Fast and numerically stable algorithms for discrete cosine transforms
作者： Gerlind Plonka , Manfred Tasche
DOI: 10.1016/J.LAA.2004.07.015
关键词: Round-off error 、 Discrete cosine transform 、 Rotation (mathematics) 、 Mathematics 、 Numerical stability 、 Polynomial arithmetic 、 Orthogonal matrix 、 Matrix decomposition 、 Algorithm 、 Sparse matrix
摘要: Abstract In this paper, we derive fast and numerically stable algorithms for discrete cosine transforms (DCT) of radix-2 length which are based on real factorizations the corresponding matrices into products sparse, (almost) orthogonal simple structure. These completely recursive, to implement use only permutations, scaling with 2 , butterfly operations, plane rotations/rotation–reflections. Our have low arithmetic costs compare known DCT algorithms. Further, a detailed analysis roundoff errors presented shows their excellent numerical stability outperforms algorithm polynomial arithmetic.
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