On the nonlinearity of linear prediction

Abstract

This paper analyzes adaptive linear prediction and the effects of the underlying optiniality criterion on the prediction error. It is well known that the signal-dependent optimization process converts the linear filter into a nonlinear signal processing device and that this will influence the statistics of the filter output in a way not expected from linear filter theory. For minimum-phase L p -optimal linear predictors, we can show that the prediction error is maximally close to an i.i.d. process whose probability density function is given by A exp(-λ|x|p). This result is applied to linear predictive analysis-by-synthesis coding of speech and to predictive decision-feedback equalization of channels with nongaussian noise. Implications for testing time series for linearity or gaussianity are discussed, too.