Speech enhancement using state dependent dynamical system model

A time-varying linear dynamical system model for speech signals is proposed. The model generalizes the standard hidden Markov model (HMM) in the sense that vectors generated from a given sequence of states are assumed a first order Markov process rather than a sequence of statistically independent vectors. The reestimation formulas for the model parameters are developed using the Baum algorithm. The forward formula for evaluating the likelihood of a given sequence of signal vectors in speech recognition applications is also developed. The dynamical system model is used in developing minimum mean square error (MMSE) and maximum a posteriori (MAP) signal estimators given noisy signals. Both estimators are shown to be significantly more complicated than similar estimators developed earlier using the standard HMM. A feasible approximate MAP estimation approach in which the states of the signal and the signal itself are alternatively estimated using Viterbi decoding and Kalman filtering is also presented