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Some discrete Fourier kind transforms (DFKT) which include the discrete Fourier transform (DFT), discrete chirp Fourier transform (DCFT), three-order discrete chirp Fourier transform (TDCFT), discrete matched transform based on phase compensation (DMTPC) are studied in the symmetric alpha-stable ( SalphaS ) noise environment. Some DFKTs based on the fractional lower order statistics (FLOS) (DFKT_FLOS) are studied or presented. The DFT based on FLOS (DFT_FLOS) is studied. The DCFT based on FLOS (DCFT_FLOS), TDCFT based on FLOS (TDCFT_FLOS), DMTPC based on FLOS (DMTPC_FLOS) are presented. The simulation shows that in the impulsive noise environment, DFKT_FLOS outperforms their respective DFKT counterpart.