窗口八元二次相傅里叶变换：信号处理中的锐不等式、不确定性原理和示例

IF 3.4 3区计算机科学 Q2 COMPUTER SCIENCE, INFORMATION SYSTEMS

IEEE Access Pub Date : 2024-10-03 DOI:10.1109/ACCESS.2024.3473298

Manish Kumar;Bhawna

{"title":"窗口八元二次相傅里叶变换：信号处理中的锐不等式、不确定性原理和示例","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":"{\"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}","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

摘要

在本文中，我们定义了有窗八分二次相傅里叶变换（WOQPFT），并推导出其反转公式，包括其基本特性，如线性、反线性、奇偶性、缩放、调制、移位和时频联合移位，以及与八分二次相傅里叶变换（OQPFT）的联系。此外，我们还利用这种变换推导出黎曼-莱伯斯格（Riemann-Lebesgue）两难。根据本分析，我们提出了夏普-皮特不等式和夏普-豪斯多夫-杨不等式。此外，我们还提出了对数不确定性原理、海森堡不确定性原理和多诺霍-斯塔克不确定性原理。讨论了 WOQPFT 的实际应用和信号理论的五个基本例子，并通过图形可视化分析了它们的特殊情况，包括解释。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Windowed Octonion Quadratic Phase Fourier Transform: Sharp Inequalities, Uncertainty Principles, and Examples in Signal Processing

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.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

IEEE Access COMPUTER 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.