New radix-3 fast algorithm for the discrete cosine transform

In this paper a new radix-3 fast algorithm for the length -3^m discrete cosine transform (DCT) is proposed, to further extend the applicability of the fast cosine transform (FCT) algorithm. First, the basic 3-point DCT is considered. Then, the formulae of the new radix-3 FCT algorithm are derived. Next, a block diagram of the radix-3 FCT algorithm is shown and the signal flowgraph for length-3² FCT is given to illustrate the proposed algorithm. Finally, the computational complexity is analysed. The proposed algorithm requires less number of arithmetic operations and allows in-place computation. The simple and regular structure makes it easy to be implemented. One can compute effectively the length-2¹·3^m DCT using this length-3^m algorithm together with the existing length-2¹ algorithm by prime factor decomposition. The proposed new radix-3 FCT algorithm is expected to find wide practical applications