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Structural Results for Quaternionic Gabor Frames

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Structural Results for Quaternionic Gabor Frames. / Cerejeiras, Paula; Hartmann, Stefan; Orelma, Heikki.

In: Advances in Applied Clifford Algebras, Vol. 28, No. 5, 86, 01.11.2018.

Research output: Contribution to journalArticleScientificpeer-review

Harvard

Cerejeiras, P, Hartmann, S & Orelma, H 2018, 'Structural Results for Quaternionic Gabor Frames', Advances in Applied Clifford Algebras, vol. 28, no. 5, 86. https://doi.org/10.1007/s00006-018-0901-8

APA

Cerejeiras, P., Hartmann, S., & Orelma, H. (2018). Structural Results for Quaternionic Gabor Frames. Advances in Applied Clifford Algebras, 28(5), [86]. https://doi.org/10.1007/s00006-018-0901-8

Vancouver

Cerejeiras P, Hartmann S, Orelma H. Structural Results for Quaternionic Gabor Frames. Advances in Applied Clifford Algebras. 2018 Nov 1;28(5). 86. https://doi.org/10.1007/s00006-018-0901-8

Author

Cerejeiras, Paula ; Hartmann, Stefan ; Orelma, Heikki. / Structural Results for Quaternionic Gabor Frames. In: Advances in Applied Clifford Algebras. 2018 ; Vol. 28, No. 5.

Bibtex - Download

@article{034f29db71924253a6a423fb5dd6631d,
title = "Structural Results for Quaternionic Gabor Frames",
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.",
keywords = "Frame bounds, Janssen’s representation, Quaternionic frame operator, Quaternionic Gabor frames, Two-sided QWFT, Wexler–Raz biorthogonality",
author = "Paula Cerejeiras and Stefan Hartmann and Heikki Orelma",
year = "2018",
month = "11",
day = "1",
doi = "10.1007/s00006-018-0901-8",
language = "English",
volume = "28",
journal = "Advances in Applied Clifford Algebras",
issn = "0188-7009",
publisher = "Springer Verlag",
number = "5",

}

RIS (suitable for import to EndNote) - Download

TY - JOUR

T1 - Structural Results for Quaternionic Gabor Frames

AU - Cerejeiras, Paula

AU - Hartmann, Stefan

AU - Orelma, Heikki

PY - 2018/11/1

Y1 - 2018/11/1

N2 - 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.

AB - 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.

KW - Frame bounds

KW - Janssen’s representation

KW - Quaternionic frame operator

KW - Quaternionic Gabor frames

KW - Two-sided QWFT

KW - Wexler–Raz biorthogonality

U2 - 10.1007/s00006-018-0901-8

DO - 10.1007/s00006-018-0901-8

M3 - Article

VL - 28

JO - Advances in Applied Clifford Algebras

JF - Advances in Applied Clifford Algebras

SN - 0188-7009

IS - 5

M1 - 86

ER -