A hearing aid system utilizing digital signal processing is programmable to fit the hearing deficit of a particular use and adaptive to the sound environment to maximize the intelligibility of the desired audio signal relative to noise. An analog signal picked from a microphone is amplified, filtered and converted to digital data. A digital signal processor preferably performs spectral shaping on the data to match the user's preference and performs a non-linear adaptive amplification function on the digital data. The amplification gain function may include several piecewise linear sections, including a first section providing expansion up to a first knee point, a second section providing linear amplification from the first knee point to a second knee point, and a third section providing compression for signals above the second knee to reduce the effort of over range signals and minimize loudness discomfort to the user. An estimate of the level of background noise is made as a function of the energy envelope of the input signal data, with the noise estimate then being used to adjust the position of the first knee up or down or to change the expansion ratio to reduce the noise component of the amplified signal supplied to the user. The digital signal processor includes a programmable read only memory which contains the desired spectral shaping characteristics and non-linear amplification characteristics suited to the user.