In this paper, we proposed that ｉ) noise-tolerant four kinds of AM(Amplitude Modulation)-FM(Frequency Modulation) demodulators are designed, ⅱ) we derived undersampling frequency through the product via energy operator of the monocomponent AM-FM signals separated form two-component AM-FM signals, and ⅲ) these four kinds of AM-FM demodulators detect respectively information signals of the IA(Instantaneous Amplitude) and IF(Instantaneous Frequency) by undersampling frequency to be different each other from the undersampled monocomponet AM-FM signals. Particularly, the proposed algorithm can control undersampling frequency by an integer factor. And these efficient AM-FM demodulators are well worked with the undersampled AM-FM signals.