Perfect reconstruction modulated filter banks without cosine constraints

The theory of perfect reconstruction (PR) quadrature mirror filter (QMF) banks is used to analyze the general class of modulated filter banks (MFBs). It is found that there is an inherent tradeoff between the constraints imposed on the prototype and the modulation matrix to achieve PR. The authors propose a set of constraints on the modulation to achieve PR while retaining the desirable power complementary conditions on the polyphase components. The prototype filter can then be designed using the two-channel lossless lattice. It is surprising that the complete solution to this set of constraints is generated by the set of unitary matrices. This greatly increases the possible choices of modulation in the design of finite-impulse-response PR QMF banks. The usefulness of the proposed approach is demonstrated by deriving several existing MFBs, such as the extended lapped transform, as special cases of the unitary class of solution.<>