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This paper deals with the problem of binaural noise reduction in the time domain with a stereophonic sound system. We first form a complex signal from the stereo inputs with one channel being its real part and the other being its imaginary part. By doing so, the binaural noise reduction problem is converted to a single-channel noise reduction problem via the widely linear (WL) model. The WL estimation theory is then used to derive the minimum variance distortionless response (MVDR) noise reduction filter that can fully take advantage of the noncircularity of the complex speech signal to achieve noise reduction while preserving the desired signal (speech) and spatial information. Experiments are provided to justify the effectiveness of this MVDR filter.

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