A demodulator of an FM signal modulated about a carrier frequency with a modulation frequency has an RF oscillator configured to be synchronized, under identical conditions of operation, with oscillations at first and second frequencies used in the FM signal to encode respective pieces of information. The oscillator has a magnetoresistive device; and a low-pass filter connected to an output electrode of the magnetoresistive device to filter an oscillating signal, generated by the oscillator and to a rendering terminal to provide, as a demodulated electrical signal, the filtered signal, the cut-off frequency fc at −3 dB of this filter being strictly lower than the frequency and higher than the modulation frequency.