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.