Structural Results for Quaternionic Gabor Frames

被引：9

作者：

Cerejeiras, Paula ^{[1
]}

Hartmann, Stefan ^{[1
]}

Orelma, Heikki ^{[2
]}

机构：

[1] Univ Aveiro, Dept Math, CIDMA Ctr Res & Dev Math & Applicat, Campus Univ Santiago, P-3810193 Aveiro, Portugal

[2] Tampere Univ Technol, Lab Civil Engn, Korkeakoulunkatu 10, Tampere 33720, Finland

来源：

ADVANCES IN APPLIED CLIFFORD ALGEBRAS | 2018年 / 28卷 / 05期

关键词：

Quaternionic Gabor frames; Two-sided QWFT; Quaternionic frame operator; Janssen's representation; Wexler-Raz biorthogonality; Frame bounds; FOURIER-TRANSFORM;

D O I：

10.1007/s00006-018-0901-8

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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.

引用

页数：12

共 11 条

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