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This paper discusses a nonlinear spectrum processing approach to speech enhancement. The technique incorporates a "soft" nonlinearity which suppresses low-level noise components while passing higher-level speech components. Although the algorithm is an extension of the spectral subtraction concept, the soft nonlinearity provides less distortion of low-amplitude speech components and less sensitivity to the subtraction level than previously reported techniques. In addition to noticeable improvement in perceptual quality, the algorithm offers a substantial increase in SNR.