A Novel Two-Dimensional Wigner Distribution Framework via the Quadratic Phase Fourier Transform with a Non-Separable Kernel
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866916965155602432 |
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| author | Chauhan, Mukul Lone, Waseem Z. Verma, Amit K. |
| author_facet | Chauhan, Mukul Lone, Waseem Z. Verma, Amit K. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_19310 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Novel Two-Dimensional Wigner Distribution Framework via the Quadratic Phase Fourier Transform with a Non-Separable Kernel Chauhan, Mukul Lone, Waseem Z. Verma, Amit K. Signal Processing Information Theory Functional Analysis 42B10, 42A38, 44A35, 65R10, 81S30 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. |
| title | A Novel Two-Dimensional Wigner Distribution Framework via the Quadratic Phase Fourier Transform with a Non-Separable Kernel |
| topic | Signal Processing Information Theory Functional Analysis 42B10, 42A38, 44A35, 65R10, 81S30 |
| url | https://arxiv.org/abs/2509.19310 |