一种新的等角紧框架构造方法

A New Construction Method of Equiangular Tight Frame

框架是一组继承了正交基的良好性质并且具有一定冗余度的线性序列,可以有效地表示信号并获得信号的重要特征.而格拉斯曼框架一直是框架理论中最重要的组成部分.针对于格拉斯曼框架的构造难题,提出了一种新的等角紧框架构造方法.方法基于区组设计和斯坦纳系统的联合.可构造出较高维度的等角紧框架,拓宽了格拉斯曼框架构造的范围,为格拉斯曼框架的构造提供了新的思路.

The frame is a linear redundancy sequence which inherits the good properties of orthogonal basis. The frame can express signals efficiently and get the key characters. And the Grassmannian frame is the most important part in frame theory. The paper aims at the difficulties in constructing Grassmannian frames and proposes a new method in constructing equiangular tight frame（ETF）. The new construction method is based on hlock design and Steiner system. It can construct high dimensionality ETF frames, expand the limits of Grassmannian frames construction, and provide new ideas for the construction methods.