二次相傅里叶变换域的高级维格纳分布和模糊函数：数学基础和实际应用

IF 1.2 3区数学 Q1 MATHEMATICS

Journal of Mathematical Analysis and Applications Pub Date : 2025-06-10 DOI:10.1016/j.jmaa.2025.129786

Aamir H. Dar, Neeraj Kumar Sharma

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引用次数: 0

摘要

在非平稳信号处理中，先前的工作将二次相傅立叶变换（QPFT）纳入模糊函数（AF）和维格纳分布（WD）中以提高其性能。本文介绍了二次相傅里叶变换域（AWDQ/AAFQ）的一种先进的Wigner分布和模糊函数，扩展了经典的WD/AF公式。建立了关键性质，包括Moyal公式、不定导数性质、位移、共轭对称性和边际性质。此外，所提出的分布在线性调频（LFM）信号检测中显示出更高的有效性。仿真结果表明，AWDQ/AAFQ方法在检测精度和综合性能上均优于传统WD/AF方法和现有的基于qpft的WD/AF方法。

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Advanced Wigner distribution and ambiguity function in the quadratic-phase Fourier transform domain: Mathematical foundations and practical applications

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.

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来源期刊

Journal of Mathematical Analysis and Applications 数学-数学

CiteScore

2.50

自引率

7.70%

发文量

790

审稿时长

6 months

期刊介绍： The Journal of Mathematical Analysis and Applications presents papers that treat mathematical analysis and its numerous applications. The journal emphasizes articles devoted to the mathematical treatment of questions arising in physics, chemistry, biology, and engineering, particularly those that stress analytical aspects and novel problems and their solutions. Papers are sought which employ one or more of the following areas of classical analysis: • Analytic number theory • Functional analysis and operator theory • Real and harmonic analysis • Complex analysis • Numerical analysis • Applied mathematics • Partial differential equations • Dynamical systems • Control and Optimization • Probability • Mathematical biology • Combinatorics • Mathematical physics.