Design of two-channel linear-phase FIR PR filter banks with even length filters using convolution matrices

In this paper, the design problem of two-channel linear-phase finite-impulse response perfect reconstruction fitter banks in which both the filters are of even length (which are known as type A filter banks) is addressed. The condition on the determinant of the polyphase matrix is translated in terms of well-known convolution matrices. The perfect reconstruction condition is obtained as a system of linear equations. Using the derived condition, an algorithm for the design of type A filter bank by searching the entire class in a sequential approach for both equal and unequal length cases is presented. In this approach, the first analysis filter is chosen such that there exists a filter forming a type A system. The second analysis filter is then chosen using the remaining degrees of freedom. These two steps are iterated, leading to joint optimization of both the filters.