This envelope-detecting circuit comprises: a first multiplier able to multiply a first example of a signal received on an input port by itself, a modifier able to modify the amplitude of the power spectrum, of a second example of the signal received on the input port, at the frequency fc without modifying the amplitude of this power spectrum in a useful frequency band, a second multiplier able to multiply the modified signal by itself, a subtractor able to subtract from each other the signals delivered by the multipliers, a filter able to remove frequency components higher than or equal to 2fc in a signal obtained from the signal delivered by the subtractor, this filter being able to deliver the result of this filtering on an output connected to an output port of the envelope-detecting circuit.