Nonstationary Gabor frames for l2(Z)

Recently, continuous‐time nonstationary Gabor (NSG) frames were introduced in adaptive signal analysis. They allow for efficient reconstruction with flexible sampling and varying window functions. In this paper, we focus on the existence and construction of NSG frames in the discrete‐time setting. W...

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Bibliographic Details
Published in:Mathematical methods in the applied sciences 2019-03, Vol.42 (5), p.1335-1351
Main Author: Lian, Qiaofang
Format: Article
Language:English
Subjects:
adaptive representation
Decay rate
discrete space
Frames
Gabor frame
Gabor transformation
Signal analysis
Time setting
Window functions
Online Access:Get full text
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Summary:Recently, continuous‐time nonstationary Gabor (NSG) frames were introduced in adaptive signal analysis. They allow for efficient reconstruction with flexible sampling and varying window functions. In this paper, we focus on the existence and construction of NSG frames in the discrete‐time setting. We provide existence results for painless NSG frames and for NSG frames with fast decaying window functions. We also construct NSG frames with noncompactly supported window functions from a known painless NSG frame. Some examples are provided to illustrate the general theory.
ISSN:0170-4214
1099-1476
DOI:10.1002/mma.5278