New approach for design of paraunitary filter banks with linear phase

In this paper we propose a novel way to design nonparaunitary and paraunitary filter banks that each individual filter has linear phase. M channel filter banks, which have perfect reconstruction (PR) and linear phase (LP) properties, have been well studied and some design methods were reported. Since almost these methods are based on lattice structure whose sections are consist of orthogonal matrix, that design require the nonlinear programing technique. Here, we consider the design method which require only to solve linear equations iteratively. In our proposed method, we minimize least square error of PR constraints so as to get around using the nonlinear programing technique. We first observe the minimization problem of a quadratic function with two valuables, which is a basic idea of our new approach. Next, we apply it to the design of nonparaunitary filter banks. Then, we show that this method is applicable to the paraunitary filter banks design with some modification. Several design examples are given to validate our proposed methods.