Decomposition and simulation of quaternion linear canonical transform based on parity properties

JI Jinyi; FENG Zijian; GUO Ziyuan; YANG Xi; FENG Qiang

doi:10.11714/acta.snus.ZR20250139

您当前的位置：

首页 >

文章列表页 >

Decomposition and simulation of quaternion linear canonical transform based on parity properties

Research articles | 更新时间：2026-05-22

- Decomposition and simulation of quaternion linear canonical transform based on parity properties
- Acta Scientiarum Naturalium Universitatis Sunyatseni Vol. 65, Issue 3, Pages: 170-178(2026)
- 作者机构：
  
  1.延安大学数学与计算机科学学院，陕西延安 716000
  2.天津大学数学学院，天津 300354
  3.陕西省能源大数据智能处理省市共建重点实验，陕西延安 716000
- 作者简介：
- 基金信息：
- DOI：10.11714/acta.snus.ZR20250139
  CLC： TN911.72
- Received：24 July 2025，
  
  Revised：2025-10-12，
  
  Accepted：27 October 2025，
  
  Online First：11 March 2026，
  
  Published：25 May 2026
- 稿件说明：
移动端阅览
姬锦仪,冯子健,郭子园等.基于奇偶性的四元数线性正则变换分解及仿真[J].中山大学学报(自然科学版)(中英文),2026,65(03):170-178.

JI Jinyi,FENG Zijian,GUO Ziyuan,et al.Decomposition and simulation of quaternion linear canonical transform based on parity properties[J].Acta Scientiarum Naturalium Universitatis Sunyatseni,2026,65(03):170-178.
姬锦仪,冯子健,郭子园等.基于奇偶性的四元数线性正则变换分解及仿真[J].中山大学学报(自然科学版)(中英文),2026,65(03):170-178. DOI： 10.11714/acta.snus.ZR20250139.

JI Jinyi,FENG Zijian,GUO Ziyuan,et al.Decomposition and simulation of quaternion linear canonical transform based on parity properties[J].Acta Scientiarum Naturalium Universitatis Sunyatseni,2026,65(03):170-178. DOI： 10.11714/acta.snus.ZR20250139.

摘要

在信号处理与代数分析领域，四元数及其变换理论因其独特的数学特性受到广泛关注. 本文研究右侧四元数线性正则变换（QLCT）. 首先，介绍了四元代数的基本概念，包括四元数的表示、运算规则、共轭、范数等，并给出了QLCT的定义；其次，基于信号的奇偶性，提出了右侧QLCT的偶分量与奇分量分解方法，深入探讨了该变换的相关性质并给出证明. 最后，以高斯信号为例进行仿真实验，验证了理论推导，并展示了四元数值信号及其QLCT变换后各分量的特性.

Abstract

In the fields of signal processing and algebraic analysis， quaternions and their transformation theory have attracted extensive attention due to their unique mathematical properties. This paper studies the right-sided quaternion linear canonical transform （QLCT）. Firstly， it introduces the basic concepts of quaternion algebra， including the representation of quaternions， operation rules， conjugation， and norm； and provides the definition of QLCT. Secondly， based on the parity of the signal， it proposes the decomposition method of even and odd components of the QLCT， deeply explores the relevant properties of this transformation， and provides proofs. Finally， taking Gaussian signals as an example， simulation experiments are conducted to verify the theoretical derivation and demonstrate the characteristics of each component of the quaternion-valued signal and its QLCT transformation.

关键词

Keywords

references

BHAT M Y ， DAR A H ， 2022 . Convolution and correlation theorems for Wigner-Ville distribution associated with the quaternion offset linear canonical transform ［J］. Signal Image Video Process ， 16 （ 5 ）： 1235 - 1242 .

BRACEWELL R N ， 1989 . The Fourier transform ［J］. Sci Am ， 260 （ 6 ）： 86 - 95 .

GAO W B ， LI B Z ， 2020 . Quaternion windowed linear canonical transform of two-dimensional signals ［J］. Adv Appl Clifford Algebr ， 30 （ 1 ）： 16 .

HAMILTON W R ， 1866 . Elements of quaternions ［M］. London ： Longmans， Green and Co .

HEALY J J ， KUTAY M A ， OZAKTAS H M ， et al ， 2016 . Linear canonical transforms：Theory and applications ［M］. New York ： Springer .

HU X ， CHENG D ， KOU K I ， 2023 . Convolution theorems associated with quaternion linear canonical transform and applications ［J］. Signal Process ， 202 ： 108743 .

JIANG N ， FENG Q ， YANG X ， et al ， 2025 . The octonion linear canonical transform： Properties and applications ［J］. Chaos Solitons Fractals ， 192 ： 116039 .

LI M ， YUAN X ， CHEN H ， et al ， 2020 . Quaternion discrete Fourier transform-based color image watermarking method using quaternion QR decomposition ［J］. IEEE Access ， 8 ： 72308 - 72315 .

LIU C ， HAN P ， KANG J ， 2025 . Integrating short-time linear canonical transform and joint space-time-frequency analysis for advanced representation of subsurface information in ground penetrating radar ［J］. Sci Rep ， 15 ： 23315 .

MAJORKOWSKA-MECH D ， CARIOW A ， 2023 . One-dimensional quaternion discrete Fourier transform and an approach to its fast computation ［J］. Electronics ， 12 （ 24 ）： 4974 .

MEI Y Y ， FENG Q ， GAO X X ， et al ， 2023 . Convolution theorem associated with the QWFRFT ［J］. Chin J Electron ， 32 （ 3 ）： 485 - 492 .

SHAH F A ， TANTARY A Y ， 2022 . Multi-dimensional linear canonical transform with applications to sampling and multiplicative filtering ［J］. Multidimens Syst Signal Process ， 33 （ 2 ）： 621 - 650 .

SIDDIQUI S ， SAMAD M A ， ISMOILJONOVICH F D ， 2024 . One dimensional quaternion linear canonical transform in probability theory ［J］. Signal Image Video Process ， 18 （ 12 ）： 9419 - 9430 .

WANG R B ， FENG Q ， 2024a . Weighted convolution for quaternion linear canonical cosine transform and its application ［J］. Axioms ， 13 （ 6 ）： 402 .

WANG R B ， FENG Q ， 2024b . Fractional mixed weighted convolution and its application in convolution integral equations ［J］. J Math ， 2024 ： 5375401 .

WANG R B ， FENG Q ， JI J Y ， 2024c . The discrete convolution for fractional cosine-sine series and its application in convolution equations ［J］. AIMS Math ， 9 （ 2 ）： 2641 - 2656 .

XIANG Y ， YUAN S ， FENG Q ， 2023 . Fractional Fourier cosine and sine Laplace weighted convolution and its application ［J］. IET Signal Process ， 17 （ 2 ）： e12170 .

YANG H H ， FENG Q ， WANG X X ， et al ， 2024 . Reduced biquaternion windowed linear canonical transform： Properties and applications ［J］. Mathematics ， 12 （ 5 ）： 743 .

YANG X ， FENG Q ， JIANG N ， et al ， 2025 . Properties and applications of octonion fractional Fourier transform for 3-D octonion signals ［J］. Digit Signal Process ， 165 ： 105339 .

ZHU X ， ZHENG S ， 2021 . Uncertainty principles for the two-sided offset quaternion linear canonical transform ［J］. Math Methods App Sciences ， 44 （ 18 ）： 14236 - 14255 .

Views

412

下载量

CSCD

Alert me when the article has been cited

提交

Tools

Publicity Resources

DOA estimation for underwater acoustic array signals based on eigenvalue weighting

Exploration and practice in big brand cultivation： Re-evaluating quality and efficacy of post-marketed TCM

The existence of solutions for a class of nonlinear elliptic equations with Hardy potential

Qingkailing Oral Liquid modulates AMPK/PI3K/AKT signaling to attenuate NAFLD pathogenesis

Analysis of chemical components and blood plasma constituents of Zhangyanming Tablet extract based on UFLC-Q-TOF-MS/MS method

Related Author

No data

Related Institution

No data

Postal code：510275
Tel：020-84112585，84113223 Email：xuebaozr@mail.sysu.edu.cn
Technical support is provided by Beijing Founder electronics co., LTD 京ICP备09064830号-19 京公网安备11010802024621
It is recommended to read the content of this site in Chrome&IE9+. Please switch to extreme mode in browser 360.
Cookies We use cookies to help provide and enhance our service and tailor content. By continuing, you agree to the use of cookies.

⁰