IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v12y2024i5p743-d1349760.html
   My bibliography  Save this article

Reduced Biquaternion Windowed Linear Canonical Transform: Properties and Applications

Author

Listed:
  • Hehe Yang

    (School of Mathematics and Computer Science, Yanan University, Yanan 716000, China)

  • Qiang Feng

    (School of Mathematics and Computer Science, Yanan University, Yanan 716000, China)

  • Xiaoxia Wang

    (School of Mathematics and Computer Science, Yanan University, Yanan 716000, China)

  • Didar Urynbassarova

    (National Engineering Academy of the Republic of Kazakhstan, Almaty 050000, Kazakhstan)

  • Aajaz A. Teali

    (Department of Mathematics, School of Chemical Engineering and Physical Sciences, Lovely Professional University, Jalandhar 144411, Punjab, India)

Abstract

The quaternion windowed linear canonical transform is a tool for processing multidimensional data and enhancing the quality and efficiency of signal and image processing; however, it has disadvantages due to the noncommutativity of quaternion multiplication. In contrast, reduced biquaternions, as a special case of four-dimensional algebra, possess unique advantages in computation because they satisfy the multiplicative exchange rule. This paper proposes the reduced biquaternion windowed linear canonical transform (RBWLCT) by combining the reduced biquaternion signal and the windowed linear canonical transform that has computational efficiency thanks to the commutative property. Firstly, we introduce the concept of a RBWLCT, which can extract the time local features of an image and has the advantages of both time-frequency analysis and feature extraction; moreover, we also provide some fundamental properties. Secondly, we propose convolution and correlation operations for RBWLCT along with their corresponding generalized convolution, correlation, and product theorems. Thirdly, we present a fast algorithm for RBWLCT and analyze its computational complexity based on two dimensional Fourier transform (2D FTs). Finally, simulations and examples are provided to demonstrate that the proposed transform effectively captures the local RBWLCT-frequency components with enhanced degrees of freedom and exhibits significant concentrations.

Suggested Citation

  • Hehe Yang & Qiang Feng & Xiaoxia Wang & Didar Urynbassarova & Aajaz A. Teali, 2024. "Reduced Biquaternion Windowed Linear Canonical Transform: Properties and Applications," Mathematics, MDPI, vol. 12(5), pages 1-21, March.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:5:p:743-:d:1349760
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/12/5/743/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/12/5/743/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Kit Ian Kou & Jian-Yu Ou & Joao Morais, 2013. "On Uncertainty Principle for Quaternionic Linear Canonical Transform," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-14, April.
    2. Lei Huang & Ke Zhang & Yi Chai & Shuiqing Xu, 2017. "Computation of the Short-Time Linear Canonical Transform with Dual Window," Mathematical Problems in Engineering, Hindawi, vol. 2017, pages 1-8, September.
    3. Didar Urynbassarova & Aajaz A. Teali, 2023. "Convolution, Correlation, and Uncertainty Principles for the Quaternion Offset Linear Canonical Transform," Mathematics, MDPI, vol. 11(9), pages 1-24, May.
    4. Mawardi Bahri & Ryuichi Ashino, 2016. "A Simplified Proof of Uncertainty Principle for Quaternion Linear Canonical Transform," Abstract and Applied Analysis, Hindawi, vol. 2016, pages 1-11, January.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Morais, J. & Ferreira, M., 2023. "Hyperbolic linear canonical transforms of quaternion signals and uncertainty," Applied Mathematics and Computation, Elsevier, vol. 450(C).

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:12:y:2024:i:5:p:743-:d:1349760. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.