2025/03/20 by Aamir H. Dar, Dar, Aamir H., Neeraj Kumar Sharma +1
Decision Sciences · Mathematics · #42A38 #42B10 #44A35 #81S30 #FOS: Mathematics #Functional Analysis (math.FA) #Mathematical functions and polynomials #Numerical methods in inverse problems #Scientific Measurement and Uncertainty Evaluation
paper · pdf · doi:10.48550/arxiv.2503.16258
openalex publication_date 2025/03/20 · openalex created_date 2025/10/17 · openalex updated_date 2026/07/28
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.