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Two optimum algorithms for short convolutions

YU Pin-neng~1,JIANG Zeng-rong~2,QIAN Xiao-fu~2(1.Institute of Sciences,PLA Univ.of Sci.& Tech.,Nanjing 211101,China;2.Dept.of Appl Math,National Univ.of Defense Technology,Changsha 410073,China)  
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 11point cyclic convolutions were derived based on the Chinese remainder theory and the modular polynomial representations of convolutions.The arithmetic complexity are M_(16)=35,(A_(16)=159) and M_(11)=41,A_(11)=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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