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An adaptive beamforming algorithm that enhances the quality of the signal recorded by a microphone array is presented. The system described here attenuates the interference from spatially scattered sources while preserving the desired signal quality in the speech frequency range. A novel method for defining additional constraints within the adaptation process and performing beamforming in parallel across several frequency bands achieves undistorted recording even with slight errors in localizing the speaker. Moreover, a tracking algorithm is developed which adjusts the beamformer parameters while keeping its wideband characteristics and the interference reducing capabilities. Simulation results show nearly optimal improvement of speech quality in various noisy environments. The algorithm is modified to perform in a real environment by introducing two modes of adaptation that switch according to the speaker activity. The implementation of this modified system demonstrates signal-to-noise ratio (SNR) gain close to that of the original simulated system. It is robust to localization errors and non-ideal environmental effects.