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Quadratic-phase scaled Wigner distribution: convolution and correlation

Quadratic-phase scaled Wigner distribution

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Abstract

In this paper, we propose the novel integral transform coined as the quadratic-phase scaled Wigner distribution (QSWD) by extending the Wigner distribution associated with quadratic-phase Fourier transform (QWD) to the novel one inspired by the definition of fractional bispectrum. A natural magnification effect characterized by the extra degrees of freedom of the quadratic-phase Fourier transform (QPFT) and by a factor k on the frequency axis enables the QSWD to have flexibility to be used in cross-term reduction. By using the machinery of QSWD and operator theory, we first establish the general properties of the proposed transform, including the conjugate symmetry, non-linearity, shifting, scaling and marginal. Then, we study the main properties of the proposed transform, including the inverse, Moyal’s, convolution and correlation. Finally, the applications of the newly defined QSWD for the detection of single-component and bi-component linear frequency-modulated (LFM) signal are also performed to show the advantage of the theory.

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Acknowledgements

This work is supported by the Research Grant (No. JKST &IC/SRE/J/357-60) provided by JKST &IC, UT of J &K, India.

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  1. Department of Mathematical Sciences, Islamic University of Science and Technology, Kashmir, 192122, India

    M. Younus Bhat & Aamir H. Dar

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  1. M. Younus Bhat
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  2. Aamir H. Dar
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Correspondence to Aamir H. Dar.

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Bhat, M.Y., Dar, A.H. Quadratic-phase scaled Wigner distribution: convolution and correlation. SIViP 17, 2779–2788 (2023). https://doi.org/10.1007/s11760-023-02495-1

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