The present disclosure refers to a digital microphone device providing a single-bit Pulse Density Modulation PDM output signal. The digital microphone comprises a microphone, arranged to convert an acoustic input signal into an analog electrical signal, and a preamplifier, having a variable gain, arranged to receive the analog electrical signal and to provide an amplified analog electrical signal, depending on the variable gain. The variable gain depends on a gain control signal. The digital microphone further comprises an Analog-to-Digital Converter block, arranged to receive the amplified analog electrical signal and to convert it into a respective digital signal; and a compensation block, arranged to receive the digital signal and to perform a digital operation on such digital signal, on the basis of a compensation signal, to generate a compensated signal. Furthermore, the digital microphone comprises an Automatic Gain Controller block 25, arranged to detect the digital signal and to generate said gain control signal, on the basis of the detected digital signal. The Automatic Gain Controller block is further arranged to generate the compensation signal, on the basis of the control signal, and to provide the compensation signal to the compensation block, to compensate a variation of the digital signal resulting from the variable gain of the preamplifier. Finally, the digital microphone device comprises a conversion block, arranged to receive the compensated signal and to convert it into the single-bit PDM output signal.