Design of linear-phase M-channel perfect reconstruction finite impulse response filter banks using Lagrange-Newton method

Filter banks are separated roughly into paraunitary and nonparaunitary ones. Paraunitary filter banks are excellent and have several good characteristics, but it is difficult to design such a system. This research focuses on nonparaunitary filter banks and presents a design method for the linear-phase (LP) M-channel perfect reconstruction (PR) finite impulse response (FIR) filter banks. In this method, M-2 analysis filters are arbitrarily designed and then the remaining ones are optimized using the Lagrange-Newton method. Using the proposed method, PR filter banks with arbitrary order can be designed easily. Furthermore, the design method that considers the pairwise-shift symmetry is shown and such a system is easy to design.