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Scaling Wigner Distribution in the Framework of Linear Canonical Transform

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Abstract

In this article, we introduce a novel scaling Wigner distribution by intertwining the merits of fractional instantaneous auto-correlation and the linear canonical transform. We initiate the study by investigating the fundamental properties of the scaling Wigner distribution, including the nonlinearity, marginal, shifting, conjugate-symmetry, convolution, and anti-derivative properties. Subsequently, the Moyal’s formula is also examined in detail. To testify the efficiency, the proposed distribution is employed for the detection of single-component, bi-component, and tri-component linear frequency modulated signals. The simulation results lucidly demonstrate that the scaling Wigner distribution performs exceptionally well in comparison with the conventional Wigner distribution. Nonetheless, owing to the higher degrees of freedom of the linear canonical transform, the proposed distribution benefits in cross-term reduction while maintaining a perfect time–frequency resolution and clear auto-terms angle resolution.

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Authors and Affiliations

  1. Department of Mathematics, University of Kashmir, South Campus, Anantnag, Jammu and Kashmir, 192101, India

    Firdous A. Shah & Aajaz A. Teali

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  1. Firdous A. Shah
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  2. Aajaz A. Teali
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Correspondence to Firdous A. Shah.

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Shah, F.A., Teali, A.A. Scaling Wigner Distribution in the Framework of Linear Canonical Transform. Circuits Syst Signal Process 42, 1181–1205 (2023). https://doi.org/10.1007/s00034-022-02184-3

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  • DOI: https://doi.org/10.1007/s00034-022-02184-3

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