Linear prediction on a warped frequency scale
Linear prediction is considered with respect to a nonlinear frequency scale obtained by a first‐order all‐pass transformation. The predictor can be computed from a frequency‐warped autocorrelation function obtained from the power spectrum or by a direct linear transformation of the original acf. Three numerical procedures are compared. Alternatively, the predictor can be determined from a covariance matrix or (adaptively) from continuously formed correlations, suitably defined according to the all‐pass transformation. Prediction‐error minimization and spectral flattening are no longer equivalent criteria. In the synthesis part of a vocoder or APC system, no inverse transformation is required, since the direct form of the analysis and synthesis filters can be modified so as to immediately realize the warped transfer function. Single‐word intelligibility is compared for a predictive vocoder on a ’’Bark’’ scale and a linear frequency scale. The Bark scale yields results around 90% even at predictor orders of 5 to 7. More possible applications have been given previously by other authors.