2025/09/08 by Chauhan, Mukul, Lone, Waseem Z., Verma, Amit K.
#42A38 #42B10 #44A35 #65R10 #81S30 #FOS: Computer and information sciences #FOS: Electrical engineering #FOS: Mathematics #Functional Analysis (math.FA) #Information Theory (cs.IT) #Signal Processing (eess.SP) #electronic engineering #information engineering
paper · doi:10.48550/arxiv.2509.19310
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.