Extracting a hidden procedure by non-commutative harmonic analysis

作为建立利用非交换谐波分析提取隐藏过程的方法的一步，本研究提出了几种方法，从非交换群的傅里叶展开中提取信号的一些重要特征，例如：(1)一种通过有效卷积在二面体群的频域上对给定信号进行运算的方法(2)一种将三维旋转群中离散网格的信号域转换为更精细网格的插值方法；利用信号的平滑分量对频域中某些分量的集中贡献(3)一种提供定量度量的方法，该方法表示n个对象的排列组上的函数受到对象标记变化1,2，…的影响程度。, n。

As a step toward establishment of the way to extract a hidden procedure by using non-commutative harmonic analysis, this research presented several methods which extract some important features of signals defined over a non-commutative group from their Fourier expansion, such as: (1) A method which operates a given signal over a dihedral group in its frequency domain, by an efficient convolution (2) An interpolation method which transform the domain of a signal which is a discrete mesh in the3-dimensional rotation group into a more finer mesh, exploiting the concentration of the contribution from smooth component of the signal to certain components in the frequency domain (3) A method that provides a quantitative measure representing to what extent a function over the group of permutations of n objects is affected by the change of the labeling of objects by 1, 2, ..., n.