On the regular structure for the fast 2-D DCT algorithm

N. I. Cho and S. U. Lee (1991) proposed a fast algorithm for 2-D N×N DCT, where N=2^m. It requires only half the number of multiplications of the conventional row-column approach. However, the signal flow graph for the postaddition stage seems very complicated and the order of the output index is seemingly irregular, because the postaddition stage was not based on the mathematical expressions. Consequently, derivation of the signal flow graph becomes complicated as the transform size increases. Systematic expressions for the postaddition stage of the algorithm that enable any N×N DCT to be implemented in a straightforward manner are provided here. The results show that the signal flow graph from input to output has a recursive structure in which the structure for smaller N reappears for larger N. However, the number of additions increases in the new signal flow graph at the expense of improving the regularity in the structure