Mixed-radix discrete cosine transform

Abstract

This note presents two new fast discrete cosine transform computation algorithm: a radix-3 and a radix-6 algorithm. These two new algorithms are superior to the conventional radix-2 algorithm as they i) require less computational complexity in terms of the number of multiplications per point, ii) provide a wider choice of the sequence length for which the DCT can be realized and, iii) support the prime factor-decomposed computation algorithm to realize the 2[sup m]3ⁿ-point DCT. Furthermore, a mixed-radix algorithm is also proposed such that an optimal performance can be achieved by applying the proposed radix-3 and radix-6 and the well-developed radix-2 decomposition techniques in a proper sequence.