螺旋坐标系统:多维滤波向一维滤波的转化

把一根线绕到圆柱体上就形成了一条螺旋线。利用螺旋坐标系统可以把笛卡尔坐标空间中的多维滤波和递归滤波转化到一维空间中来处理。相应地多维递归滤波的稳定性问题就可以在一维空间中进行刻画。本文证明了二维滤波和一维螺旋滤波的等价性，并且给出一维螺旋滤波和递归滤波的算法，实际的算例说明了算法的可靠性和有效性

MULTIDIMENSIONAL FILTERING TRANSFORMED INTO ONE DIMENSIONAL FILTERING VIA HELICAL COORDINATE SYSTEM

Wind a wire onto a cylinder to create a helix. By using the helical coordinate system,multidimensional filtering and recursive filtering on Cartesian space can be transformed into onedimension space to process. Correspondingly,the stability problem of multidimensional recursive filters can be characterized in onedimension space. The paper illustrates and proves the equality between twodimension filtering and onedimension helical filtering,and gives the idea of designing the 1D helical filters and recursive filters. The example shows the reliability and effectiveness of the algorithm.