Oversampled cosine modulated filter banks with perfect reconstruction

Oversampled filter banks (PB's) offer more design freedom and better noise immunity than critically sampled FB's, Due to the increased computational complexity caused by oversampling, oversampled FB's allowing an efficient implementation, such as cosine modulated filter banks (CMFB's), are of particular interest. So far, only critically sampled CMFB's have been considered. In this paper, we introduce oversampled CMFB's with perfect reconstruction (PR), Extending a classification of CMFB's recently proposed by Gopinath, we consider two types of oversampled CMFB's with PR. One of these types allows linear phase filters in all channels, and comprises CMFB's recently introduced by Lin and Vaidyanathan as well as Wilson-type CMFB's, For both types of oversampled CMFB's, we formulate PR conditions in the time, frequency, and polyphase domains. It is shown that any PR CMFB corresponds to a PR DFT FB with twice the oversampling factor and that (under a specific condition) the same PR prototype can be used for both CMFB types. We also show that the frame-theoretic properties of a CMFB and of the corresponding DFT FB are closely related. In particular, it is demonstrated that the minimum-norm synthesis prototype in an oversampled PR CMFB equals that in the corresponding DFT FB, Finally, we briefly address design methods and the efficient DCT/DST-based implementation of oversampled CMFB's.