Noise Suppression of Linear Frequency Modulated Signals Based on Fractional Fourier Transform

The Fractional Fourier Transform (FrFT) is effective at focusing the energy of Linear Frequency Modulation (LFM) signals, making it commonly used for estimating unknown parameters and filtering LFM signals. Based on this, the paper proposes a precise estimation algorithm that combines a discrete polynomial transformation method with a fractional spectral fourth-order moment method in the FrFT domain. The algorithm first utilizes the discrete polynomial transform method to determine the initial rotational order and interval of the LFM signal. Following this, it employs the fourth-order moment characteristics of the fractional spectrum to further refine the search range and step size, achieving the most accurate modulation frequency and thus determining the optimal order of transformation. Simulation results demonstrate that compared to traditional filtering in the FrFT u-domain, the proposed filtering algorithm minimizes computational effort, preserves more information, and performs better under low signal-to-noise ratios with reduced computational load.