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This paper describes a general approach for reducing the level of broadband noise in speech. The method is derived by considering the probability density functions of the complex spectrum parameters corrupted by additive noise. This leads to a general formulatian of the problem and a class of speech spectral estimators is introduced, which include spectral subtraction as a special case. An optimum speech signal estimator is then derived from this class. Preliminary tests on spoken digit sequences with this estimator indicate a significant improvement in intelligibility at low signal-to-noise levels.