In the presence of impulse noise modeled by the α-stable distribution, conventional noise suppression methods inevitably introduce cross-terms when processing multi-component signal, leading to significant deviations in subsequent signal representation and parameter estimation. To effectively address this issue, this paper develops an impulsive noise suppression technique based on K-medoids cluster (KMC), and proposes two representation methods for multi-component linear frequency modulation (LFM) signal under impulse noise. Firstly, the reason for cross-terms introduction is analyzed from the mathematical perspective, and subsequently a KMC-based impulsive noise suppression technology is developed. Secondly, KMC-fractional Fourier transform (KMC-FRFT) and KMC-synchrosqueezing transform (KMC-SST) are proposed, enabling precise characterization of multi-component LFM signal in the fractional domain and time-frequency domain, respectively. Finally, KMC-FRFT is applied to the parameter estimation of multi-component LFM signal under impulsive noise. Simulation experiments demonstrate that, from fractional domain and time-frequency domain, KMC not only suppresses high-amplitude burst impulsive noise, but also completely resolves the cross-terms problem inherent in existing methods. On this basis, under impulsive noise, KMC-FRFT and KMC-SST effectively capture the fractional spectral characteristic and time-frequency distribution characteristic of multi-component LFM signal from complementary perspectives. For both simulated and measured impulsive noise, RMSE demonstrates that KMC-FRFT can accurately estimate the parameters of weak component signal when GSNR ≥ 6dB, addressing the issue of incorrect parameter estimation caused by the cross-terms interference.
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