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Temporally weighted linear predictive methods have recently been successfully used for robust feature extraction in speech and speaker recognition. This paper introduces their general formulation, where various efficient temporal weighting functions can be included in the optimization of the all-pole coefficients of a linear predictive model. Temporal weighting is imposed by multiplying elements of instantaneous autocorrelation "snapshot" matrices computed from speech data. With this novel autocorrelation-snapshot formulation of weighted linear prediction, it is demonstrated that different temporal aspects of speech can be emphasized in order to enhance robustness of feature extraction in speech emotion recognition.