Fast radix-3/6 algorithms for the realization of the discrete cosine transform

Two fast discrete cosine transform (DCT) algorithms, the radix-3 and radix-6 algorithms, are proposed. They are less computationally complex than the radix-2 algorithm. They also provide a wider choice of the sequence length for which the DCT can be realized and support the prime-factor-decomposed computation algorithm for realizing the 2^m 3ⁿ-point DCT. A mixed-radix algorithm that achieves an optimal performance by applying the radix-3, radix-6, and radix-2 decomposition techniques in a proper sequence is proposed. This mixed-radix algorithm possesses the advantages mentioned above. Compared with the prime-factor-decomposed algorithm, it requires less computational effort and avoids complicated data routing and mapping procedures