A hearing aid system comprising an acoustical-electrical input transducer, an analog-digital converter, a digital signal processor, a digital-analog converter and an electrical-acoustical output transducer; wherein the digital signal processor comprises a time-varying filter and a deconvolution filter; wherein the acoustical-electrical input transducer provides an analog input signal that is converted into a digital input signal by the analog-digital converter and provided to the deconvolution filter and subsequently to the time-varying filter and then provided to the digital-analog converter and further on to the electrical-acoustical output transducer for conversion of the signal into sound, wherein the time-varying filter is configured to apply a frequency dependent gain that is adapted to at least one of suppressing noise and alleviating a hearing deficit of an individual wearing the hearing aid system; wherein the deconvolution filter is configured to have a transfer function that is the inverse of a minimum phase part of a combined transfer function of at least one hearing aid component selected from a group comprising the acoustical-electrical input transducer, the analog-digital converter, the digital-analog converter and the electrical-acoustical output transducer, wherein the hearing aid system is further configured to: - determine a first amplitude response for the transfer function resulting from a multiplication of the deconvolution filter transfer function with the combined transfer function, - determine a target amplitude response for the time-varying filter based on the first amplitude response and a time-varying target gain adapted to at least one of suppressing noise and alleviating a hearing deficit of an individual wearing the hearing aid system, and - select filter coefficients for the time-varying filter in order to provide an amplitude response that at least approximates the target amplitude response the acoustical-electrical input transducer provides an analog input signal that is converted into a digital input signal by the analog-digital converter and provided to the deconvolution filter and subsequently to the time-varying filter and then provided to the digital-analog converter and further on to the electrical-acoustical output transducer for conversion of the signal into sound, wherein the time-varying filter is configured to apply a frequency dependent gain that is adapted to at least one of suppressing noise and alleviating a hearing deficit of an individual wearing the hearing aid system; wherein the deconvolution filter is configured to have a transfer function that is the inverse of a minimum phase part of a combined transfer function of at least one hearing aid component selected from a group comprising the acoustical-electrical input transducer, the analog-digital converter, the digital-analog converter and the electrical-acoustical output transducer, wherein the hearing aid system is further configured to: - determine a first amplitude response for the transfer function resulting from a multiplication of the deconvolution filter transfer function with the combined transfer function, - determine a target amplitude response for the time-varying filter based on the first amplitude response and a time-varying target gain adapted to at least one of suppressing noise and alleviating a hearing deficit of an individual wearing the hearing aid system, and - select filter coefficients for the time-varying filter in order to provide an amplitude response that at least approximates the target amplitude response - determine a first amplitude response for the transfer function resulting from a multiplication of the deconvolution filter transfer function with the combined transfer function, - determine a target amplitude response for the time-varying filter based on the first amplitude response and a time-varying target gain adapted to at least one of suppressing noise and alleviating a hearing deficit of an individual wearing the hearing aid system, and - select filter coefficients for the time-varying filter in order to provide an amplitude response that at least approximates the target amplitude response