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This paper introduces a novel technique for estimating the signal power spectral density to be used in the transfer function of a microphone array post-filter. The technique is a generalization of the existing Zelinski post-filter, which uses the auto- and cross-spectral densities of the array inputs to estimate the signal and noise spectral densities. The Zelinski technique, however, assumes zero cross-correlation between the noise on different sensors. This assumption is inaccurate, particularly at low frequencies and for arrays with closely spaced sensors, and thus the corresponding post-filter is suboptimal in realistic noise conditions. In this paper, a more general expression of the post-filter estimation is developed based on an assumed knowledge of the complex coherence of the noise field. This general expression can be used to construct a more appropriate post-filter in a variety of different noise fields. In experiments using real noise recordings from a computer office, the modified post-filter results in significant improvement in terms of objective speech quality measures and speech recognition performance using a diffuse noise model.