| 一种新的基于矩的改进离散余弦变换及其反变换快速算法 |
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| 引用本文： | 董志芳,伍家松,王膂,舒华忠.一种新的基于矩的改进离散余弦变换及其反变换快速算法[J].东南大学学报(自然科学版),2009,39(4). |
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| 作者姓名： | 董志芳 伍家松 王膂 舒华忠 |
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| 作者单位： | 东南大学影像科学与技术实验室,南京,210096 |
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| 基金项目： | 国家自然科学基金资助项目，江苏省自然科学基金资助项目 |
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| 摘 要： | 为了提高离散余弦变换(MDCT)及其反变换(IMDCT)的计算效率,提出一种新的基于一维离散矩的快速算法.首先把MDCT和IMDCT的核函数映射到另外一个集合进行合并化简,再用三角函数泰勒级数展开的方法,将MDCT和IMDCT的计算用有限项的一维离散矩的线性加权和近似.一维离散矩的快速计算可以采用p+1维的矢量加法结构进行,用加法运算代替乘法运算,有效地减少了乘法的运算量.该算法的乘法计算量仅为O(Nlog2N/log2log2N),少于通常快速算法所需的O(Nlog2N),可以有效地降低运算时间.理论分析和实验结果都表明:用一维矩近似的方法计算MDCT和IMDCT的结果精度很高,运行速度比较快,能够很好地满足实际计算的要求.
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| 关 键 词： | 矩 快速算法 |
Novel approach for fast computation of MDCT and IMDCT based on moments |
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| Dong Zhifang,Wu Jiasong,Wang Lü,Shu Huazhong.Novel approach for fast computation of MDCT and IMDCT based on moments[J].Journal of Southeast University(Natural Science Edition),2009,39(4). |
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| Authors: | Dong Zhifang Wu Jiasong Wang Lü Shu Huazhong |
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| Abstract: | For fast computation of the modified discrete cosine transform(MDCT) and its inverse MDCT(IMDCT),a novel approach based on one-dimensional discrete moments is proposed.By using the Taylor expansion of trigonometric function,both MDCT and IMDCT are approximated by a linear sum of a finite sequence of onedimensional discrete moments after the kernel modular mapping and simplification. Then one-dimensional discrete moments can be calculated by an addition map of p+1 dimensional vector,which replaces most multi... |
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| Keywords: | MDCT IMDCT |
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