A Novel Two-Dimensional Wigner Distribution Framework via the Quadratic Phase Fourier Transform with a Non-Separable Kernel
Abstract
This paper introduces a novel time-frequency distribution, referred to as the Two-Dimensional Non-Separable Quadratic Phase Wigner Distribution (2D-NSQPWD), formulated within the framework of the Two-Dimensional Non-Separable Quadratic Phase Fourier Transform (2D-NSQPFT). By replacing the classical Fourier kernel with the NSQPFT kernel, the proposed distribution generalizes the classical Wigner distribution and effectively captures complex, non-separable signal structures. We rigorously establish several key properties of the 2D-NSQPWD, including time and frequency shift invariance, marginal behavior, conjugate symmetry, convolution relations, and Moyal's identity. Furthermore, the connection between the 2D-NSQPWD and the two-dimensional short-time Fourier transform (2D-STFT) is explored. The distribution's effectiveness is demonstrated through its application to single-, bi-, and tri-component two-dimensional linear frequency modulated (2D-LFM) signals, where it shows superior performance in cross-term suppression and signal localization.
Keywords
Cite
@article{arxiv.2509.19310,
title = {A Novel Two-Dimensional Wigner Distribution Framework via the Quadratic Phase Fourier Transform with a Non-Separable Kernel},
author = {Mukul Chauhan and Waseem Z. Lone and Amit K. Verma},
journal= {arXiv preprint arXiv:2509.19310},
year = {2025}
}