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A speech enhancement system which utilizes an optimal (in the minimum mean square error sense) short-time spectral amplitude estimator is described. The derivation of the optimal estimator is based on modeling speech as a quasi-periodic signal, and on applying spectral decomposition. The optimal spectral amplitude estimator and a recently developed vector spectral subtraction amplitude estimator, are round to be nearly equivalent. The optimal spectral amplitude estimator coincides with a Wiener spectral amplitude estimator at high signal to noise ratio (SNR) values, and is found to be superior to it at low SNR values. The enhanced speech obtained by using the proposed system, is less spectrally distorted, although contains some more residual noise, than the enhanced speech obtained by using the Wiener spectral amplitude estimator, in the same system. In addition, it is free of the "musical noise" characteristic to the spectral subtraction algorithm. Both systems, the proposed one and spectral subtraction, have approximately the same complexity.