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This paper introduces a new adaptive microphone-array system for noise reduction (AMNOR system). It is first shown that there exists a tradeoff relationship between reducing the output noise power and reducing the frequency response degradation of a microphone-array to a desired signal. It is then shown that this tradeoff can be controlled by the introduction of a fictitious desired signal. A new optimization criterion is presented which minimizes the output noise power while maintaining the frequency response degradation below some pre-determined value (AMNOR criterion). AMNOR determines an optimal noise reduction filter based on this criterion by controlling the tradeoff utilizing the fictitious desired signal. Experiments on noise reduction processing were carried out in a room with a 0.4-s reverberation time. The superiority of the AMNOR criterion over conventional LMS and constrained LMS criteria for reducing noise in speech signals was confirmed in subjective preference tests. The AMNOR system improved the SNR by more than 15 dB in the 300-3200 Hz range.