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Matematicheskie Zametki, 2024, Volume 116, Issue 2, paper published in the English version journal (Mi mzm14381)  

Papers published in the English version of the journal

A class of general multi-window Gabor frames and its (weak) Gabor dual frames

Y. Zhang, Y.-P. Wang

School of Mathematics and Information Science, North Minzu University, Yinchuan, Ningxia, China
Abstract: A general multi-window Gabor frame whose window functions enjoy different time-frequency shifts has potential applications in processing practical signals with rich time-frequency information. It is known from existing literature that one should be careful to construct or define such Gabor frames in the Zak transform domain; they may not even be defined in this domain. Motivated by this, the present paper addresses general multi-window Gabor frames in the time domain. We provide necessary and sufficient conditions for these Gabor frames, characterize their weak Gabor dual frames, and, for comparison, use a Zak transform matrix to characterize (weak) Gabor dual frames for such Gabor frames with rational time-frequency product. Also some examples are provided both in the time and the Zak transform domains.
Keywords: Gabor frame, multi-window Gabor frame, Gabor dual frame, weak Gabor dual frame, Zak transform matrix.
Funding agency Grant number
National Natural Science Foundation of China 12061002
11961072
Natural Science Foundation of Ningxia Province 2022AAC05037
Construction Project of First-Class Disciplines in Ningxia Higher Education NXYLXK2017B09
The first author is supported by National Natural Science Foundation of China (grants nos. 12061002 and 11961072); Natural Science Foundation of Ningxia (grant no. 2022AAC05037); Construction Project of First-Class Disciplines in Ningxia Higher Education (grant no. NXYLXK2017B09).
Received: 20.08.2023
Revised: 20.08.2023
English version:
Mathematical Notes, 2024, Volume 116, Issue 2, Pages 356–372
DOI: https://doi.org/10.1134/S0001434624070290
Bibliographic databases:
Document Type: Article
MSC: 42C40, 42C15
Language: English
Citation: Y. Zhang, Y.-P. Wang, “A class of general multi-window Gabor frames and its (weak) Gabor dual frames”, Math. Notes, 116:2 (2024), 356–372
Citation in format AMSBIB
\Bibitem{ZhaWan24}
\by Y.~Zhang, Y.-P.~Wang
\paper A class of general multi-window Gabor frames and its (weak) Gabor dual frames
\jour Math. Notes
\yr 2024
\vol 116
\issue 2
\pages 356--372
\mathnet{http://mi.mathnet.ru/mzm14381}
\crossref{https://doi.org/10.1134/S0001434624070290}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85207199835}
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