Oversampled cosine modulated filter banks with perfect reconstruction

摘要

Oversampled filter banks (FBs) offer more design freedom and better noise immunity than critically sampled FBs. Due to the increased computational complexity caused by oversampling, oversampled FBs allowing an efficient implementation, such as cosine modulated filter banks (CMFBs), are of particular interest. So far, only critically sampled CMFBs have been considered. In this paper, we introduce oversampled CMFBs with perfect reconstruction (PR). Extending a classification of CMFBs recently proposed by Gopinath, we consider two types of oversampled CMFBs with PR. One of these types allows linear phase filters in all channels, and comprises CMFBs recently introduced by Lin and Vaidyanathan as well as Wilson-type CMFBs. For both types of oversampled CMFBs, 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 CMFBs.