FIR paraunitary filter banks given several analysis filters: Factorizations and constructions

FIR paraunitary filter banks have been extensively studied and well understood recently. In this correspondence, we address the following problem: how to characterize and construct an FIR paranunitary filter bank when its several analysis filters are given a priori. To study this problem is not only useful in orthogonal M-band wavelets with certain regularity where we need to construct wavelet filters when a scaling filter with certain regularity is found a priori but is also useful in the design of multirate filter banks where we have already had several desired analysis filters. One such recent example is multiwavelet transforms. This work presents a method to construct all possible FIR paraunitary filter banks in terms of a McMillan degree when several analysis filters are given.