Rational time-frequency super Gabor frames and their duals

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:403

Article

Li, Yun-Zhang¹  Zhou, Feng-Ying² 

[1] Beijing Univ Technol, Coll Appl Sci, Beijing 100124, Peoples R China

[2] E China Inst Technol, Sch Sci, Nanchang 330013, Peoples R China

关键词: Gabor frame;    Super Gabor frame;    Super Gabor dual;    Zak transform;   

DOI  :  10.1016/j.jmaa.2013.02.057

来源: Elsevier

【 摘 要 】

This paper addresses general super Gabor systems with rational time-frequency product lattices. A Zak transform matrix method is developed for such super Gabor systems. We characterize complete super Gabor systems and super Gabor frames. Given a super Gabor frame, we obtain an explicit expression of its canonical dual and a parametrization of all its super Gabor duals and prove that the canonical dual is the norm-minimal one among all super Gabor duals. We also prove that a super Gabor frame has a unique super Gabor dual if and only if it is a Riesz basis. (C) 2013 Elsevier Inc. All rights reserved.

【 授权许可】

Free