On the nonlinearity of linear prediction

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.