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Novel two-dimensional Wigner distribution and ambiguity function in the framework of the two-dimensional nonseparable linear canonical transform

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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.

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Acknowledgements

The author would like to thank the anonymous referees very much for suggestions and valuable remarks which have helped to improve the exposition of the paper.

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  1. Department of Mathematics, Hanoi Architectural University, Hanoi, 100000, Vietnam

    Lai Tien Minh

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L. T Minh wrote the main manuscript text and reviewed the manuscript.

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Correspondence to Lai Tien Minh.

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Minh, L.T. Novel two-dimensional Wigner distribution and ambiguity function in the framework of the two-dimensional nonseparable linear canonical transform. Multidim Syst Sign Process (2024). https://doi.org/10.1007/s11045-024-00886-2

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