Computations of the symmetric cosine transform using Forsythe and Clenshaw's recurrence formulae
Maurice F. Aburdene, Hoang M. Le, John E. Dorband · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE · 2005
The discrete cosine transform (DCT) is commonly used in signal processing, image processing, communication systems and control systems. We use two methods based on the algorithms of Clenshaw and Forsyth to compute the recursive DCT in parallel. The symmetrical discrete cosine transform (SCT) is computed first and then it can be used as an intermediate tool to compute other forms of the DCT. The advantage of the SCT is that both the forward SCT and its inverse can be computed by the same method and hardware implementation. Although Clenshaw’s algorithm is the more efficient in computational complexity, it is not necessarily the more accurate one. The computational accuracy of these algorithms is discussed. In addition, the front-to-back forms of Clenshaw and Forsyth’s algorithms are implemented in aCe C, a parallel programming language.