A digital hearing aid (10) is provided that includes a microphone (12), a control and modeling circuitry (18), and a receiver (20). The microphone (12) receives an input sound signal x(t) and generates a digital input signal x(n) in response. The control and modeling circuitry (18) filters and amplifies the digital input signal x(n) and performs feedback neutralization and feedback path modeling to generate a digital output signal y(n). The receiver (20) receives the digital output signal y(n) and generates an output sound signal y(t) in response.