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 filter banks in which both the filters are of even length (which are known as type 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 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 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.