B. I. Valeev, T. A. Agliullin, A. Zh. Sakhabutdinov
{"title":"Refinement Method of Frequency Shift Definition of Spectrum Obtained at Low Resolution of Analyzer","authors":"B. I. Valeev, T. A. Agliullin, A. Zh. Sakhabutdinov","doi":"10.1134/S0020441223050159","DOIUrl":null,"url":null,"abstract":"<p>The paper proposes a new method for the frequency shift determination of the spectrum obtained under conditions of low resolution of the analyzer, which allows, due to mathematical processing of the signal describing the spectrum, to determine its frequency shift with a resolution two orders of magnitude greater than the instrumental one. The method is based on representing a signal describing a frequency-shifted spectrum as a continuous function differentiable everywhere, expanding it into a Taylor series, approximating its derivatives by finite differences of a given order, and determining the frequency shift by the least squares method. The mathematical substantiation of the method as well as the results of numerical experiments are given. The prospects for the application of the proposed method are discussed.</p>","PeriodicalId":587,"journal":{"name":"Instruments and Experimental Techniques","volume":null,"pages":null},"PeriodicalIF":0.4000,"publicationDate":"2023-09-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Instruments and Experimental Techniques","FirstCategoryId":"5","ListUrlMain":"https://link.springer.com/article/10.1134/S0020441223050159","RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"ENGINEERING, MULTIDISCIPLINARY","Score":null,"Total":0}
引用次数: 0
Abstract
The paper proposes a new method for the frequency shift determination of the spectrum obtained under conditions of low resolution of the analyzer, which allows, due to mathematical processing of the signal describing the spectrum, to determine its frequency shift with a resolution two orders of magnitude greater than the instrumental one. The method is based on representing a signal describing a frequency-shifted spectrum as a continuous function differentiable everywhere, expanding it into a Taylor series, approximating its derivatives by finite differences of a given order, and determining the frequency shift by the least squares method. The mathematical substantiation of the method as well as the results of numerical experiments are given. The prospects for the application of the proposed method are discussed.
期刊介绍：
Instruments and Experimental Techniques is an international peer reviewed journal that publishes reviews describing advanced methods for physical measurements and techniques and original articles that present techniques for physical measurements, principles of operation, design, methods of application, and analysis of the operation of physical instruments used in all fields of experimental physics and when conducting measurements using physical methods and instruments in astronomy, natural sciences, chemistry, biology, medicine, and ecology.
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