Constructing super Gabor frames:the rational time-frequency lattice case

作     者：LI ZhongYan 1 & HAN DeGuang 2, 1 Department of Mathematics and Physics, North China Electric Power University, Beijing 102206, China 2 Department of Mathematics, University of Central Florida, Orlando, FL 32816, USA 

作者机构：Department of Mathematics and Physics North China Electric Power University Beijing China Department of Mathematics University of Central Florida Orlando USA 

出 版 物：《Science China Mathematics》 (中国科学：数学（英文版）)

年 卷 期：2010年第53卷第12期

页      面：3179-3186页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

基　　金：supported by Scientific Research Foundation for the Returned Overseas Chinese Scholars, State Education Ministry the Fundamental Research Funds for the Central Universities the grant of Young Teachers Study Abroad of China Scholarship Council (2005) 

主　　题：super Gabor frame orthonormal super frame full rank lattice tiles 

摘      要：For a time-frequency lattice Λ = A Z d × B Z d , it is known that an orthonormal super Gabor frame of length L exists with respect to this lattice if and only if |det( AB) | = 1 L . The proof of this result involves various techniques from multi-lattice tiling and operator algebra theory, and it is far from constructive. In this paper we present a very general scheme for constructing super Gabor frames for the rational lattice case. Our method is based on partitioning an arbitrary fundamental domain of the lattice in the frequency domain such that each subset in the partition tiles R d by the lattice in the time domain. This approach not only provides us a simple algorithm of constructing various kinds of orthonormal super Gabor frames with flexible length and multiplicity, but also allows us to construct super Gabor (non-Riesz) frames with high order smoothness and regularity. Several examples are also presented.