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In this paper we present a new method of signal processing for robust speech recognition using two microphones. The method, loosely based on the human binaural hearing system, consists of passing the speech signals detected by two microphones through bandpass filtering. We develop a spatial masking function based on normalized cross-correlation, which provides rejection of off-axis interfering signals. To obtain improvements in reverberant environments, a temporal masking component, which is closely related to our previously-described de-reverberation technique known as SSF. We demonstrate that this approach provides substantially better recognition accuracy than conventional binaural sound-source separation algorithms.