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A dual-microphone speech-signal enhancement algorithm, utilizing phase-error based filters that depend only on the phase of the signals, is proposed. This algorithm involves obtaining time-varying, or alternatively, time-frequency (TF), phase-error filters based on prior knowledge regarding the time difference of arrival (TDOA) of the speech source of interest and the phases of the signals recorded by the microphones. It is shown that by masking the TF representation of the speech signals, the noise components are distorted beyond recognition while the speech source of interest maintains its perceptual quality. This is supported by digit recognition experiments which show a substantial recognition accuracy rate improvement over prior multimicrophone speech enhancement algorithms. For example, for a case with two speakers with a 0.1 s reverberation time, the phase-error based technique results in a 28.9% recognition rate gain over the single channel noisy signal, a gain of 22.0% over superdirective beamforming, and a gain of 8.5% over postfiltering.