Octonion short-time linear canonical transform

Wen Biao Gao; Bing Zhao Li

doi:10.1002/mma.8513

Octonion short-time linear canonical transform

Wen Biao Gao, Bing Zhao Li^*

^*Corresponding author for this work

School of Mathematics and Statistics

Research output: Contribution to journal › Article › peer-review

4 Citations (Scopus)

Abstract

We investigate the octonion short-time linear canonical transform (OCSTLCT) in this paper. First, we propose the new definition of the OCSTLCT, and then several important properties of newly defined OCSTLCT, such as bounded, shift, modulation, time-frequency shift, inversion formula, and orthogonality relation, are derived based on the spectral representation of the octonion linear canonical transform (OCLCT). Second, by the Heisenberg uncertainty principle for the OCLCT and the orthogonality relation property for the OCSTLCT, the Heisenberg uncertainty principle for the OCSTLCT is established. Finally, we give an example of the OCSTLCT.

Original language	English
Pages (from-to)	321-338
Number of pages	18
Journal	Mathematical Methods in the Applied Sciences
Volume	46
Issue number	1
DOIs	https://doi.org/10.1002/mma.8513
Publication status	Published - 15 Jan 2023

Keywords

octonion
octonion linear canonical transform
octonion short-time linear canonical transform
uncertainty principle

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10.1002/mma.8513

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abstract = "We investigate the octonion short-time linear canonical transform (OCSTLCT) in this paper. First, we propose the new definition of the OCSTLCT, and then several important properties of newly defined OCSTLCT, such as bounded, shift, modulation, time-frequency shift, inversion formula, and orthogonality relation, are derived based on the spectral representation of the octonion linear canonical transform (OCLCT). Second, by the Heisenberg uncertainty principle for the OCLCT and the orthogonality relation property for the OCSTLCT, the Heisenberg uncertainty principle for the OCSTLCT is established. Finally, we give an example of the OCSTLCT.",

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T1 - Octonion short-time linear canonical transform

AU - Gao, Wen Biao

AU - Li, Bing Zhao

PY - 2023/1/15

Y1 - 2023/1/15

N2 - We investigate the octonion short-time linear canonical transform (OCSTLCT) in this paper. First, we propose the new definition of the OCSTLCT, and then several important properties of newly defined OCSTLCT, such as bounded, shift, modulation, time-frequency shift, inversion formula, and orthogonality relation, are derived based on the spectral representation of the octonion linear canonical transform (OCLCT). Second, by the Heisenberg uncertainty principle for the OCLCT and the orthogonality relation property for the OCSTLCT, the Heisenberg uncertainty principle for the OCSTLCT is established. Finally, we give an example of the OCSTLCT.

AB - We investigate the octonion short-time linear canonical transform (OCSTLCT) in this paper. First, we propose the new definition of the OCSTLCT, and then several important properties of newly defined OCSTLCT, such as bounded, shift, modulation, time-frequency shift, inversion formula, and orthogonality relation, are derived based on the spectral representation of the octonion linear canonical transform (OCLCT). Second, by the Heisenberg uncertainty principle for the OCLCT and the orthogonality relation property for the OCSTLCT, the Heisenberg uncertainty principle for the OCSTLCT is established. Finally, we give an example of the OCSTLCT.

KW - octonion

KW - octonion linear canonical transform

KW - octonion short-time linear canonical transform

KW - uncertainty principle

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JF - Mathematical Methods in the Applied Sciences

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Octonion short-time linear canonical transform

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