Fractional Fourier Transform Frequency Estimation Based on Improved Particle Swarm Optimization

Abstract The fractional Fourier transform (FRFT) frequency estimation is a frequently utilized frequency estimation approach for linear frequency modulation (LFM) signals. The search for the optimal order is a crucial element influencing the frequency estimation effect, and fixed-step search is typically adopted. Nevertheless, this algorithm is inefficient and time-consuming, thereby affecting the application of the fractional Fourier transform. To address this deficiency, the particle swarm optimization (PSO) algorithm was incorporated during the search for the optimal order. Based on this, this paper extends the conventional PSO to a PSO algorithm with adaptive inertia weights. This paper discusses and analysis the impact of different PSO algorithms on the FRFT frequency estimation effect. The simulation results present that the performance of the FRFT frequency estimation based on the two PSO algorithms is better than that based on the fixed-step FRFT. Among them, the FRFT frequency estimation based on the PSO algorithm with adaptive inertia weights is more efficient and precise than that based on the fixed-step algorithm.