwavelets

We reconsider the problem of generating a dual filterbank to a given one with N channels such that its N - 1 mother wavelets will be related to those of the original one by the Hilbert-transform. Known solutions treat the case of unitary filterbanks, while treats the biorthogonal case and the overcomplete case. We present a solution which is valid for arbitrary filterbanks and obtain identical results. This fact indicates that the proposition of unitarity is not necessary at all. Moreover, the phase condition is obtained in a constructive way and is given by a closed form expression.