A fast algorithm forn-D discrete cosine transform

A generalized fast computational algorithm for then-dimensional discrete cosine transform (n-D DCT) of lengthN=2 ^m (m≥2) is presented. The developed algorithm is theoretically proved and its efficiency is evaluated. The theoretical results show that compared with the conventional method to compute the 1-D DCTs inn directions, the number of multiplications needed by this algorithm is only 1/n of that required by the conventional method; for the total number of additions, it is a bit more whenN≤8 and much less whenN≥16 than the coventional one. To validate the proposed algorithm, the case whenn=3 is taken as an example and applied to the motion picture compression. The results show that the proposed method is superior to MPEG-2. Project supported by the Climbing Programme—National Key Project for Fundamental Research in China.