In a listening device such as for example a hearing aid (1) where an input signal (10) is received by a microphone (2), converted from analog to digital (3), digitally processed (4) including a conversion from a time domain into a frequency domain, converted from digital to analog (5) and transmitted to a user by means of a loudspeaker (6), the internal digital processing (4) generates an unwanted noise signal, the so called undesired periodic noise (12), at specific frequencies. The undesired periodic noise is coupled via ground and the battery (7) into the signal processing path. According to the invention, the undesired periodic noise is filtered out of the input signal (10.2) during the digital signal processing (4), after the conversion of the digital signal into the frequency domain.