{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,6]],"date-time":"2026-07-06T17:28:50Z","timestamp":1783358930141,"version":"3.54.6"},"reference-count":13,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2023,2,19]],"date-time":"2023-02-19T00:00:00Z","timestamp":1676764800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>The Hilbert transform is a commonly used linear operator that separates the real and imaginary parts of an analytic signal and is employed in various fields, such as filter design, signal processing, and communication theory. However, it falls short in representing signals in generalized domains. To address this limitation, we propose a novel integral transform, coined the quadratic-phase Hilbert transform. The preliminary study encompasses the formulation of all the fundamental properties of the generalized Hilbert transform. Additionally, we examine the relationship between the quadratic-phase Fourier transform and the proposed transform, and delve into the convolution theorem for the quadratic-phase Hilbert transform. The Bedrosian theorem associated with the quadratic-phase Hilbert transform is explored in detail. The validity and accuracy of the obtained results were verified through simulations.<\/jats:p>","DOI":"10.3390\/axioms12020218","type":"journal-article","created":{"date-parts":[[2023,2,20]],"date-time":"2023-02-20T02:29:08Z","timestamp":1676860148000},"page":"218","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Quadratic-Phase Hilbert Transform and the Associated Bedrosian Theorem"],"prefix":"10.3390","volume":"12","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-9277-8092","authenticated-orcid":false,"given":"Hari M.","family":"Srivastava","sequence":"first","affiliation":[{"name":"Department of Medical Research, China Medical University Hospital, China Medical University, Taichung 40402, Taiwan"},{"name":"Department of Mathematics and Informatics, Azerbaijan University, 71 Jeyhun Hajibeyli Street, AZ1007 Baku, Azerbaijan"},{"name":"Center for Converging Humanities, Kyung Hee University, 26 Kyungheedae-ro, Dongdaemun-gu, Seoul 02447, Republic of Korea"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8461-869X","authenticated-orcid":false,"given":"Firdous A.","family":"Shah","sequence":"additional","affiliation":[{"name":"Department of Mathematics, South Campus, University of Kashmir, Anantnag 192101, India"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Huzaifa L.","family":"Qadri","sequence":"additional","affiliation":[{"name":"Department of Mathematical Sciences, Islamic University of Science and Technology, Kashmir 192122, India"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Waseem Z.","family":"Lone","sequence":"additional","affiliation":[{"name":"Department of Mathematics, South Campus, University of Kashmir, Anantnag 192101, India"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Musadiq S.","family":"Gojree","sequence":"additional","affiliation":[{"name":"Department of Mathematics, South Campus, University of Kashmir, Anantnag 192101, India"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2023,2,19]]},"reference":[{"key":"ref_1","first-page":"107","article-title":"Theory of reproducing kernels: Applications to approximate solutions of bounded linear operator functions on Hilbert spaces","volume":"230","author":"Saitoh","year":"2010","journal-title":"Am. 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