Computationally efficient design of NPR paraunitary cosine modulated filter banks

A computationally efficient design approach for paraunitary cosine modulated filter banks (CMFBs) is proposed here. Usually the design methodology entails designing a prototype filter by minimizing stopband energy subject to two sets of perfect reconstruction (PR) conditions. By combining these sets of PR conditions into one using power complementary properties of its polyphase components, we seek to lay them out in such a way as to allow their computation during optimization by referencing the indices of a suitably constructed matrix. We also seek to define a dimensionally energy-like objective function for optimization with the use of a simple penalty number. An iterative quadratic-constrained least-squares (QCLS) approach is then used to solve the problem. The results show marked improvement over existing methods in that, even for very long prototype filters, the computational complexity is much less and hence, shorter design time.