Fast Algorithms for the 2-D Discrete Cosine Transform

Two types of efficient algorithms for fast implementation of the 2-D discrete cosine transform (2-D DCT) are developed. One involves recursive structure which implies that the algorithm for (M/2 X N/2) block be extended to (M X N/2) (M/2 X M) and (M X N) blocks (M and N are integer powers of two). The second algorithm is nonrecursive and therefore it has to be tailored for each block size. Both algorithms involve real arithmetic and they reduce the number of multiplications significantly compared to the fast algorithm developed by Chen et al. [8], while the number of additions remain unchanged.