In prior art hearing devices, nonlinear compression of a microphone signal prior to frequency analysis inherently creates artefacts in the analysis signals. Furthermore, prior art signal processing often does not provide sufficient enhancement of speech signals compared to other acoustic signals. It is an object of the present invention to provide a signal processor and a method for operating a hearing device that overcome the problems of the prior art. This is achieved by a signal processor (25) for a hearing device (1) with an implantable stimulator (3) having two or more electrodes (10) for emitting electric charge pulses to neural fibres of an individual. The signal processor (25) according to the invention has a signal path (20, 21, 22) comprising: an input circuit (20) adapted to receive an acoustic signal from the individual's surroundings and provide at least one corresponding input audio signal; a filter bank (21) adapted to provide at least one band-limited audio signal in dependence on the at least one input audio signal; and a noise filter (22) adapted to attenuate undesired signal components in the at least one band-limited audio signal and to provide at least one corresponding noise-filtered signal. The signal processor (25) is characterised in that the portion of the signal path (20, 21, 22) preceding the noise filter (22) neither causes an effective level compression nor an effective level expansion of the at least one noise-filtered signal when the at least one noise-filtered signal is derived from an acoustic signal having a level within the comfortable acoustic range.