{"title":"Novel two-dimensional Wigner distribution and ambiguity function in the framework of the two-dimensional nonseparable linear canonical transform","authors":"Lai Tien Minh","doi":"10.1007/s11045-024-00886-2","DOIUrl":null,"url":null,"abstract":"<p>This paper is to propose a new definition of two-dimensional (2D) Wigner distribution (2D-WD) and two-dimensional ambiguity function (2D-AF) associated with two-dimensional nonseparable linear canonical transform (2D-NS-LCT), namely 2D-NLCWD and 2D-NLCAF. This allows for several consequences of the basic properties of the proposed distributions such as the shift properties, the conjugation symmetry property, the marginal properties, the Moyal formula, and the relationships with the two-dimensional short-time Fourier transform (2D-STFT). Furthermore, we point out the usefulness and efficacy of newly defined distributions for detecting two-dimensional linear frequency-modulated (2D-LFM) signals.</p>","PeriodicalId":19030,"journal":{"name":"Multidimensional Systems and Signal Processing","volume":null,"pages":null},"PeriodicalIF":1.7000,"publicationDate":"2024-04-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Multidimensional Systems and Signal Processing","FirstCategoryId":"5","ListUrlMain":"https://doi.org/10.1007/s11045-024-00886-2","RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"COMPUTER SCIENCE, THEORY & METHODS","Score":null,"Total":0}
引用次数: 0
Abstract
This paper is to propose a new definition of two-dimensional (2D) Wigner distribution (2D-WD) and two-dimensional ambiguity function (2D-AF) associated with two-dimensional nonseparable linear canonical transform (2D-NS-LCT), namely 2D-NLCWD and 2D-NLCAF. This allows for several consequences of the basic properties of the proposed distributions such as the shift properties, the conjugation symmetry property, the marginal properties, the Moyal formula, and the relationships with the two-dimensional short-time Fourier transform (2D-STFT). Furthermore, we point out the usefulness and efficacy of newly defined distributions for detecting two-dimensional linear frequency-modulated (2D-LFM) signals.
期刊介绍：
Multidimensional Systems and Signal Processing publishes research and selective surveys papers ranging from the fundamentals to important new findings. The journal responds to and provides a solution to the widely scattered nature of publications in this area, offering unity of theme, reduced duplication of effort, and greatly enhanced communication among researchers and practitioners in the field.
A partial list of topics addressed in the journal includes multidimensional control systems design and implementation; multidimensional stability and realization theory; prediction and filtering of multidimensional processes; Spatial-temporal signal processing; multidimensional filters and filter-banks; array signal processing; and applications of multidimensional systems and signal processing to areas such as healthcare and 3-D imaging techniques.
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