New polynomial transform algorithm for 2-D DCT using Ramanujan ordered numbers

A new algorithm for the type II 2-D discrete cosine transform (2D-DCT) using Ramanujan ordered numbers is proposed. Based on the polynomial transform, the 2-D DCT with size N₁ × N₂, where N_i is a power of 2, can be converted to a series of one dimensional (1-D) DCT´s. The proposed algorithm would be completely multiplierless with the evaluation of the cosine angles of the DCT by Ramanujan ordered numbers. The cosine angles which are the multiples of 2π/N are represented by numbers of the form 2^-l +2^-m which are then computed by using shift and addition operations only. The proposed algorithm achieves a considerable savings on the number of operations compared with the row-column method. The number of shifters for computing a 2-D DCT is 1/2 times that needed by the row-column method using Ramanujan ordered Numbers and the number of adders required is also considerably reduced. The proposed algorithm is less complex when compared with the other multiplierless algorithm like the integer DCT´s as it avoids any lifting operations.