{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,13]],"date-time":"2025-10-13T03:49:03Z","timestamp":1760327343872,"version":"build-2065373602"},"reference-count":37,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2023,2,6]],"date-time":"2023-02-06T00:00:00Z","timestamp":1675641600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Fractal Fract"],"abstract":"<jats:p>Two-dimensional hyper-complex (Quaternion) quadratic-phase Fourier transforms (Q-QPFT) have gained much popularity in recent years because of their applications in many areas, including color image and signal processing. At the same time, the applications of Wigner\u2013Ville distribution (WVD) in signal analysis and image processing cannot be ruled out. In this paper, we study the two-dimensional hyper-complex (Quaternion) Wigner\u2013Ville distribution associated with the quadratic-phase Fourier transform (WVD-QQPFT) by employing the advantages of quaternion quadratic-phase Fourier transforms (Q-QPFT) and Wigner\u2013Ville distribution (WVD). First, we propose the definition of the WVD-QQPFT and its relationship with the classical Wigner\u2013Ville distribution in the quaternion setting. Next, we investigate the general properties of the newly defined WVD-QQPFT, including complex conjugate, symmetry-conjugation, nonlinearity, boundedness, reconstruction formula, Moyal\u2019s formula, and Plancherel formula. Finally, we propose the convolution and correlation theorems associated with WVD-QQPFT.<\/jats:p>","DOI":"10.3390\/fractalfract7020159","type":"journal-article","created":{"date-parts":[[2023,2,6]],"date-time":"2023-02-06T02:06:43Z","timestamp":1675649203000},"page":"159","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":9,"title":["An Interplay of Wigner\u2013Ville Distribution and 2D Hyper-Complex Quadratic-Phase Fourier Transform"],"prefix":"10.3390","volume":"7","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-3369-0883","authenticated-orcid":false,"given":"Mohammad Younus","family":"Bhat","sequence":"first","affiliation":[{"name":"Department of Mathematical Sciences, Islamic University of Science and Technology, Kashmir 192122, India"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5124-2761","authenticated-orcid":false,"given":"Aamir Hamid","family":"Dar","sequence":"additional","affiliation":[{"name":"Department of Mathematical Sciences, Islamic University of Science and Technology, Kashmir 192122, India"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2655-949X","authenticated-orcid":false,"given":"Irfan","family":"Nurhidayat","sequence":"additional","affiliation":[{"name":"Department of Mathematics, School of Science, King Mongkut\u2019s Institute of Technology Ladkrabang, Bangkok 10520, Thailand"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0984-0159","authenticated-orcid":false,"given":"Sandra","family":"Pinelas","sequence":"additional","affiliation":[{"name":"Departamento De Ciencias Exatas E Engenharia, Academia Militar, Av. Conde Castro Guimaraes, 2720-113 Amadora, Portugal"}]}],"member":"1968","published-online":{"date-parts":[[2023,2,6]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"10","DOI":"10.15352\/afa\/1391614564","article-title":"Quadratic Fourier transforms","volume":"5","author":"Castro","year":"2014","journal-title":"Ann. Funct. Anal."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/s00009-017-1063-y","article-title":"New convolutions for quadratic-phase Fourier integral operators and their applications","volume":"15","author":"Castro","year":"2018","journal-title":"Mediterr. J. Math."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"169120","DOI":"10.1016\/j.ijleo.2022.169120","article-title":"Quadratic-phase wave packet transform","volume":"261","author":"Bhat","year":"2022","journal-title":"Optik. Int. J. 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