Skew-circular/circular correlation decomposition of prime-factor DCT

An algorithm to decompose the prime-factor DCT into skew-circular/circular correlation (SCC/CC) by coset decomposition is proposed. The simplest case is when the two factors are odd and relatively prime. In this case, the DCT output components are split into six subgroups. Each subgroup contains three short-length CC or SCC matrix-vector products, and the three products can further be merged into only one short-length SCC or CC matrix-vector product. The six subgroups are independent, thus parallel computing is feasible. By fast computation of the short-length SCC and CC, this algorithm reaches the same or less number of multiplications compared to other efficient prime-factor algorithms