紧支撑最小能量框架的构造(英文)

The Construction of Minimum-energy Frames with Compact Support

本文研究了对应于紧支撑加细函数的最小能量框架,并得到了最小能量框架存在的准则,该准则是建立在加细函数的Laurent多项式符号上的不等式。其次给出了显式构造最小能量框架的公式。最后构造出了数值算例。

We study minimum-energy frames with compact supports which correspond to some refinable functions with compact supports, and we give a precise existence criterion for minimum-energy frames in terms of an inequality condition on the Laurent polynomial symbols of the refinable functions. A explicit formula for constructing minimum-energy frame is also presented. Finally, numerical examples are given.