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In this paper we propose a feature to distinguish frequency shift keying modulation from amplitude shift keying and phase shift keying modulations in the presence of carrier offset. The feature is based on the product of two consecutive signal values and on time averaging of the imaginary part of the product. First, the conditional probability density functions of the feature given the present modulation are determined. In order to overcome the complexity of calculating the probability density functions, the central limit theorem for strictly stationary m-dependent sequences is used to obtain Gaussian approximations. The classification threshold is based on the minimization of the total probability of misclassification. Finally the paper studies effects of carrier offset on the performance in the case of known and unknown carrier offset.