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The purpose of this paper is to introduce a spectral-flatness measure into the study of linear prediction analysis of speech. A spectral-flatness measure is introduced to give a quantitative measure of "whiteness," of a spectrum. It is shown that maximizing the spectral flatness of an inverse filter output or linear predictor error is equivalent to the autocorrelation method of linear prediction. Theoretical properties of the flatness measure are derived, and compared with experimental results. It is shown that possible ill-conditioning of the analysis problem is directly related to the spectral-flatness measure and that prewhitening by a simple first-order linear predictor to increase spectral flatness can greatly reduce the amount of ill-conditioning.