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Convolution and correlation theorems for Wigner–Ville distribution associated with the quaternion offset linear canonical transform

Convolution and correlation theorems for WVD associated with the QOLCT

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Abstract

The quaternion offset linear canonical transform (QOLCT) has gained much popularity in recent years because of its applications in many areas, including image and signal processing. At the same time, the applications of Wigner–Ville distribution (WVD) in signal analysis and image processing cannot be excluded. In this paper, we investigate the Wigner–Ville distribution associated with quaternion offset linear canonical transform (WVD-QOLCT). Firstly, we propose the definition of the WVD-QOLCT, and then, several important properties of newly defined WVD-QOLCT, such as reconstruction formula, orthogonality relation, are derived. Secondly, a novel canonical convolution operator and a related correlation operator for WVD-QOLCT are proposed. Based on the proposed operators, the corresponding generalized convolution and correlation theorems are studied. Moreover on the application part, detection of the linear frequency modulated signals is established in detail by constructing an example.

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Acknowledgements

This work was supported by the UGC-BSR Research Start Up Grant(No. F.30-498/2019(BSR)) provided by UGC, Govt. of India.

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  1. Department of Mathematical Sciences, Islamic University of Science and Technology Awantipora, Pulwama, Jammu and Kashmir, 192122, India

    M. Younus Bhat & Aamir H. Dar

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  1. M. Younus Bhat
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  2. Aamir H. Dar
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Bhat, M.Y., Dar, A.H. Convolution and correlation theorems for Wigner–Ville distribution associated with the quaternion offset linear canonical transform. SIViP 16, 1235–1242 (2022). https://doi.org/10.1007/s11760-021-02074-2

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  • DOI: https://doi.org/10.1007/s11760-021-02074-2

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