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Structural Results for Quaternionic Gabor Frames

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Details

Original languageEnglish
Article number86
Number of pages12
JournalAdvances in Applied Clifford Algebras
Volume28
Issue number5
DOIs
Publication statusPublished - 1 Nov 2018
Publication typeA1 Journal article-refereed

Abstract

We study quaternionic Gabor frames based on the two-sided quaternionic windowed Fourier transform. Since classical Hilbert space based methods do not work in this case we introduce appropriated versions of translation and modulation operators. We prove Janssen’s and Walnut’s representations, as well as modified versions of the Wexler–Raz biorthogonality and Ron–Shen duality based on the concept of correlation function. We end up with a characterization of tight quaternionic Gabor frames.

ASJC Scopus subject areas

Keywords

  • Frame bounds, Janssen’s representation, Quaternionic frame operator, Quaternionic Gabor frames, Two-sided QWFT, Wexler–Raz biorthogonality

Publication forum classification

Field of science, Statistics Finland