A filter bank with a sufficiently high resolution for amplification and noise reduction and with the lowest possible computational complexity is provided for a hearing device and, in particular, for a hearing aid. Two-stage frequency transformation with little latency is therefore proposed for hearing aids. Some of the processing, for example the amplification, is carried out after high stopband attenuation in the first stage. An increased frequency resolution is achieved in a second stage before the back-transformation in the first stage, which is favorable for noise reduction, for example.