Hierarchical stochastic modelling for speech compression

In this paper, we consider the hierarchical modeling of signals in a scale space using autoregressive and moving average (ARMA) models with applications to speech compression. We show that the AR polynomial can be uniquely determined when the scale is changed. When the scale changes from fine to coarse (aggregation) and from coarse to fine (disaggregation), the model parameters can be obtained from the parameters of the model at different scales. Data disaggregation is the estimation of data at a finer scale from data at a coarse scale. We present a data disaggregation algorithm based on the minimum mean square error (MMSE) criterion. The MMSE data disaggregation algorithm is computationally more efficient than the weighted least squares (WLS) approach. The data disaggregation algorithm is then applied to speech compression.<>