On the paraunitary and perfect reconstruction filter banks with arbitrary filter lengths

This paper investigates a more general class of M-channel FIR filter banks (FBs) with arbitrary equal filter lengths L = KM +β (0 ≤ β < M). The motivation for such FBs is to develop more general theories, factorizations and designs to overcome the limitations of traditional works with unnecessary length constraint L = KM, and to achieve a better trade-off between the design and computational complexities and the filter length. The existence conditions and lattice factorizations are developed for both paraunitary and perfect reconstruction FBs with any number of channels M ≥ 2. Furthermore, it can be shown that the novel derived lattice factorization is complete for any FIR paraunitary FB and for any order-one perfect reconstruction FB. Finally, a design example is presented to validate the proposed lattice structure.