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The existing decision-theory based classifiers for M-ary frequency shift keying (MFSK) signals have assumed that there is some prior knowledge of the transmitted MFSK signal parameters; while the feature-based classifiers have some limitations such as that their thresholds are signal-to-noise-ratio-dependent (SNR-dependent). In this paper, we investigate some useful properties of the amplitude spectrum of MFSK signals. Using these properties as classification criteria, a fast Fourier transform based classifier (FFTC) of MFSK signals has been developed. The FFTC algorithm is practical since it only requires some reasonable knowledge of a received signal. It is found that the FFTC algorithm works well in classifying 2-FSK, 4-FSK, 8-FSK, 16-FSK, and 32-FSK signals when SNR>0dB. The FFTC algorithm also gives good estimation of the frequency deviation of the received MFSK signal.