Vector-valued nonstationary Gabor frames

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:469

Article

Lian, Qiaofang¹  Song, Linlin¹ 

[1] Beijing Jiaotong Univ, Dept Math, Beijing 100044, Peoples R China

关键词: Time-frequency analysis;    Adaptive representation;    Gabor frames;    Vector-valued space;    Nonstationary Gabor frames;   

DOI  :  10.1016/j.jmaa.2018.09.019

来源: Elsevier

【 摘 要 】

As an extension of Gabor frames, nonstationary Gabor (NSG) frames were recently introduced in adaptive signal analysis. They allow for efficient reconstruction with flexible sampling and varying window functions. In this paper we generalize the notion of NSG frames from L-2(R) to the vector-valued Hilbert space L-2(R, C-L), and investigate the resulting vector-valued NSG frames. We derive a Walnut's representation of the mixed frame operator, and provide some necessary/sufficient conditions for a vector-valued NSG system to be a frame for L-2(R, C-L). Furthermore, we show the existence of painless vector-valued NSG frames, and of vector-valued NSG frames with fast decaying window functions. (C) 2018 Elsevier Inc. All rights reserved.

【 授权许可】

Free