多元多项式变换及其在计算多维数字卷积中的应用

Polynomial Transforms of Many Variables and Their Applications of the Computation of Multidimensional Convolutions

在本文内,我们首先引进多元多项式变换的概念,详细研究这种变换成立的条件。我们将看到,当模M_1(Z_1),M_2(Z_2)是可约多项式时,我们建立了一系列充分必要条件,并且证明了这种变换具有循环卷积特性(CCP),然后简要的讨论了多元多项式变换在计算多维数字卷积中的应用。

In this paper, first a, we shall introduce the polynomial transforms of many variables, and study the conditions of these transforms. As can be seen, We shall establish a series of necessary and sufficient conditions of these transforms when modul M1 (Z_1), M2 (Z_2) are reducible polynomials and shall show that in this ease the transforms have the cyclic convolution property (CCP). Then we shall discuss simply the applications of the polynomial transforms of many variables.