A signal processing system, such as a hearing aid system, adapted to enhance binaural input signals is provided. The signal processing system is essentially a system with a first signal channel having a first filter and a second signal channel having a second filter for processing first and second channel inputs and producing first and second channel outputs, respectively. Filter coefficients of at least one of the first and second filters are adjusted to minimize the difference between the first channel input and the second channel input in producing the first and second channel outputs. The resultant signal match processing of the signal processing system gives broader regions of signal suppression than using the Wiener filters alone for frequency regions where the interaural correlation is low, and may be more effective in reducing the effects of interference on the desired speech signal. Modifications to the algorithms can be made to accommodate sound sources located to the sides as well as the front of the listener. Processing artifacts can be reduced by using longer averaging time constants for estimating the signal power and cross-spectra as the signal-to-noise ratio decreases. A stability constant can also be incorporated in the transfer functions of the first and second filters to increase the stability of the signal processing system.