Advanced Wigner Distribution and Ambiguity Function in the Quadratic-phase Fourier Transform Domain: Mathematical Foundations and Practical Applications
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arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866916658170298368 |
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| author | Dar, Aamir H. Sharma, Neeraj Kumar |
| author_facet | Dar, Aamir H. Sharma, Neeraj Kumar |
| contents | In non-stationary signal processing, prior work has incorporated the quadratic-phase Fourier transform (QPFT) into the ambiguity function (AF) and Wigner distribution (WD) to enhance their performance. This paper introduces an advanced Wigner distribution and ambiguity function in the quadratic-phase Fourier transform domain (AWDQ/AAFQ), extending classical WD/AF formulations. Key properties, including the Moyal formula, anti-derivative property, shift, conjugation symmetry, and marginal properties, are established. Furthermore, the proposed distributions demonstrate improved effectiveness in linear frequency-modulated (LFM) signal detection. Simulation results confirm that AWDQ/AAFQ outperforms both traditional WD/AF and existing QPFT-based WD/AF methods in detection accuracy and overall performance. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_16258 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Advanced Wigner Distribution and Ambiguity Function in the Quadratic-phase Fourier Transform Domain: Mathematical Foundations and Practical Applications Dar, Aamir H. Sharma, Neeraj Kumar Functional Analysis 42B10, 81S30, 42A38, 44A35 In non-stationary signal processing, prior work has incorporated the quadratic-phase Fourier transform (QPFT) into the ambiguity function (AF) and Wigner distribution (WD) to enhance their performance. This paper introduces an advanced Wigner distribution and ambiguity function in the quadratic-phase Fourier transform domain (AWDQ/AAFQ), extending classical WD/AF formulations. Key properties, including the Moyal formula, anti-derivative property, shift, conjugation symmetry, and marginal properties, are established. Furthermore, the proposed distributions demonstrate improved effectiveness in linear frequency-modulated (LFM) signal detection. Simulation results confirm that AWDQ/AAFQ outperforms both traditional WD/AF and existing QPFT-based WD/AF methods in detection accuracy and overall performance. |
| title | Advanced Wigner Distribution and Ambiguity Function in the Quadratic-phase Fourier Transform Domain: Mathematical Foundations and Practical Applications |
| topic | Functional Analysis 42B10, 81S30, 42A38, 44A35 |
| url | https://arxiv.org/abs/2503.16258 |