A method and an appropriate acoustic signal processing device estimate a set of linear predictive coding coefficients of a microphone signal using minimum mean-square error estimation with a codebook containing several predetermined sets of linear predictive coding coefficients. The method includes determining sums of weighted backward transition probabilities describing the transition probabilities between the predetermined sets of linear predictive coding coefficients. The backward transition probabilities are obtained from signal training data by mapping the signal training data to one set of the codebook and by determining relative frequencies of transitions between two of the sets of the codebook. Modelling the “memory” of the codebook has the advantage that the accuracy of estimating linear predictive coding coefficients is increased considerably also for speech components.