System identification of the speech production process based on a state-space representation

In this paper a new method for analysis of speech signals based on a representation in terms of an autoregressive moving-average (ARMA) process with variable order is presented. The process of speech production is approximated by an ARMA process described by a state equation and an observation equation. An algorithm for the minimal realization of the model of speech production process is proposed. The state transition matrix that characterizes the autoregressive (AR) scheme is determined to minimize the mean squared error in the estimation of the speech signal by Kalman filtering. The state transition matrix and the autocorrelation function of the signal are used to determine parameters of the moving-average (MA) scheme. Application to spectral density estimation of speech corrupted by additive noise is also discussed.