Perfect reconstruction modulated filter banks without cosine constraints

Abstract

In this paper, we use the theory of perfect reconstruction QMF banks to analyze the general class of modulated filter banks. It is found that there is an inherent tradeoffs between the constraints imposed on the prototype and the modulation matrix to achieve PR. We then proposed 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 to know that the complete solution to this set of constraints is generated by the set of unitary matrices. In other words, the PR property of the modulated filter banks is not due to the use of the cosine modulation but the unitariness of an underlying unitary matrix. This greatly increases the possible choices of modulation in the design of FIR PR QMF banks. We demonstrate the usefulness of our approach by deriving several existing MFB, such as the Extended Lapped Transform (ELT) as special cases of our unitary class of solutions.