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Since the second-order statistics based methods rely heavily on Gaussianity assumption and the fractional lower-order statistics based methods depend on a priori knowledge of non-Gaussian noise, there remains a void in stochastic signal processing. In this paper, a novel signal analysis method referred to as cyclic correntropy is proposed to deal with cyclostationary signals under impulsive noise environment based on kernel methods. Furthermore, the cyclic correntropy spectrum is also defined. The application in frequency estimation is presented to illustrate the advantages of the cyclic correntropy over the second-order and the fractional lower-order cyclic statistics based methods in the presence of α-stable impulsive noise.