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本文利用有限交换环的基本概念和性质讨论了DFT和卷积计算中的一维化多维问题。文中论述了DFT一维化多维同Levy-Walsh变换的关系,论证了利用多维技术计算一维DFT和循环卷积时序号变换的充要条件,并给出了一种序号重排快速算法。
In this paper, we discuss the one-dimensional multidimensional problems in DFT and convolutional computation by using the basic concepts and properties of finite switching rings. In this paper, the relationship between one-dimensional multidimensional DFT and Levy-Walsh transform is discussed. The necessary and sufficient conditions for the transformation of sequence numbers with one-dimensional DFT and cyclic convolution are demonstrated by using multidimensional techniques. A fast algorithm of sequence number rearrangement is given.