{"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":"5 3","pages":"0"},"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}
引用次数: 0
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.
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.
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