In current audio coding standards such as MPEG-1 Layers 1-3, MPEG-II Layers 1-4, MPEG-IV, and AC-3, various forms of the cosine modulated filter bank (CMFBs) have been adopted for compression. This paper proves that all these MCTs can be derived into two modules: the permutation and the discrete cosine transform. The derived DCTs are either type II, type-III, or type IV. On the three types of the DCT, this paper proposes a fast computing algorithm to uniformly compute all the three types of the DCTs. The new fast algorithm will be demonstrated to have good features in regularity, complexity, and general applicability.
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