通过威尔逊基准实现可变带宽

IF 2.6 2区数学 Q1 MATHEMATICS, APPLIED

Applied and Computational Harmonic Analysis Pub Date : 2024-02-21 DOI:10.1016/j.acha.2024.101641

Beatrice Andreolli, Karlheinz Gröchenig

{"title":"通过威尔逊基准实现可变带宽","authors":"Beatrice Andreolli, Karlheinz Gröchenig","doi":"10.1016/j.acha.2024.101641","DOIUrl":null,"url":null,"abstract":"<div><p>We introduce a new concept of variable bandwidth that is based on the frequency truncation of Wilson expansions. For this model we derive sampling theorems, a complete reconstruction of <em>f</em> from its samples, and necessary density conditions for sampling. Numerical simulations support the interpretation of this model of variable bandwidth. In particular, chirps, as they arise in the description of gravitational waves, can be modeled in a space of variable bandwidth.</p></div>","PeriodicalId":55504,"journal":{"name":"Applied and Computational Harmonic Analysis","volume":"71 ","pages":"Article 101641"},"PeriodicalIF":2.6000,"publicationDate":"2024-02-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S1063520324000186/pdfft?md5=a1bc8edd6739aca166f773e9d3ff503a&pid=1-s2.0-S1063520324000186-main.pdf","citationCount":"0","resultStr":"{\"title\":\"Variable bandwidth via Wilson bases\",\"authors\":\"Beatrice Andreolli, Karlheinz Gröchenig\",\"doi\":\"10.1016/j.acha.2024.101641\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>We introduce a new concept of variable bandwidth that is based on the frequency truncation of Wilson expansions. For this model we derive sampling theorems, a complete reconstruction of <em>f</em> from its samples, and necessary density conditions for sampling. Numerical simulations support the interpretation of this model of variable bandwidth. In particular, chirps, as they arise in the description of gravitational waves, can be modeled in a space of variable bandwidth.</p></div>\",\"PeriodicalId\":55504,\"journal\":{\"name\":\"Applied and Computational Harmonic Analysis\",\"volume\":\"71 \",\"pages\":\"Article 101641\"},\"PeriodicalIF\":2.6000,\"publicationDate\":\"2024-02-21\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://www.sciencedirect.com/science/article/pii/S1063520324000186/pdfft?md5=a1bc8edd6739aca166f773e9d3ff503a&pid=1-s2.0-S1063520324000186-main.pdf\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Applied and Computational Harmonic Analysis\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S1063520324000186\",\"RegionNum\":2,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Applied and Computational Harmonic Analysis","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S1063520324000186","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}

引用次数: 0

摘要

我们引入了一个新的可变带宽概念，它基于威尔逊展开的频率截断。针对这一模型，我们推导出了采样定理、从采样中完整重建 f 的方法，以及采样的必要密度条件。数值模拟支持对这一可变带宽模型的解释。特别是，引力波描述中出现的啁啾，可以在可变带宽空间中建模。

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

Variable bandwidth via Wilson bases

We introduce a new concept of variable bandwidth that is based on the frequency truncation of Wilson expansions. For this model we derive sampling theorems, a complete reconstruction of f from its samples, and necessary density conditions for sampling. Numerical simulations support the interpretation of this model of variable bandwidth. In particular, chirps, as they arise in the description of gravitational waves, can be modeled in a space of variable bandwidth.

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

Applied and Computational Harmonic Analysis 物理-物理：数学物理

CiteScore

5.40

自引率

4.00%

发文量

审稿时长

22.9 weeks

期刊介绍： Applied and Computational Harmonic Analysis (ACHA) is an interdisciplinary journal that publishes high-quality papers in all areas of mathematical sciences related to the applied and computational aspects of harmonic analysis, with special emphasis on innovative theoretical development, methods, and algorithms, for information processing, manipulation, understanding, and so forth. The objectives of the journal are to chronicle the important publications in the rapidly growing field of data representation and analysis, to stimulate research in relevant interdisciplinary areas, and to provide a common link among mathematical, physical, and life scientists, as well as engineers.