Blind Identification of Non-Gaussian Autoregressive Models for Efficient Analysis of Speech Signals

Speech signals, especially voiced speech, can be better modeled by non-Gaussian auto regressive (AR) models than by Gaussian ones. Non-Gaussian AR estimators are usually highly non-linear and computationally prohibitive. This paper presents an efficient algorithm that jointly estimates the AR parameters and the excitation statistics and dynamics of voiced speech signals. A model called the hidden Markov-autoregressive model (HMARM) is designed for this purpose. The HMARM models the excitation to the AR model using a hidden Markov model with two Gaussian states that have, respectively, a small and a large mean but identical variances. This formulation enables a computationally efficient exact EM algorithm to learn all parameters jointly, instead of resorting to pure numerical optimization or relaxed EM algorithms. The algorithm converges in typically 3 to 5 iterations. Experimental results show that the estimated AR parameters have much lower bias and variance than the conventional least squares solution. We also show that the new estimator has a very good shift-invariance property that is useful in many applications