Nonlinear long-term prediction of speech signals

This paper presents an in-depth study of nonlinear long-term prediction of speech signals. While previous studies of nonlinear prediction focused on short-term prediction (with only moderate performance advantage over adaptive linear prediction in most cases), successful long-term prediction strongly depends on the nonlinear oscillator framework for speech modeling. This hypothesis has been confirmed in a series of experiments run on a voiced speech database. We provide results for the prediction gain as a function of the prediction delay using two methods. One is based on an extended form of radial basis function networks and is intended to show what performance can be reached using a nonlinear predictor. The other relies on calculating the mutual information between multiple signal samples. We explain the role of this mutual information function as the upper bound on the achievable prediction gain. We show that with matching memory and dimension, the two methods yield nearly the same value for the achievable prediction gain. We try to make a fair comparison of these values against those obtained using optimized linear predictors of various orders. It turns out that the nonlinear predictor's gain is significantly higher than that for a linear predictor using the same parameters.