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The goal of this paper is to suppress the narrowband interference (NBI) and wideband interference (WBI) in synthetic aperture radar (SAR) by using a nonparametric method. The method is based on the analysis of time–frequency characteristic of NBI and WBI from which an interference suppression filter combined with the constant false alarm rate algorithm is designed. In this approach, the short-time Fourier transform (STFT) is used to estimate the instantaneous frequency of the SAR echo data with interference. In the STFT domain, the instantaneous frequency spectrum is represented by wavelet, and then, the designed filter filters the corresponding wavelet coefficients of the interference components. In addition, this algorithm is robust to time-varying NBI and WBI. The performance of the proposed approach is evaluated by the simulated and measured data, and the effectiveness is demonstrated. [ABSTRACT FROM AUTHOR]