一种实现Reed-Muller展开系数与谱系数相互转换的有效算法及其图形方法

Efficient Algorithm and Map Method for Realizing a Direct Transformation Between Reed-Muller Expansion Coefficients and Spectral Coefficients

通过引入 p bj系数 ,将模 2运算中“1”的个数信息包含其中 ,提出了一种实现Reed Muller展开系数与谱系数之间直接相互转换的有效算法 .在此基础上 ,结合bj系数图与谱系数图的特点 ,建立了实现bj系数图与谱系数图相互转换的规则及步骤 .在变量数较少时 ,图形转换方法具有直观、便捷等特点 .最后以函数对称性的检测为例讨论了它的应用 .Reed Muller展开系数与谱系数之间直接相互转换算法的建立为进一步研究两种展开形式之间的关系提供了有效的途径 ,同时也给两类系数的计算以及为一些数字逻辑问题的解决提供了新的方法 .

By introducing p-bj, coefficients, which reflects the number of 1 in modulo-2 sum operation, an efficient algorithm for Reed-Muller canonical expansion coefficients and spectral coefficients are proposed in this paper. Based on the proposed algorithm, the transformation from Reed-Muller canonical expansion coefficients to spectral coefficients can be realized directly, and vice versa. Furthermore, according to the characteristics of bj coefficient map and spectral coefficient map, the transformation rules and procedures between the two maps are established. Generally, the transformation of map method is suitable for the function with variables less than four. Finally, as an application example, rising the proposed algorithm to identify the symmetry of the function is discussed. The results of the research discussed in this paper provide an efficient approach for further investigating the relationships between two canonical expansions and provide a new method for computing the two kinds of expansion coefficients. Besides, it can act as an alternative approach for solving some problem of digital logic.