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Abstract:
Due to its potential application in signal analysis and image processing, quaternionic Fourier analysis has received increasing attention. This paper addresses quaternionic subspace Gabor frames under the condition that the products of time-frequency shift parameters are rational numbers. We characterize subspace quaternionic Gabor frames in terms of quaternionic Zak transformation matrices. For an arbitrary subspace Gabor frame, we give a parametric expression of its Gabor duals of type I and type II, and characterize the uniqueness Gabor duals of type I and type II. And as an application, given a Gabor frame for the whole space L2(R2,H)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L<^>{2}({\mathbb {R}}<^>{2},\,{\mathbb {H}})$$\end{document}, we give a parametric expression of its all Gabor duals, and derive its unique Gabor dual of type II. Some examples are also provided.
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Source :
ADVANCES IN APPLIED CLIFFORD ALGEBRAS
ISSN: 0188-7009
Year: 2024
Issue: 4
Volume: 34
Cited Count:
SCOPUS Cited Count:
ESI Highly Cited Papers on the List: 0 Unfold All
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Chinese Cited Count:
30 Days PV: 4
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