{"title":"Windowed Octonion Quadratic Phase Fourier Transform: Sharp Inequalities, Uncertainty Principles, and Examples in Signal Processing","authors":"Manish Kumar;Bhawna","doi":"10.1109/ACCESS.2024.3473298","DOIUrl":null,"url":null,"abstract":"In this paper, we define the Windowed Octonion Quadratic Phase Fourier Transform (WOQPFT) and derive its inversion formula, including its essential properties, such as linearity, anti-linearity, parity, scaling, modulation, shifting, and joint time-frequency shifting, as well as its link to Octonion Quadratic Phase Fourier Transform (OQPFT). Additionally, we derive the Riemann-Lebesgue lemma using this transform. Following the present analysis, we formulated Sharp Pitt’s and Sharp Hausdorff-Young’s inequalities. Further, Logarithmic, Heisenberg’s, and Donoho-Stark’s uncertainty principles are also formulated. The practical application of WOQPFT and the five elementary examples of signal theory are discussed, and their particular cases are analyzed through graphical visualization, including interpretation.","PeriodicalId":13079,"journal":{"name":"IEEE Access","volume":"12 ","pages":"146771-146794"},"PeriodicalIF":3.4000,"publicationDate":"2024-10-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=10704622","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"IEEE Access","FirstCategoryId":"94","ListUrlMain":"https://ieeexplore.ieee.org/document/10704622/","RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"COMPUTER SCIENCE, INFORMATION SYSTEMS","Score":null,"Total":0}
引用次数: 0
Abstract
In this paper, we define the Windowed Octonion Quadratic Phase Fourier Transform (WOQPFT) and derive its inversion formula, including its essential properties, such as linearity, anti-linearity, parity, scaling, modulation, shifting, and joint time-frequency shifting, as well as its link to Octonion Quadratic Phase Fourier Transform (OQPFT). Additionally, we derive the Riemann-Lebesgue lemma using this transform. Following the present analysis, we formulated Sharp Pitt’s and Sharp Hausdorff-Young’s inequalities. Further, Logarithmic, Heisenberg’s, and Donoho-Stark’s uncertainty principles are also formulated. The practical application of WOQPFT and the five elementary examples of signal theory are discussed, and their particular cases are analyzed through graphical visualization, including interpretation.
IEEE AccessCOMPUTER SCIENCE, INFORMATION SYSTEMSENGIN-ENGINEERING, ELECTRICAL & ELECTRONIC
CiteScore
9.80
自引率
7.70%
发文量
6673
审稿时长
6 weeks
期刊介绍：
IEEE Access® is a multidisciplinary, open access (OA), applications-oriented, all-electronic archival journal that continuously presents the results of original research or development across all of IEEE''s fields of interest.
IEEE Access will publish articles that are of high interest to readers, original, technically correct, and clearly presented. Supported by author publication charges (APC), its hallmarks are a rapid peer review and publication process with open access to all readers. Unlike IEEE''s traditional Transactions or Journals, reviews are "binary", in that reviewers will either Accept or Reject an article in the form it is submitted in order to achieve rapid turnaround. Especially encouraged are submissions on:
Multidisciplinary topics, or applications-oriented articles and negative results that do not fit within the scope of IEEE''s traditional journals.
Practical articles discussing new experiments or measurement techniques, interesting solutions to engineering.
Development of new or improved fabrication or manufacturing techniques.
Reviews or survey articles of new or evolving fields oriented to assist others in understanding the new area.
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