The factorization of M-channel FIR and IIR cosine-modulated filter banks and their multiplier-less realizations using SOPOT coefficients

This paper proposes a factorization for the M-channel perfect reconstruction (PR) IIR cosine-modulated filter banks (CMFB) proposed previously by the authors. This factorization, which is based on the lifting scheme, is also complete for the PR FIR CMFB as well as the general two-channel PR MR filter banks if the determinant of the polyphase matrix is equal to constant multiplies of signal delays. It can be used to convert a numerically optimized nearly PR CMFB to a structurally PR system. Furthermore, the arithmetic complexity of the FB using this structure can be reduced asymptotically by a factor of two. When the forward and inverse transforms are implemented with the same set of SOPOT coefficients, a multiplier-less CMFB can be obtained. Its arithmetic complexity is further reduced and it becomes very attractive for VLSI implementation.