All-pole Modeling of Wide-band Speech U Polynomial

The autocorrelation function of the all-pole filter given by the conventional linear prediction (LP) matches exactly the autocorrelation function of the input signal between indices 0 and m, when the prediction order equals m. This study describes a recently developed technique, Weighted-Sum Line Spectrum Pair (WLSP), where an all-pole filter is defined by using a sum of weighted LSP (Line Spectrum Pair) polynomials. WLSP yields a stable all-pole filter of order m, whose autocorrelation function coincides to that of the input between indices 0 and m − 1. By sacrificing the exact matching of the autocorrelations at index m, WLSP models the autocorrelation of the input at the indices above m more accurately than conventional LP. In the current paper, the performance of WLSP in spectral modelling of wide-band speech is analysed. It is shown that WLSP yields all-pole spectra that model the formant structure of vowels more accurately than conventional LP of the same prediction order.