A device and a method for processing an analog input signal (S) which varies widely in amplitude, such as speech, for the purpose of reducing the ratio of maximum to minimum amplitude variations of an output signal (P), after the processing, to the square root of the ratio existing before processing in order better to transmit said signal through a channel of restricted dynamic range in the presence of additive noise. The device comprises a converter (2) arranged to change the input signal (S) into a stream of integer numbers (N1,N2,N3 . . .). The numbers in the stream represent in some proportional way the instantaneous value of the input signal (S) divided by a reference voltage (R). This reference voltage (R) is generated by a smoothed amplitude measuring device (4) in proportion to the amplitude of the output signal (P) that is produced, when the number stream is reconverted to an analog signal waveform by means of a converter (6) working with a constant reference voltage. A device and a method for processing a signal of compressed amplitude variation, such as might be produced by the method and device described above, in order to produce a signal of amplitude variation restored to the normal range, being the square of the compressed range is also disclosed.