基于过采样和傅立叶级数的带限外推快速算法

IF 1.7 4区工程技术 Q3 ENGINEERING, ELECTRICAL & ELECTRONIC

Eurasip Journal on Advances in Signal Processing Pub Date : 2023-10-24 DOI:10.1186/s13634-023-01060-9

Weidong Chen

{"title":"基于过采样和傅立叶级数的带限外推快速算法","authors":"Weidong Chen","doi":"10.1186/s13634-023-01060-9","DOIUrl":null,"url":null,"abstract":"Abstract In this paper, fast algorithms for the extrapolation of band-limited signals are presented by the sampling theorem and Fourier series in the case of over sampling. Assume the band-limited signal is known in a finite interval. We update the signal outside the interval by the Shannon sampling theorem in the case of over sampling. Then we obtain a fast algorithm in the form of Fourier series instead of the Fourier transform in the Papoulis–Gerchberg algorithm. Gibbs phenomena is analyzed in the method. An algorithm is presented to control the Gibbs phenomena, and some examples are given in the experimental results.","PeriodicalId":49203,"journal":{"name":"Eurasip Journal on Advances in Signal Processing","volume":null,"pages":null},"PeriodicalIF":1.7000,"publicationDate":"2023-10-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Fast algorithms for band-limited extrapolation by over sampling and Fourier series\",\"authors\":\"Weidong Chen\",\"doi\":\"10.1186/s13634-023-01060-9\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Abstract In this paper, fast algorithms for the extrapolation of band-limited signals are presented by the sampling theorem and Fourier series in the case of over sampling. Assume the band-limited signal is known in a finite interval. We update the signal outside the interval by the Shannon sampling theorem in the case of over sampling. Then we obtain a fast algorithm in the form of Fourier series instead of the Fourier transform in the Papoulis–Gerchberg algorithm. Gibbs phenomena is analyzed in the method. An algorithm is presented to control the Gibbs phenomena, and some examples are given in the experimental results.\",\"PeriodicalId\":49203,\"journal\":{\"name\":\"Eurasip Journal on Advances in Signal Processing\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":1.7000,\"publicationDate\":\"2023-10-24\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Eurasip Journal on Advances in Signal Processing\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1186/s13634-023-01060-9\",\"RegionNum\":4,\"RegionCategory\":\"工程技术\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"ENGINEERING, ELECTRICAL & ELECTRONIC\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Eurasip Journal on Advances in Signal Processing","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1186/s13634-023-01060-9","RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"ENGINEERING, ELECTRICAL & ELECTRONIC","Score":null,"Total":0}

引用次数: 0

摘要

摘要本文利用采样定理和傅立叶级数，给出了带限信号在过采样情况下的快速外推算法。假设在有限区间内已知带限信号。在过采样的情况下，利用香农抽样定理对区间外的信号进行更新。然后用傅里叶级数的形式代替Papoulis-Gerchberg算法中的傅里叶变换，得到了一种快速算法。该方法对吉布斯现象进行了分析。提出了一种控制吉布斯现象的算法，并在实验结果中给出了一些实例。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

Fast algorithms for band-limited extrapolation by over sampling and Fourier series

查看原文本刊更多论文

Fast algorithms for band-limited extrapolation by over sampling and Fourier series

Abstract In this paper, fast algorithms for the extrapolation of band-limited signals are presented by the sampling theorem and Fourier series in the case of over sampling. Assume the band-limited signal is known in a finite interval. We update the signal outside the interval by the Shannon sampling theorem in the case of over sampling. Then we obtain a fast algorithm in the form of Fourier series instead of the Fourier transform in the Papoulis–Gerchberg algorithm. Gibbs phenomena is analyzed in the method. An algorithm is presented to control the Gibbs phenomena, and some examples are given in the experimental results.

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

Eurasip Journal on Advances in Signal Processing ENGINEERING, ELECTRICAL & ELECTRONIC-

CiteScore

3.40

自引率

10.50%

发文量

109

审稿时长

3-8 weeks

期刊介绍： The aim of the EURASIP Journal on Advances in Signal Processing is to highlight the theoretical and practical aspects of signal processing in new and emerging technologies. The journal is directed as much at the practicing engineer as at the academic researcher. Authors of articles with novel contributions to the theory and/or practice of signal processing are welcome to submit their articles for consideration.