{"title":"Derivative Sampling of Periodic and Nonperiodic Band-Limited Signals — Fourier Spectrum and Interpolation Formula","authors":"Olav Breinbjerg","doi":"10.1109/TAP.2024.3449069","DOIUrl":null,"url":null,"abstract":"For periodic and nonperiodic band-limited signals, the sampling of both the signal and the signal derivative enables the number of sampling points to be reduced and the sampling step between the sampling points, thus, increased by a factor of 2 compared to the standard Nyquist-Whittaker–Shannon-Kotelnikov–Someya sampling theorem. This article presents closed-form expressions for the Fourier spectra and the interpolation formulas based on sampling of signal and signal derivative; the expressions for periodic signals are exact, whereas the expressions for nonperiodic signals are necessarily approximate due to the unavoidable truncation error.","PeriodicalId":13102,"journal":{"name":"IEEE Transactions on Antennas and Propagation","volume":"72 10","pages":"7821-7829"},"PeriodicalIF":4.6000,"publicationDate":"2024-08-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"IEEE Transactions on Antennas and Propagation","FirstCategoryId":"94","ListUrlMain":"https://ieeexplore.ieee.org/document/10659359/","RegionNum":1,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"ENGINEERING, ELECTRICAL & ELECTRONIC","Score":null,"Total":0}
引用次数: 0
Abstract
For periodic and nonperiodic band-limited signals, the sampling of both the signal and the signal derivative enables the number of sampling points to be reduced and the sampling step between the sampling points, thus, increased by a factor of 2 compared to the standard Nyquist-Whittaker–Shannon-Kotelnikov–Someya sampling theorem. This article presents closed-form expressions for the Fourier spectra and the interpolation formulas based on sampling of signal and signal derivative; the expressions for periodic signals are exact, whereas the expressions for nonperiodic signals are necessarily approximate due to the unavoidable truncation error.
期刊介绍：
IEEE Transactions on Antennas and Propagation includes theoretical and experimental advances in antennas, including design and development, and in the propagation of electromagnetic waves, including scattering, diffraction, and interaction with continuous media; and applications pertaining to antennas and propagation, such as remote sensing, applied optics, and millimeter and submillimeter wave techniques
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