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This paper reviews the fundamental concepts of Linear Prediction (LP) and Maximum Entropy (ME) spectral analysis, and elucidates the reasons for their practical importance in the world of real signals. Subsequently, the paper introduces the powerful principle of Minimum Cross-Entropy (MCE) spectral analysis. MCE permits the incorporation of prior information into signal analysis. In a new approach to speech signal analysis, application of the MCE principle reduces the average number of predictor coefficients (poles) that have to be specified per time frame for a given spectral resolution by relying on prior spectral information. Such prior spectral information may be given by glottal source and lip radiation Characteristics, microphone and transmission frequency responses, and spectral information from preceding time frames-particularly during steady-state or slowly-varying portions of a speech utterance.