Fast Algorithms for the Recursive Computation of Two-Dimensional Discrete Cosine Transform

• Main Authors: Shih Shih-Kuo, 施世國
• Other Authors: Wen-Hsien Fang
• Format: Others
• Language: zh-TW
• Published: 1998
• Online Access: http://ndltd.ncl.edu.tw/handle/15341230838786539253

碩士 === 國立臺灣科技大學 === 電子工程技術研究所 === 86 === This thesis presents an efficient algorithm for computingthe two-dimensional discrete cosine transform (2-D DCT) of size p^r ×p^r, where p is a prime. Based on a generalized 2-D to one-dimensional (1-D) index mapping scheme, the proposedalgorithm decomposes the 2-D DCT outputs into three parts. The first part contains outputs whose indices are both multiples of p and forms a 2-D DCT of size p^{r-1} ×p^{r-1}.The remaining outputs are further decomposed into two parts,depending on the summation of their indices. The latter two parts can be reformulated as a set of circular correlation (CC)or skew-circular correlation (SCC) matrix-vector products byutilizing the recently addressed maximum coset decomposition. Such a decomposition procedure can be repetitively carried outfor the 2-D DCT of the first part, resulting in a sequence of CCand SCC matrix-vector products of various sizes. Employing fastalgorithms for the computation of these CC/SCC operations, we can thus substantially reduce the numbers of multiplicationsas compared with those of the conventional row-column decompositionapproach. In the special case when p=2, the proposed algorithm can be further simplified, calling for computations comparable to those of previous works.