JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2017, Vol. 52 ›› Issue (8): 17-24.doi: 10.6040/j.issn.1671-9352.0.2016.189

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Existence and stability for multiple gabor frames

SONG Liang1, FENG Jin-shun1, CHENG Zheng-xing2   

  1. 1. School of Mathematics and Statistics, Nanyang Institute of Technology, Nanyang 473004, Henan, China;
    2. School of Mathematics and Statistics, Xian Jiaotong University, Xian 710049, Shaanxi, China
  • Received:2016-04-28 Online:2017-08-20 Published:2017-08-03

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Abstract: Since redundant frames are play very important role in signal processing and image processing, existence and perturbation for multiple Gabor frames are studied in this paper. The sufficient condition for the existence of multiple Gabor frames is proposed. It is shown that a function which is the generator of Gabor frames is also a generator of Gabor frames after it is perturbed. According to the frame stability criterion, we prove that a class of irregular Gabor frames are stable frames as well.

Key words: perturbation, gabor frame, frame generator, frame multiresolution analysis, stability

CLC Number: 

  • O174.2
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