Sparsity of frequency modulation signals based on fractional Fourier transform and maximum dispersion

Frequency Modulation (FM) signals are extensively utilized in sonar, radar, optics, and emerging optical cross-cutting domains, among others. The sparsity (or compactness) of FM signals is a fundamental issue in these fields, playing a critical role in signal sampling, detection, compression, and filtering. This paper proposes a FRFT-based MDPF model designed to enhance the sparsity of FM signals in the fractional-order Fourier transform (FRFT) domain by optimizing metrics and search strategies in the compactness domain. The maximum dispersion of the signal amplitude spectrum serves as an effective index for evaluating the signal compactness domain, while the standard deviation reflects dispersion to mitigate information loss. To explore the optimal compactness domain, the Hunger Games search algorithm (HGS) is employed. Simulation results demonstrate that this method significantly enhances the sparsity of the signals compared to other existing techniques.