High-accuracy implementation of fast DCT algorithms based on algebraic integer encoding

The paper presents a systematic approach to synthesizing and implementing fast algorithms for computing the DCT of a power-of-two size. The main features of the obtainable algorithms are regularity of their signal flow graphs and low arithmetic complexity. Multiplierless implementation of the algorithms is based on the algebraic integer (AI) technique. A general AI encoding scheme for fast DCT algorithms is presented. The approach is demonstrated by using it to derive an AI-based low-error fast implementation of the 16-point DCT.