FIR PARAUNITARY FILTER BANKS GIVEN SEVERAL ANALYSIS FILTERS - FACTORIZATIONS AND CONSTRUCTIONS

FIR paraunitary filter banks have been extensively studied and well un derstood recently. In this correspondence, we address the following pr oblem: how to characterize and construct an FIR paranunitary filter ba nk 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 severa l desired analysis filters. One such recent example is multiwavelet tr ansforms. This work presents a method to construct all possible FIR pa raunitary filter banks in terms of a McMillan degree when several anal ysis filters are given.