Structures, factorizations, and design criteria for oversampled paraunitary filterbanks yielding linear-phase filters

We present here a special class of oversampled filterbanks (FBs), namely, paraunitary FBs with linear-phase filters. We propose some necessary conditions for the existence of such banks, based on the repartition between type VII and type III/IV linear-phase filters in the bank. For a subset of these FBs, we develop a factorization that leads to a minimal implementation, as well as a direct parameterization of the FBs in terms of elementary rotation angles. This factorization is applied to some design examples, with two different optimization criteria: coding gain and reconstructibility of lost coefficients.