{"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":1776650016077,"version":"3.51.2"},"reference-count":16,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2022,9,26]],"date-time":"2022-09-26T00:00:00Z","timestamp":1664150400000},"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>Wavelet transform is a powerful tool for analysing the problems arising in harmonic analysis, signal and image processing, sampling, filtering, and so on. However, they seem to be inadequate for representing those signals whose energy is not well concentrated in the frequency domain. In pursuit of representations of such signals, we propose a novel time-frequency transform coined as quadratic-phase wave packet transform in L2(R). The proposed transform is aimed at rectifying the conventional wavelet transform by employing a quadratic-phase Fourier transform with extra degrees of freedom. Besides the formulation of all the fundamental results, including the orthogonality relation, reconstruction formula and the characterization of range, we also derive a direct relationship between the well-known Wigner-Ville distribution and the proposed transform. In addition, we study the quadratic-phase wave-packet transform in the framework of almost periodic functions. Finally, we extend the scope of the present work by investigating the composition of quadratic-phase wave packet transforms.<\/jats:p>","DOI":"10.3390\/sym14102018","type":"journal-article","created":{"date-parts":[[2022,9,29]],"date-time":"2022-09-29T01:23:16Z","timestamp":1664414596000},"page":"2018","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["Quadratic-Phase Wave-Packet Transform in L2(R)"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-9277-8092","authenticated-orcid":false,"given":"Hari M.","family":"Srivastava","sequence":"first","affiliation":[{"name":"Department of Mathematics and Statistics, University of Victoria, Victoria, BC V8W 3R4, Canada"},{"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"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8461-869X","authenticated-orcid":false,"given":"Firdous A.","family":"Shah","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University of Kashmir, South Campus, Anantnag 192101, Jammu and Kashmir, India"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9826-9475","authenticated-orcid":false,"given":"Waseem Z.","family":"Lone","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University of Kashmir, South Campus, Anantnag 192101, Jammu and Kashmir, India"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,9,26]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Debnath, L., and Shah, F.A. 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