The Wigner distribution one of the most celebrated time–frequency tool for analyzing non-transient signals and has been widely employed in signal processing and other allied fields. In this article, we introduce a novel quadratic-phase Wigner distribution (QWD) by intervening the advantages of quadratic-phase Fourier transforms and Wigner distribution. We initiate our investigation by studying the fundamental properties of the proposed distribution, including the marginal, shifting, conjugate-symmetry, anti-derivative, Moyal’s and inversion formulae by using the machinery of quadratic-phase Fourier transforms and operator theory. Moreover, the convolution and correlation theorems associated with QWD are derived. Finally, we broaden the scope of the proposed distribution by detecting the parameters of the linear frequency modulated signals.

Wigner 分布是用于分析非瞬态信号的最著名的时频工具之一，已广泛应用于信号处理和其他相关领域。在本文中，我们通过干预二次相位傅里叶变换和 Wigner 分布的优点，介绍了一种新颖的二次相位 Wigner 分布 (QWD)。我们通过使用二次相位傅里叶变换和算子理论的机制研究所提议分布的基本属性，包括边际、移位、共轭对称、反导数、莫亚尔公式和反演公式，从而开始我们的研究。此外，还导出了与 QWD 相关的卷积和相关定理。最后，我们通过检测线性调频信号的参数来扩大所提出的分布范围。