{"title":"与二次相傅里叶变换相关的修正模糊函数和维格纳分布","authors":"Tien Minh Lai","doi":"10.1007/s00041-023-10058-8","DOIUrl":null,"url":null,"abstract":"<p>The ambiguity function (AF) and Wigner distribution (WD) play an important role not only in non-stationary signal processing but also in radar and sonar systems. In this paper, we introduce modified ambiguity function and Wigner distribution associated with quadratic-phase Fourier transform (QAF, QWD). Moreover, many various useful properties of QAF and QWD are also proposed. Marginal properties and Moyal’s formulas of these distributions have elegance and simplicity comparable to those of the AF and WD. Besides, convolutions via quadratic-phase Fourier transform are also introduced. Furthermore, convolution theorems for QAF and QWD are also derived, which seem similar to those of the classical Fourier transform (FT). In addition, applications of QAF and QWD are established such as the detection of the parameters of single-component and multi-component linear frequency-modulated (LFM) signals.</p>","PeriodicalId":1,"journal":{"name":"Accounts of Chemical Research","volume":null,"pages":null},"PeriodicalIF":16.4000,"publicationDate":"2024-01-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Modified Ambiguity Function and Wigner Distribution Associated With Quadratic-Phase Fourier Transform\",\"authors\":\"Tien Minh Lai\",\"doi\":\"10.1007/s00041-023-10058-8\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>The ambiguity function (AF) and Wigner distribution (WD) play an important role not only in non-stationary signal processing but also in radar and sonar systems. In this paper, we introduce modified ambiguity function and Wigner distribution associated with quadratic-phase Fourier transform (QAF, QWD). Moreover, many various useful properties of QAF and QWD are also proposed. Marginal properties and Moyal’s formulas of these distributions have elegance and simplicity comparable to those of the AF and WD. Besides, convolutions via quadratic-phase Fourier transform are also introduced. Furthermore, convolution theorems for QAF and QWD are also derived, which seem similar to those of the classical Fourier transform (FT). In addition, applications of QAF and QWD are established such as the detection of the parameters of single-component and multi-component linear frequency-modulated (LFM) signals.</p>\",\"PeriodicalId\":1,\"journal\":{\"name\":\"Accounts of Chemical Research\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":16.4000,\"publicationDate\":\"2024-01-04\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Accounts of Chemical Research\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1007/s00041-023-10058-8\",\"RegionNum\":1,\"RegionCategory\":\"化学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"CHEMISTRY, MULTIDISCIPLINARY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Accounts of Chemical Research","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s00041-023-10058-8","RegionNum":1,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"CHEMISTRY, MULTIDISCIPLINARY","Score":null,"Total":0}
Modified Ambiguity Function and Wigner Distribution Associated With Quadratic-Phase Fourier Transform
The ambiguity function (AF) and Wigner distribution (WD) play an important role not only in non-stationary signal processing but also in radar and sonar systems. In this paper, we introduce modified ambiguity function and Wigner distribution associated with quadratic-phase Fourier transform (QAF, QWD). Moreover, many various useful properties of QAF and QWD are also proposed. Marginal properties and Moyal’s formulas of these distributions have elegance and simplicity comparable to those of the AF and WD. Besides, convolutions via quadratic-phase Fourier transform are also introduced. Furthermore, convolution theorems for QAF and QWD are also derived, which seem similar to those of the classical Fourier transform (FT). In addition, applications of QAF and QWD are established such as the detection of the parameters of single-component and multi-component linear frequency-modulated (LFM) signals.
期刊介绍：
Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance.
Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.
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