| 两个最佳短卷积算法 |
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| 引用本文： | 余品能,蒋增荣,钱校夫. 两个最佳短卷积算法[J]. 解放军理工大学学报(自然科学版), 2006, 7(1): 94-98 |
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| 作者姓名： | 余品能 蒋增荣 钱校夫 |
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| 作者单位： | 解放军理工大学,理学院,江苏,南京,211101;国防科技大学,应用数学系,湖南,长沙,410073 |
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| 摘 要： | 借助卷积的模多项式表示式及中国剩余定理推导出计算16点和11点短卷积的最佳算法，其算术复杂性分别为M16=35，A16=159；M11=41，A=-137，是目前公布的运算量最小的算法。与已有的7种最佳短卷积算法一起，使可嵌套计算的卷积长度范围由48种扩展到120种，满足了实际应用的需要。
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| 关 键 词： | 循环卷积 中国剩余定理 嵌套算法 |
| 文章编号： | 1009-3443（2006）01-0094-05 |
| 收稿时间： | 2005-05-31 |
| 修稿时间： | 2005-05-31 |
Two optimum algorithms for short convolutions |
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| YU Pin-neng,JIANG Zeng-rong and QIAN Xiao-fu. Two optimum algorithms for short convolutions[J]. Journal of PLA University of Science and Technology(Natural Science Edition), 2006, 7(1): 94-98 |
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| Authors: | YU Pin-neng JIANG Zeng-rong QIAN Xiao-fu |
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| Affiliation: | Institute of Sciences,PLA Univ.of Sci.& Tech.,Nanjing 211101,China;Dept.of Appl Math,National Univ.of Defense Technology,Changsha 410073,China;Dept.of Appl Math,National Univ.of Defense Technology,Changsha 410073,China |
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| Abstract: | Theory and practical applications indicate that the short convolutions nested algorithm is the most effective method in computing the convolutions with the non-high composite length. Two optimum algorithms for 16-point and 11-point cyclic convolutions were derived based on the Chinese remainder theory and the modular polynomial representations of convolutions. The arithmetic complexity are M16= 35, A10= 159 and M11=41,A11= 137, respectively, which means two new algorithms involving the least operation. Along with the seven known optimum short convolution algorithms, the kinds of calculable length of convolutions are extended from 48 to 120, which meets the needs of practical applications. |
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| Keywords: | cyclic convolutions the Chinese remainder theory nested algorithm |
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