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

FIR paraunitary filter banks have been extensively studied and well understood. We address the following problem: how to characterize and construct an FIR paraunitary 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 example is multiwavelet transforms. We present a method of constructing all possible FIR paraunitary filter banks in terms of a McMillan degree when several analysis filters are given.