Small-Size FDCT/IDCT Algorithms with Reduced Multiplicative Complexity

Resumo

Discrete orthogonal transforms including the discrete Fourier transform, the discrete Walsh transform, the discrete Hartley transform, the discrete Slant transform, etc. are extensively used in radio-electronic and telecommunication systems for data processing and transmission. The popularity of using these transform is explained by the presence of fast algorithms that minimize the computational and hardware complexity of their implementation. A special place in the list of transforms is occupied by the forward and inverse discrete cosine transforms (FDCT and IDCT respectively). This article proposes a set of parallel algorithms for the fast implementation of FDCT/IDCT. The effectiveness of the proposed solutions is justified by the possibility of the factorization of the FDCT/IDCT matrices, which leads to a decrease in computational and implementation complexity. Some fully parallel FDCT/IDCT algorithms for small lengths N = 2, 3, 4, 5, 6, 7 are presented.