Free multiplication integer transformation for the HEVC standard

This paper presents an optimized algorithm to compute the 4×4, 8×8 and 16×16 efficient one-dimensional (1-D) transform. The suggested algorithm is based on fast integer transform algorithms for the HEVC standard. Based on the similarity in the transform matrix operations and the symmetric properties, the efficient fast 1-D algorithms are developed. The developed architecture is designed only with adders and shifters. Therefore, the computational complexities of the proposed algorithm are smaller than those of the direct method while keeping similar quality.