A generalized fast algorithm for n-D discrete cosine transform and its application to motion picture coding

In this paper, a generalized fast computational algorithm for the n-dimensional discrete cosine transform (DCT) of length N=2^m (m⩾2) is presented. The developed algorithm is proved and its efficiency is evaluated theoretically. The theoretical results show that compared with the conventional method of computing the one-dimensional along n directions, the number of multiplications needed by our algorithm is only 1/n of that required by the conventional method; for the total number of additions, the latter is a bit more when N⩽8 and much fewer when N⩾16 than the former. To validate the proposed algorithm, we take the case when n=3 as an example and apply it to motion-picture coding. The results show that our method is superior to MPEG-2 in speed and coding performance. The algorithm is clearly described and it is easy to make a computer program for implementation