COUPLED FRACTIONAL WIGNER DISTRIBUTION WITH APPLICATIONS TO LFM SIGNALS

Aajaz A. Teali (), Firdous A. Shah, Azhar Y. Tantary () and Kottakkaran S. Nisar
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Aajaz A. Teali: Department of Mathematics, University of Kashmir, South Campus, Anantnag 192101, Jammu and Kashmir, India
Firdous A. Shah: Department of Mathematics, University of Kashmir, South Campus, Anantnag 192101, Jammu and Kashmir, India
Azhar Y. Tantary: Department of Mathematics, University of Kashmir, South Campus, Anantnag 192101, Jammu and Kashmir, India
Kottakkaran S. Nisar: ��Department of Mathematics, College of Arts and Sciences, Prince Sattam bin Abdulaziz University, Wadi Aldawasir 11991, Saudi Arabia‡School of Technology, Woxsen University, Hyderabad 502345, Telangana, India

FRACTALS (fractals), 2023, vol. 31, issue 02, 1-18

Abstract: The coupled fractional Fourier transform is a much recent ramification of the two-dimensional fractional Fourier transform, wherein the kernel is not a tensor product of one-dimensional copies, but relies on two angles that are coupled to yield a new pair of transform parameters. In this paper, we introduce a novel two-dimensional Wigner distribution, coined as coupled fractional Wigner distribution (CFrWD). The prime advantage of such a ramification of the Wigner distribution lies in the fact that the CFrWD can efficiently tackle the higher-order-phase and chirp signals, which constitute a wider class of signals arising in modern communication systems. To begin with, we study some fundamental properties of the proposed CFrWD, including marginal, shifting, conjugate-symmetry and anti-derivative properties. In addition, we also formulate the Moyal’s principle, inversion formula and the convolution and correlation theorems associated with CFrWD. Nevertheless, we demonstrate the efficacy of CFrWD for estimating and detecting both the one-component and multi-component linear-frequency-modulated signals.

Keywords: Wigner–Ville Distribution; Coupled Fractional Fourier Transform; Convolution; Correlation; Linear Frequency Modulated Signal (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1142/S0218348X23400200

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