{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,20]],"date-time":"2026-04-20T01:53:36Z","timestamp":1776650016339,"version":"3.51.2"},"reference-count":31,"publisher":"MDPI AG","issue":"12","license":[{"start":{"date-parts":[[2022,12,15]],"date-time":"2022-12-15T00:00:00Z","timestamp":1671062400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>A recent addition to the class of integral transforms is the quaternion quadratic-phase Fourier transform (Q-QPFT), which generalizes various signal and image processing tools. However, this transform is insufficient for addressing the quadratic-phase spectrum of non-stationary signals in the quaternion domain. To address this problem, we, in this paper, study the (two sided) quaternion windowed quadratic-phase Fourier transform (QWQPFT) and investigate the uncertainty principles associated with the QWQPFT. We first propose the definition of QWQPFT and establish its relation with quaternion Fourier transform (QFT); then, we investigate several properties of QWQPFT which includes inversion and the Plancherel theorem. Moreover, we study different kinds of uncertainty principles for QWQPFT such as Hardy\u2019s uncertainty principle, Beurling\u2019s uncertainty principle, Donoho\u2013Stark\u2019s uncertainty principle, the logarithmic uncertainty principle, the local uncertainty principle, and Pitt\u2019s inequality.<\/jats:p>","DOI":"10.3390\/sym14122650","type":"journal-article","created":{"date-parts":[[2022,12,15]],"date-time":"2022-12-15T02:20:57Z","timestamp":1671070857000},"page":"2650","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":11,"title":["Uncertainty Principles for the Two-Sided Quaternion Windowed Quadratic-Phase Fourier Transform"],"prefix":"10.3390","volume":"14","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":[[2022,12,15]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"543","DOI":"10.1109\/78.558467","article-title":"Highly concentrated time-frequency distributions: Pseudo quantum signal representation","volume":"45","author":"Stankovi","year":"1997","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"81","DOI":"10.1109\/79.752053","article-title":"Joint time-frequency analysis for radar signal and image processing","volume":"16","author":"Chen","year":"1999","journal-title":"IEEE Signal Process. Mag."},{"key":"ref_3","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. 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