Leja Ordering LSFs for Accurate Estimation of Predictor Coefficients

Linear prediction (LP) is the most prevalent method for spectral modelling of speech, and line spectrum pair (LSP) decomposition is the standard method to robustly represent the coefficients of LP models. Specifically, the angles of LSP polynomial roots, i.e. line spectrum frequencies (LSFs), encode exactly the same information as LP coefficients. The conversion of LP coefficients to LSFs and back, has received considerable attention since mid 1970s when LSFs were introduced. The present paper demonstrates how Leja ordering LSFs reduce amplification of rounding errors when converting LSFs to LP coefficients. The theory behind Leja ordering and the LSFs to LP coefficients conversion is presented. To supplement theory, numerical experiments illustrate the accuracy gain achieved by Leja ordering LSFs prior to conversion. Accuracy is measured as the root mean square deviation between estimated coefficient vectors with and without prior Leja ordering.